gsm bss dimensioning alcatel

GSM BSS Dimensioning1062A

Student GuideGuide release: 15.02Guide status: StandardDate: July, 2005

Part Number: 1062A

NORTEL CONFIDENTIAL – FOR TRAINING PURPOSES ONLY

Copyright © 2005 Nortel Networks. All rights reserved.

NORTEL CONFIDENTIAL: The information contained in this document is the property of Nortel Networks. Except as specifically authorized in writing by Nortel Networks, the holder of this document shall not copy or otherwise reproduce, or modify, in whole or in part, this document or the information contained herein. The holder of this document shall keep the information contained herein confidential and protect same from disclosure and dissemination to third parties and use same solely for the training of authorized individuals.

THE INFORMATION PROVIDED HEREIN IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND. NORTEL NETWORKS DISCLAIMS ALL WARRANTIES, EITHER EXPRESSED OR IMPLIED, INCLUDING THE WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL NORTEL NETWORKS BE LIABLE FOR ANY DAMAGES WHATSOEVER, INCLUDING DIRECT, INDIRECT, INCIDENTAL, CONSEQUENTIAL, LOSS OF BUSINESS PROFITS OR SPECIAL DAMAGES, ARISING OUT OF YOUR USE OR RELIANCE ON THIS MATERIAL, EVEN IF NORTEL NETWORKS HAVE BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES.

Information subject to change without notice.Nortel, Nortel Networks, the Globemark device, and the Nortel Networks logo are trademarks of Nortel Networks.


Visit us at: nortel.com/training

DescriptionThis course explains the Nortel Networks method to dimension the Base Station Subsystem (BSS) of a GSM network. This course applies to the V15.0.1 version of the BSS.

Intended audienceAnyone responsible for designing BSS networks with Nortel Networks equipment (BTS, BSC, TCU) .

PrerequisitesBefore taking this course, a general knowledge of GSM/GPRS/EDGE standards and products is required. An excellent way to obtain it is to attend the 5 days 1061A course (GSM GPRS System Overview - Technical), the 3 days GP1 (GPRS Technical Description), the 2 days 1597AB (GSM GPRS System Release V15.0) and the 1 day 1599A (GSM/GPRS/EDGE System Release V15.1 Delta).

ObjectivesAfter completing this course, you will be able, from a given mobile traffic model, to dimension a BSS and:• calculate the number of signaling and traffic radio resources per sector, the number of TRX per sector, the number of Abis and Ater PCM links,• compute the size and configuration of the BSS equipment: BTS, BSC, TCU and PCUSN.

Course introduction

Overview


ReferencesThe following documents provide additional information:

Document titleNTP 000-0000-000


Contents

1. Introduction

2. Basics on Mobile Network Dimensioning

3. BTS Dimensioning

4. BSC/TCU 12000 Dimensioning

5. BSC3000/TCU3000 Dimensioning

6. PCU Dimensioning

7. BSS Dimensioning Review

8. Exercise Solutions

9. Appendix: Erlang B Tables


Publication History


Compliant with V15.1 BSS Release

July 2005

15.02

CreationCompliant with V15.0.1 BSS Release

May 2005

15.01

CommentsDateVersion

1


nortel.com/training

Section 1

Introduction

2

2 NORTEL CONFIDENTIAL – FOR TRAINING PURPOSES ONLY

About Knowledge Services

> Knowledge Services offers three programs to help you get the most out of your Nortel solutions.• Training with a focus on eLearning• Certification• Documentation

> Making the global transition to “e”• We are transitioning many of our programs so we can meet

the demands of the 21st century; including a new focus on eLearning, an industry-leading certification program, new opportunities to save, vehicles for electronic communication to keep you in the know, and more.

Knowledge Services programs help you speed your time to proficiency. Through our programs, you can:

• Save time and money on quality, comprehensive training with our new eLearning portfolio

• Build the foundation for skills needed to successfully achieve certification through our training programs

• Gain hands-on experience with Nortel Networks solutions through our advanced lab courses

• Demonstrate and validate your knowledge and hands-on skills by achieving certification through our industry-leading certification program

3


Nortel Homepage

www.nortel.com

4


Training & Certification Page

www.nortel.com• Select Training

• Select the appropriate product family …

• …Choose a product…

• …And get the content

Select the appropriate geographic region and language - allows you to customize your view

Point of Contacts: • CAMs (Customer Account Managers) – The customer can direct

questions/issues to their internal training prime, who can be in contact with the Nortel CAM.

• CSRs (Customer Service Rep) of regional calling center number

• Instructor – provide business cards/email address/phone number

5


Training Page

Page that appears when “Training” is selectedDepending on your selection, you see the training offer in your region (NA, EMEA, ASIAPAC, CALA) or the global offer.

6


Curriculum Paths Page

Page that appears when “Curriculum Path” is selected.You can select the appropriate training according to your job function.

7


Technical Documentation

www.nortel.comSelect Support & TrainingSelect Technical Documentation

8


GSM BSS Nortel Technical Publications

BSS Product Documentation411-9001-000BSS Overview411-9001-001

OMC-RArchitecture and

Reference Manual411-9001-006

TCUReference Manual

411-9001-016BSC


S4000/S4000CIndoor BTS


S2000 H/L BTSReference Manual

411-9001-035S8000/S8002/

S8003/S8006 BTSReference Manual

411-9001-063e-cell BTS


PCUSNReference Manual

411-9001-091BSC/TCU 3000


S12000Reference Manual

411-9001-142BTS 18000


Concepts

EDGE Deployment Guide411-9001-801

Planning andEngineering

What’s New in theV15 BSS NTP Suite

411-9001-088

Upgrading

CT2000User Manual411-9001-137

PCU CIQUser Manual411-9001-140CT2000 User

Procedures Manual411-9001-148

Configuring

OMC-R UserManual Vol 3 of 3:

Security, Administration,SMS-CB andHelp menus

411-9001-130

Administrationand Security

BSS OperatingPrinciples

411-9001-007BSS Operating

Procedures411-9001-034OMC-R User

Manual Vol 1 of 3:Objects and

Faults Menus411-9001-128

BSS ParameterDictionary

411-9001-124RACE Referenceand User Manual

411-9001-127

Operations Fault and Performance Management

S12000Maintenance Manual

411-9001-144BSS Maintenance

Principles411-9001-039

BTS 18000Maintenance Manual

411-9001-162Fault Number Description

Volume 1 of 6:BSC and TCU411-9001-101

Fault Number DescriptionVolume 2 of 6:S2000/2000E

and S4000 BTS411-9001-102

Fault Number DescriptionVolume 3 of 6:S8000/8002,

S8003 and S8006411-9001-103

Fault Number DescriptionVolume 4 of 6:S2000H/L and

e-cell BTS411-9001-104

Fault Number DescriptionVolume 5 of 6:

Advanced MaintenanceProcedures

411-9001-105Fault Number DescriptionVolume 6 of 6: PCUSN


S12000 BTS411-9001-143

BTS 18000Fault Number Description


BTS/TCU 3000411-9001-131

Call Trace/Call Path Trace AnalyzerUser Manual411-9001-060

OMC-R UserManual Vol 2 of 3:

Configuration,Performance and

Maintenance menus411-9001-129Observation

Counter Dictionary411-9001-125

TML (BSC/TCU)User Manual411-9001-050

TML (BTS)User Manual411-9001-051

TML(BSC 3000/TCU 3000)

User Manual411-9001-139

OMC-R Preventive and Corrective Maintenance

411-9001-032BSC

Maintenance Manual411-9001-041

TCUMaintenance Manual

411-9001-042BSC 3000


e-cell BTSMaintenance Manual

411-9001-090S2000 H/L

Maintenance Manual411-9001-049S4000 BTS


S8000/S8003 BTSMaintenance Manual

411-9001-048S8002 BTS

Maintenance Manual411-9001-084S8006 BTS


GSM BSS Nortel Technical PublicationThis suite is sorted by job functions category.

9


Contents

> GSM/GPRS/UMTS Training Curriculum

> BSS Nortel Technical Publications

> Objectives

> Course Architecture

10


Objectives

> Upon completion of this course, ability is acquired to determine or compute:• Traffic radio resources number per cell• Signaling resources number per cell• TRX number per cell• BTS types and number• BSC types and number• TCU number• PCU number• Number of Abis, Ater, Agprs and A interfaces PCM links• BSS size and configuration

During this course the method of dimensioning computation of BSS part of a GSM network is explained and given.The results obtained depend mainly on Traffic Model parameter values for transmission. Some of these values deal with field parameters as cellular planning, subscriber activity and mobility.Each operator must define his own traffic model.Other assumptions are also given, relating to traffic operation. They are operator dependent:

• No Queuing (loss of excess call attempts)

• Radio interface blocking rate: traffic = 2%; signaling = 0.1%

• A interface blocking rate: 0.1%

NotesThis course is applicable for V15.0.1 release of Nortel Networks BSS.

11


Course Architecture

> Section 1 – Introduction

> Section 2 – Basics on Mobile Network Dimensioning

> Section 3 – BTS Dimensioning

> Section 4 – BSC/TCU 12000 Dimensioning

> Section 5 – BSC3000/TCU3000 Dimensioning

> Section 6 – PCU Dimensioning

> Section 7 – BSS Dimensioning Review

> Section 8 – Exercise Solutions

> Section 9 – Appendix: Erlang B Tables

12

Student notes

1


nortel.com/training

Section 2

Basics on Mobile Network Dimensioning

2


Lesson Objectives

Upon completion of this section, the student will be able to:> Define Erlang unit

> Use Erlang Law B Tables

> Describe a Traffic Model (parameters and typical values)

> Define the Dimensioning Procedure

This is obtained through a full understanding of:> Components of the GSM System Traffic

> Definition of offered traffic, blocking rate, Erlang laws

3


Contents

> Generalities about GSM/GPRS Network

> Erlang Law

> Traffic Model

> Dimensioning Procedure

4


GSM/GPRS/EDGE Network

BTS

BSCTRAU

Abis Ater

PCU

Agprs

FrameRelay

Backbone

Gb

MSC

VLR

PSTN

SGSN

GGSN

Gn Gn

ExternalPacket NetworksIntranet, Internet

Gi

HLR/AuC

D

C

Gr

MS

PrivateIP

Backbone

Um

A

Gb

BSS

The GSM network is the foundation of the wireless network. It provides circuit-switched voice service from mobile users to other mobile and land line users. The General Packet Radio Service (GPRS) is a wireless packet data service that is an extension of the GSM network. It provides an efficient method to transfer data by optimizing the use of network resources.

New from V15.0EDGE is an extension of the GSM/GPRS Access network. In that sense, it largely inherits the administration, maintenance and supervision of the currently deployed BSS.The GPRS Coding Schemes are enhanced with 7 EDGE Modulation and Coding Schemes (MCS2, MCS3 and MCS5 to MCS9). This set of Modulation and radio coding schemes increases the peak radio throughput of a carrier by a factor 3 compared to GPRS.In order to benefit from those new Coding Schemes, a specific hardware is needed on the BTS side (namely E--DRX & E--PA) and an extension of the backhaul is requested to take benefit of the full range of MCS.EDGE is part of the rel--99 of the 3GPP specifications, and thus, BSS complies with that version of the specification on the radio interface. It is noted that a rel--97 SGSN also supports EDGE.

5


Generalities

1 – Traffic channel types: speech caseTCU BSCMSC

RadioInterfaceA Interface Ater Interface Abis Interface

NSS BSS MS

BTS

(1) depends on the AMR Full Rate mode:4.75; 5.15; 5.9; 6.7; 7.4; 7.95; 10.2 or 12.2 kbps

(2) depends on the AMR Half Rate mode:4.75; 5.15; 5.9; 6.7; 7.4 or 7.95 kbps

A Interface Ater Interface Abis Interface Radio InterfaceGross rate Raw rate Gross rate Raw rate

TCH/FSTCH/EFSTCH/AFSTCH/HS

TCH/AHS

64 kbps64 kbps64 kbps64 kbps64 kbps

64 kbps64 kbps64 kbps64 kbps64 kbps

16 kbps16 kbps16 kbps

8/16 kbps16 kbps

13 kbps12.2 kbps

(1)5.6 kbps

(2)

Gross rate Raw rate

16 kbps16 kbps16 kbps

8/16 kbps8 kbps

13 kbps12.2 kbps

(1)5.6 kbps

(2)

Gross rate Raw rate

22.8 kbps22.8 kbps22.8 kbps11.4 kbps11.4 kbps

13 kbps12.2 kbps

(1)5.6 kbps

(2)

SpeechThe raw data rate is specified by the channel type:

• TCH/FS: 13 kbps conveyed into a 16 kbps channel on Ater and Abis interfaces

• TCH/EFS: 12.2 kbps conveyed into a 16 kbps channel on Ater and Abisinterfaces

• TCH/HS: 5.6 kbps conveyed either into a 8 kbps or into a 16 kbps channel onAter and Abis interfaces. Not available at the present time.

• TCH/AFS: there are 8 AMR Full Rate modes (4.75; 5.15; 5.90; 6.70; 7.40; 7.95; 10.20 and 12.20 kbps) conveyed into a 16 kbps channel on Ater and Abisinterfaces

• TCH/AHS: there are 6 AMR Half Rate modes (4.75; 5.15; 5.90; 6.70; 7.40; 7.95) conveyed either into a 8 kbps or into a 16 kbps channel on Ater and Abisinterfaces

The speech transmission is always bi-directional.Remarks:

• On Abis and Ater interfaces, the difference between the gross rate and the raw rate is used for signaling between TRAU and BTS. On radio interface, this difference corresponds to the channel coding.

• TCH/HS is not supported by Nortel. On Abis and Ater interfaces, from the GSM recommendation (TS 08.61) point of view, there are two possible implementations: TRAU frame on 16 kbps or on 8 kbps channel.

• For TCH/AHS, there are the same two possibilities. Nevertheless, Nortel chose to use the 8 kbps TRAU frame but on a 16 kbps channel on Ater and on a 8 kbps channel on Abis.

6


Generalities

2 – Traffic channel types: data case over NSSTCU BSCMSC

RadioInterfaceA Interface Ater Interface Abis Interface

NSS BSS MS

BTS

Ater/Abis Interface Radio Interface

TCH/F14.4

TCH/F9.6TCH/F4.8TCH/F2.4TCH/H4.8TCH/H2.4

Gross rate User Service rate

16 kbps16 kbps16 kbps16 kbps8 kbps8 kbps

14.4 kbps9.6 kbps4.8 kbps2.4 kbps4.8 kbps2.4 kbps

Gross rate Raw rate

22.8 kbps22.8 kbps22.8 kbps22.8 kbps11.4 kbps11.4 kbps

14.5 kbps12 kbps6 kbps

3.6 kbps6 kbps

3.6 kbps

Data over NSS = Circuit Switched DataThe different bi-directional data transmission types are: TCH/F14.4, TCH/F9.6, TCH/F4.8, TCH/F2.4, TCH/H4.8 and TCH/H2.4.Data transmission at rates of 1200 bps or less or equal than 600 bps are also possible. There are using either a TCH/F2.4 or a TCH/H2.4.High Speed Circuit Switch Data (HSCSD) feature allows to one user up to 4 such data traffic channel type. HSCSD is really interesting with four TCH/F14.4 leading to a raw rate of 57.6 kbps. Nevertheless, it is very resource consuming as four radio and four terrestrial resources are allocated to the same user.Enhanced Circuit Switch Data (ECSD) feature defines three new channel types: E-TCH/F43.2, E-TCH/F32.0 and E-TCH/F28.8 using 8PSK modulation. It allows to reach the same data rates (on radio interface) as for HSCSD but with less terrestrial resources.

7


Generalities

3 – Traffic channel types: Data case over GPRS core network

MS

PCUSN BSC

RadioInterfaceAgprs Interface Abis Interface

BSS

BTSGb Interface

SGSN

GPRS Network

9.05/13.4 kbps - GMSK15.6/21.4 kbps - GMSK8.8/11.2 kbps - GMSK14.8/17.6 kbps - GMSK22.4 kbps - 8PSK29.6 kbps - 8PSK44.8 kbps - 8PSK54.4/59.2 kbps - 8PSK

PDTCH/CS1-CS2PDTCH/CS3-CS4

PDTCH/MCS1-MCS2PDTCH/MCS3-MCS4

PDTCH/MCS5PDTCH/MCS6PDTCH/MCS7

PDTCH/MCS8-MCS9

Gross rate Raw rate

16 kbps2x16 kbps16 kbps

2x16 kbps2x16 kbps3x16 kbps4x16 kbps5x16 kbps

9.05/13.4 kbps15.6/21.4 kbps8.8/11.2 kbps14.8/17.6 kbps

22.4 kbps29.6 kbps44.8 kbps

54.4/59.2 kbps

Gross rate Raw rate - Mod

22.8 kbps22.8 kbps22.8 kbps22.8 kbps69.6 kbps69.6 kbps69.6 kbps69.6 kbps

Abis InterfaceAgprs/ Radio Interface

Data over GPRS core network = Packet Switched DataThe data transmission over the GPRS core network always uses one and only one full rate traffic channel on the radio interface whatever the coding scheme applied (CS1 to CS4 for GPRS or MCS1 to MCS9 for EDGE). On the other hand, for high data rates (over 13.4 kbps for GPRS (CS2) and over 11.2 kbps for EDGE (MCS2)), more than one terrestrial resource (16 kbps channel) is required.For example, using MCS6, RLC user data payload is 74 bytes to be transmitted in 20 ms. For this, 26 bytes are transmitted in one "main" 16 kbps channel and 24 bytes are transmitted in each of the two "joker" channels. Therefore, the raw data rates are not the same in each of the 16 kbps channels ("main" and "joker"). In above table, only the global raw data rates (sum of the rate of the "main" and "joker" channels) are indicated.Nevertheless, from the user point of view, the data transfer mode is a packet mode. That is to say, up to 8 radio TS can be assigned to one user. And simultaneously, one radio TS can be shared between several users. Moreover, the number of radio TS allocated to one user in downlink can be different than the number of radio TS allocated to the same user in uplink.

Remarks:• From Release V15.0, EDGE supports the maximum data rate of 59.2 kbps

utilizing up thru MCS8-9.

8


Generalities EDGE : Enhanced GPRS

GMSKmodulation

8PSKmodulation

59.2

8.8

22.417.6

MCS1MCS2MCS3MCS4

MCS5MCS6MCS7MCS8MCS9

EDGECS1CS2CS3CS420.8

8.8GMSK

modulation

GPRS

GMSKmodulation

8PSKmodulation

59.2

8.8

22.417.6

MCS1MCS2MCS3MCS4


EDGE

GMSKmodulation

8PSKmodulation

59.2

8.8

22.417.6

MCS1MCS2MCS3MCS4


EDGECS1CS2CS3CS420.8

8.8GMSK

modulation

GPRSCS1CS2CS3CS420.8

8.8GMSK

modulation

GPRS

EDGE offers better performances than GPRS

> Optimized throughput versus propagation channel performance

> Enhanced Features:• Link Adaptation (GPRS/EDGE)

• Measurement coding scheme adaptation• Incremental Redundancy (EDGE)

• dynamic redundancy added with block repetition• RLC/MAC layer improvement. No window stalling limitation

EDGE uses an additional modulation scheme (8-PSK) that enables to transmit more information per radio symbol (3 bits, instead of 1 with GMSK). Drawback is that it is more dependant on radio conditions.

By adapting the coding schemes to the radio channel conditions dynamically, it ispossible to optimise communication performances and throughput. This is done by Link Adaptation: through radio measurements, the network (PCUSN) chooses the best MCS and adapts it. Estimated best MCS is used in each position of the cell.

Moreover Incremental Redundancy provides the possibility to retransmit a data block using a different puncturing method (additional redundancy) and to recombine it with retransmitted packets. By this way, probability to receive a correct block is increased.

The RLC/MAC layer has been significantly improved in EDGE development. Forhandsets supporting multiple TS, performance limitations in GPRS due to the limitedsize of the acknowledge window is not reproduced in EDGE, i.e. in GPRS RLCwindow size is 64, i.e. the transmitter cannot transmit block N+64 if block N has notbeen correctly acknowledged by the receiver. In EDGE, windows size has beenextended to 1024 blocks, avoiding loss of incorrect blocks because of too bad radioconditions.

9


Generalities

Speech on the BTS-TCU interface: Abis vs. Ater mapping

TCU BSCBTS

Ater Interface Abis Interface

0 1 2 3 4 5 6 7TS i

TS 1/0

TS 24/31

0 1 2 3 4 5 6 7TS j

AMR HR TCH (TCH/AHS)

FR TCH (TCH/FS or TCH/EFS)

AMR FR TCH (TCH/AFS6.7, TCH/AFS5.9 or TCH/AFS4.75)

8 kbps channel carrying supplementary information in downlink, padding in uplink.

0 1 2 3 4 5 6 7TS m

TS 1/0

TS 24/31

0 1 2 3 4 5 6 7TS n

TS p0 1 2 3 4 5 6 7

8 kbps channel carrying supplementary information (in uplink and in downlink).AMR FR TCH (TCH/AFS10.2)

Reminder: The Nortel BSS does only provide Half Rate Traffic Channel with AMR introduction:On the Abis interface, half rate channels induce 8 kbps TS, instead of 16 kbps for full rate channels. As the same radio TS can be used as a FR or HR channel, the associated 16 kbps Abis TS is used as one 16 kbps TS in case of FR channel and two 8 kbps TS in case of HR channel, using the following rules:

• FR: 16 kbps

• HR with T = 0: 8 kbps (the most significant bit of the 16 kbps TS)

• HR with T = 1: 8 kbps (the least significant bit of the 16 kbps TS)

where T indicates the sub-channel number of the Air interface.In case of FR channel, the 16 kbps Abis TS is naturally connected to the associated 16 kbps Ater TS.In case of HR channel, the 8 kbps Abis channel is connected to the most significant bit of the 16 kbps Ater TS. The least significant bit of the 16 kbps Ater TS is not used and padded using silent pattern by the BSC, in the uplink path.For the downlink path on the Ater interface, the TCU used always both 8 kbps whatever the AMR channel type FR or HR. But in case of HR, the BSC ignores the least significant bit and sends to the BTS the most significant bit.The 8 kbps channel (on Ater) corresponding to the least significant bit, is used to manage proprietary frame, in order to ensure a « 16 kbps quality » for the FR channel for AMR FR codec modes of 6.7 kbps, 5.9 kbps and 4.75 kbps.

10


Generalities

Network Engineering

System DimensioningSites layout

Capacity

Cost minimization

Required quality

Number & Type

of Equipment

and Links

InputsConstraintsOutputs

The result of network engineering is a definition of the equipment and links of the networks.These results must be optimized to minimize installation/operation/maintenance costs while maintaining the required quality.To reach these objectives, the available variable parameters intervene in system dimensioning, taking into account that cellular planning is fixed. Indeed, sites/cells layout are defined by site population (rural/urban), site topography, etc..

11


Generalities

Traffic model overview

TRAFFICMODEL

Qualityof

ServiceSubscribers

Behavior

CellularPlanning

System Dimensioning is based on a Traffic Model. A traffic model is a set of parameters which represent the behavior of the subscribers at the busy hour.Every operator must define his Traffic Model, which is the result of three influences:

• Cellular planning: the sites/cells layout has been fixed; for instance, a higher number of cells increases handover, then CPU capacity needs.

• Quality of service: it depends on blocking rate values of traffic and signaling channels, on network operation, on supplementary services provided, on subscription costs.

• Subscribers: higher the distribution of GSM subscribers within the population, higher the number of communications between GSM and PSTN networks. The rural/urban distribution of GSM subscribers, their activity rate, their mobility are other influent parameters.

12


Generalities

Clutters

Radio waves behave differently depending on the environment, and the radio range can vary from few hundred meters to several kilometers. It is then important to classify the different types of environment included in the area to be provided with GSM service.As an example the map presented above shows a city and its surroundings, classified into fourteen types of environment or clutters.A link budget is established for each clutter, defining a specific cell size.

Example of Dense Urban clutterAreas within urban perimeter. This includes dense urban areas with dense development where built-up features

do not appear distinct from each other. It also includes built-up features of the downtown district with heights below 40 m.

Example of Mean Urban clutterAreas with urban perimeter. The mean urban clutter

should have mean street density with no pattern, the major streets are visible, the built-up features appear distinct from each other. Some small vegetation could be included. Average height is below 40 m.

13


Generalities

Theoretical cells

All areas to be provided with GSM service are characterized and classified.For areas where traffic is the limiting factor, the site number is just resulting from the division of number of subscribers in the area by the maximum subscribers managed by one site.For each clutter where coverage is the limiting factor, one link budget is established giving a theoretical size of the corresponding cell with which the area is “paved”.This step gives a first estimation of the number and type of sites needed to reach the marketing goals.Before deployment, Cell Planning has to be performed carefully to determine the exact site positions and practical coverage, taking into account the existing and friendly sites.This is performed with the help of a planning tool which inputs are terrain database with clutters, sites characteristics and EIRP and signal strength coming from the link budgets.The final step is to deliver a list and characteristics of sites after frequency planning is performed. This process is iterative until theoretical site positions match to practical ones.

14


Generalities

Components of the GSM/GPRS System traffic

Subscriber Activity(intentional activity)

Mobility Events(transparent for the subscriber)

Traffic Model

System

SMS(Point

toPoint)

CallAttempts

rate

Attach/Detach

InterPLMN

Roaming

Location/Routing Area

updating

Handover

SMSCell broadcast

Periodic registration

DataSessions

The GSM dynamic parameters which define the Traffic Model are specified:• Subscriber activity: call attempt rate is the most influent parameter.

• Mobility events:

—Handover: their number is linked to the cell sizes

—Location updating/registration: the information concerning the location area increases with mobility and the definition of the location area

—Inter PLMN roaming: it is of negligible influence on Traffic Model

• System:

—Cell broadcast: this function allows the operator to send various types of information (traffic, weather forecast, advertising for instance) on MS in idle mode

—Periodic registration: this action is optional but most operators use it. It is a periodic update supervised by the system (SDCCH)

15


Erlang Law

Definition

Network dimensioning according to the “busy hour” traffic

Unit for occupancy averages of links = Erlang

Traffic Intensity in Erlang = Resource(s) occupancy duration

Reference period duration

The Erlang unit is not a GSM specific unit. It is used to express a traffic intensity or a traffic activity.In GSM, when we focus on a specific radio resource, we compute the traffic intensity of this resource (value < 1). When we focus on the total network traffic, we compute the network activity (value may be > 1).

Traffic in Erlangs =

1 Erlang = Total resource occupancy duration of one hour observed on the reference busy hour.Example 1: A traffic of 0.5 Erl may correspond to 1 resource occupied during 50% of the busy hour or 2 resources during 25% or ….Example 2: A traffic of 3.5 Erl may correspond to 3.5 resources during 100% of the busy hour or 14 resources during 25% or ….

ERLANGS ON THE AIR INTERFACE

SDCCHTCH

TRAFFIC(Speech, Data)

SIGNALING (Beginning of communication)

(End of communication)(Handover)

SIGNALING(various procedures)

1

2

TT

duration period referencedurationoccupancy )resource(s

=

16


Erlang Law

Offered and carried traffics

Equipment withblocking rate x% Offered Traffic Carried Traffic

Increasing blocking - Increase of subscribers number (more offered traffic)- Decrease of grade of service, while maintaining it

sufficient

Decreasing blocking - Decrease of subscribers number (less offered traffic)- Increase of grade of service

Assuming x = blocking rate:

Carried Traffic = (1 - x/100) * Offered Traffic

Carried Traffic < Offered Traffic (if x ≠ 0)

In this course we will use the following assumptions:• Blocking rate for traffic on Radio interface: 2%

• Blocking rate for signaling on radio interface (SDCCH) = 0.1%

• Blocking rate for PSTN interface = 0.5%

• Blocking rate for A interface = 0.1%

• Blocking rate for Abis interface = 0%

• Blocking rate for Ater interface = 0.1%

Those values of blocking rate are typical values. They may change according to the environment and the QoS we want to offer to the final subscriber.As blocking rates are always small, we admit that:

Carried Traffic ≅ Offered Traffic

17


Erlang Law

Erlang Law with losses (Erlang B)

Maximumresource

Resourcesrequest

Blocking factor

time1 hourYi = occupancy rate of resource i

Offered traffic on each resource

A

Y1 = 0.6 EY2 = 0.75 EY3 = 0.45 E Y4 = 0.35 EY5 = 0.4 EY6 = 0.5 EA = 3.05 EOffered traffic

6543210

123456

3 9 57

Lost calls

Carried trafficA’ = 2.9 E

We need 6 resources to match the requests

Average busy resource

It is assumed (teaching example):• Offered traffic needs, at some times, up to six resources.• At a time, only 4 resources max. are available.

Then:• For each period equal to 3 minutes, the number of resources needed is

computed: i.e. for first period, resources 1, 2 and 6 are requested, given 3 resources.

• Offered traffic on resource 1 includes 12 periods of 3 minutes, giving a traffic value equal to:(12 x 3)/60 = 0.6 Erlang.

• Total offered traffic is equal to 3.05 Erlangs, needing an average number of busy resources of 3.05.

• Three call attempts are rejected.Note 1

Traffic in Erlangs = Summation of events duration (for each event, on a reference period):for instance, reference period = one hour.

Note 2This teaching example only introduces the traffic notion evaluated in Erlangs.It does not correspond to the Erlang Law which deals with:

• Very high number of events• Number of events following a Poisson Law• Distribution of event duration following a negative exponential law

18


Erlang Law

Erlang number computation

A is the Erlang number

λ is the mean rate of events per unit of time

T is the average duration of an event

A = λT

Example on the previous page:T1 = duration of the observation period (usually it is the busy hour = 60’)T2 = total channel occupancy durationX = number of channel requests during T1

3.05Erl T A 5.0833 36183 T 0.6

6036

36 X ' 183 T2 ' 60 T1

=XT2 x

T1X

T1T2 A

hourbusy the at request per timeoccupancy channel average XT2 T

hourbusy the during time of unit per requests channel of numberT1X

======

===

==

==

==

λλ

λ

λ

T

19


Erlang Law

Erlang B Law tables

6 1.146 1.325 1.622 1.909

n B 0.001 0.002 0.005 0.010 0.020 0.030 0.050 0.070 0.100 0.200

1

2

3

4

5

7

8

9

10

0.001

0.046

0.194

0.439

0.762

1.579

2.051

2.557

3.092

0.002

0.065

0.249

0.535

0.900

1.798

2.311

2.855

3.427

0.005

0.105

0.349

0.701

1.132

2.157

2.730

3.333

3.961

0.010

0.153

0.455

0.869

1.361

2.501

3.128

3.783

4.461

0.020

0.223

0.602

1.092

1.657

2.276

2.935

3.627

4.345

5.084

0.031

0.282

0.715

1.259

1.875

2.543

3.250

3.987

4.748

5.529

0.053

0.381

0.899

1.525

2.218

2.960

3.738

4.543

5.370

6.216

0.075

0.470

1.057

1.748

2.504

3.305

4.139

4.999

5.879

6.776

0.111

0.595

1.271

2.045

2.881

3.758

4.666

5.597

6.546

7.511

0.250

1.000

1.930

2.945

4.010

5.109

6.230

7.369

8.522

9.685

Formula for lost calls (no queuing): • N = Resources number for offered traffic

• A = Erlang number

The Erlang B formula is quite complicated. A good approximate result can be obtained by using the following formula:

Resources N = A + k √(A)with

• Blocking Rate Br = 10-k

• Traffic (Erlang) = A

The results of the Erlang B formula are summarized in the Erlang B tables provided in the last section.

rate Blocking

!NA ... !1

A1!N

A]A[E N

N

N =+++

=

20


Erlang Law Erlang Law with queuing (Erlang C)

Resourcesrequest

Y1 = 0.6 Erlang Y2 = 0.75 ErlangY3 = 0.45 ErlangY4 = 0.35 ErlangY5 = 0.4 ErlangY6 = 0.5 ErlangA = 3.05 Erlang

time (minutes)

1 hourYi = occupancy rate of resource i

Offered traffic on:Resource

A

0123456

65

1234

3 69 18 42 57

Time Outcalls rejected

Queued calls

Carried trafficA’ = 3.05

A’ = Offered traffic

Offered traffic

Maximum number of available resource

Average number ofbusy resources

It is assumed (teaching example):• Offered traffic needs, at some times, up to six resources.

• At a time, only 4 resources max. are available.

Then:• For each period equal to 3 minutes, the number of resources needed is

computed: i.e. for first period, resources 1, 2 and 6 are requested, given 3 resources.

• Offered traffic on resource 1 concerns 12 periods of 3 minutes, giving a traffic value equal to:

(12 x 3)/60 = 0.6 Erlang.

• Total offered traffic is equal to 3.05 Erlangs, needing an average number of busy resources of 3.05.

• The three call attempts which would be rejected without Queuing, are registered and processed with some delay.

Nevertheless after a defined waiting delay, they are definitely rejected.

21


Erlang Law

Traffic management: Queuing of TCH requestsFIFO Management on cell basis

12

Priority 012

64

Priority 112

64

Priority 7

WT1 WT7

TCH allocation request

> r01 to r00

TCH attributedTCH attributedFIFO (*)FIFO (*) FIFO (*) TCH attributed

0 (max)1 to 7

Available TCH in the poolTCH request priority

3

WT0

T11time out

requestrejected

ExampleEmergency Call

Call Reestablishment....

PagingHandover

....

= 5= 5

64

Management performed by the BSC, only for TCH (no queuing for SDCCH).Priority 0 to 7: In order to improve the Traffic Management, priority has been defined on call basis:

• Internal priorities (0 to 7), per cell; max. priority = 0; one queue per priority• Level 0 priority can be defined for example for: emergency call, call re-establishment....

Priority threshold (allocPriorityThreshold O&M parameter; example of value: 2):• r0 resources are reserved for requests of level 0 priority in the pool of available TCH• r0 resources must be available to allow processing of a level 1 to 7 priority request• If all these r0 resources are busy, a new level 0 priority request may be queued in level zero priority Queue.

Waiting Threshold WT0 to WT7 (allocWaitThreshold O&M parameter; example of value: 10):

• This threshold defines, for each priority level 0 to 7, in each cell, a number of queued requests; its use is given just below.• For example:

—Priority 0: WT0=5 and 3 requests are queued—Priority 1: WT1=5 and 2 requests are queued

A third request in P1 queue can not be accepted because the total number of requests queued in the queue P0 and P1 (3+2) is equal to WT1.

22

This can be explained generally with the following expression:

So, a request of priority Pi can be queued only if, at this moment, the above condition is satisfied.Protection Timer (T11 time out; AllocPriorityTimers O&M parameter; standard value: 5 seconds):

• TCH request still stored at end of time out is erased from the queue.Note: when the Pi Queue is full, the related level i priority request is rejected (i range: 0 to 7).

FIFO (*): (number of Queued requests in Pj Queues) ≤ WTiΣj

j i

=

=

0

23


Erlang Law

Exercise

> How many resources are necessary for an offered traffic of 65Erl with a blocking rate value of 2%?

> What is the maximum offered traffic that 95 resources can manage without exceeding a blocking rate value of 0.1%?

> How many resources are necessary for an offered traffic of 290Erl with a blocking rate value of 0.1%?

> What is the maximum offered traffic that 960 resources can manage without exceeding a blocking rate value of 10%?


24


Traffic Model BSS Reference call and mobility profile: detailed computations for CS voice

Mobile Originating callsMO = 66%

Mobile Terminating callsMT = 34%

16.72 s 90.1 s

CallEstablishmentRinging

MO and MT calls description

Successful

No response called party

Busy

MO

85%70%

Legend MT

10%

20% 5%

10%

{

25


Traffic Model BSS Reference call and mobility profile: detailed computations

MO busy called-party:

- Setup

MO Duration *(s)

MO callsratio τ 1

MO successful:- Setup- Ringing- Conversation

70%

66%120

10%

1015 25

MO callsratio τ 2

MO no response: - Setup- Ringing

1020

30

20%10

MT successful- Ringing- Conversation

85%5120 34%

MT no response- To paging- or busy- Ringing

10%

5%25

TOTAL

MT Duration(s)

MT callsratio τ 1

MT callsratio τ 2

* : This is the duration of traffic channels occupancy on the radio interface, either for traffic (ex: conversation) or for signaling (ex: setup, ringing)

46.2

6.6%

13.2%

28.9%

3.4%

1.7%

τ1 x τ2

τ1 x τ2

46.2%

(19.8%)

28.9%

(5.1%)

-Successful calls: 75.1%

-Unsuccessful calls: 24.9%

Successful calls(unsuccessful)

Successful calls(unsuccessful)

55.44 (120 x 0.462)

11.55(25 x 0.462)

1.98(30 x 0.066)

1.32(10 x 0.132)

1.44534.66

0.425(25 x 0.017)

106.82including

conversation:90.1

TCH occupancy(s)

TCH occupancy

(s)

26


Traffic Model

Standard traffic model. Observed figures

Number of observed subscribers = 4000Total call attempts at the busy hour = 4000

Mean TCH occupancy duration per call attempt (traffic) = 90.1 sMean TCH occupancy duration per call attempt (signaling) = 16.72 s

Mean SDCCH occupancy duration per call attempt = 4 sMean SDCCH occupancy duration for Loc./Rout. Area update, Attach/Detach, SMS, Supplementary Services = 4 sCall attempts per subscriber during

the busy hour = 1

100

20

60 100

20 Average number of requests for SDCCH, except those for call attempts, during the BH, for the whole subscribers = 26920

Mean TCH occupancy per call attempt (total) = 106.82 sExercise: ATCH ?

Exercise: ASDCCH ?

Exercise: Find ATCH and ASDCCH for 1 subscriber at the busy hour.

ATCH = λTCH * TTCH

λTCH ?TTCH ?

ASDCCH = ?

What is the ratio between SDCCH and TCH traffic?

In the rest of this course we will apply this ratio. (We consider that proportion between signaling and traffic is constant).

27


Traffic Model

High mobility and short call duration traffic model

0.61.6Handover per subscriber at BH

1.724.54Loc./Rout. update, periodic update, attach/detach, SMS, per subscriber in BH

37 s90 sAverage call duration

45 s120 sAverage call holding time

5050Number of cells managed by the BSC

4000040000Active subscribers in the LAC

2.251BHCA per customer

0.025 Erl0.025 ErlTraffic per customer

Short call durationHigh mobility

28


Traffic Model

PS communication types

File Sizeper transaction

in Kbytes

Information Service & E-commerce

UL

E-mail (without attachment)

E-mail (with attachments)

Web Access (no file downloading)

Web Access (file downloading)

0.7Simple Messaging

0.3

2.7

4

12

204

612

180

8

680

10

0.3UL

UL

UL

UL

UL

DL

DL

DL

DL

DL

DL

Communication UL / DL

29


Traffic Model

Subscriber Categories

Active Data Terminalsin X’s network (k units) BH

Business 1038

Consumer 20132

Field Service 1028

Telemetry 323

Total 221

30


Traffic Model Subscriber profile example

Business File Sizeper

transaction

Number oftransactions

at BH

in Kbytes

Information Services & E-commerceUL 0.300

DL 2.700

E-mail (without attachments)UL 4.000

DL 12.000

E-mail (with attachments)UL 204.000

DL 612.000

Web Access (no file downloading)UL 8.000

DL 180.000

Web Access (file downloading)UL 10.000

DL 680.000

1.95

0.98

0.24

0.19

0.05

55.485 Kbytes in one hour (BH) in

UL


DL

GPRS and EDGE call profiles include for each type of subscriber (Business, Consumer, Field Service and Telemetry) the types of service used and the description of the amount of traffic each service generates.

31


Traffic Model Busy hour throughput example

BH peak bit/s (max UL,DL) sigma

Business 10 1857 3,00Consumer 20 986 2,00

Field Service 10 326 4,00Telemetry 3 2 20,00Network 20 503 bit/s (max UL/DL)

Subscribers’repartition

38/221132/22128/22123/221

Average throughput per subscriber according to GPRS Busy Hours

0,0

400,0

800,0

1200,0

1600,0

2000,0

0 2 4 6 810 12 14 16 18 20 22

hours

Ave

rage

bit/

s pe

r sub

s

Total (max UL, DL)BusinessConsumerTelemetryField Service

The last parameter to discuss is the subscriber Busy Hour.If we assume that the GPRS traffic profile is gaussian like, we have a sigma and a peak time (Busy Hour) for each category. Using the number of active GPRS subscribers per category (deduced from marketing inputs) as coefficients, it is possible to compute an average throughput per subscriber at each time of the day (curve “Total(max UL, DL)”). Its peak value is the average throughput per subscriber at Network Busy Hour.

Thus, according to GPRS Busy Hour, the average traffic per subscriber can be very different (almost double). If the busy hour is different for each subscriber, then the average throughput per subscriber is reduced.The Busy Hour is largely determined by Operator Tarifications and subscribers behavior. It has to be considered carefully.

32


Dimensioning Procedure

Network dimensioning according to the busy hour traffic

End dimensioning

Radio Interface

Start dimensioning

Cell

BTS

Abis

BSC

Ater

TCU (TRAU)

A interface

MSC/VLR

HLR

PCU

Agprs

SGSN

GGSN

SY2

EDGE dependant

Cell organization (omni or multi-sector sites, cell dimension) depends on expected traffic, but also on dedicated radio propagation and interference problems.These problems are in charge of radio-engineers. And cell organization is admitted as entry data for the other part of GSM dimensioning which is described hereafter:

• Radio interface: number of TCH/BCCH/SDCCH channels.• Abis/Ater/A interface: number of PCM links.• BTS: number of TRX, BTS and interface boards (possibility of “drop and insert”techniques).• BSC: number of interface boards, BSC type.• TCU (TRAU): number of shelves.

Main EDGE dimensioning constraints are:• Number of PDTCH configured per cell• Number of Joker TS configured per cell

From theses assumptions are computed additional resources (number of PCMs, HW upgrades, products adaptation) required to implement EDGE.

1


nortel.com/training

Section 3

BTS Dimensioning

2


Lesson Objectives

> For cell, compute:• The TCH and PDTCH numbers• The SDCCH number• The CCCH number• The TRX number

> For site, dimension:• The BTS type• The BTS configuration • Total PCM TS on Abis link, including LAPD TS and Joker DS0

(EDGE)You will also be able to quickly obtain these results using look-up tables summarizing all above computations

Upon completion of this section, the student will be able to

This section describes and justifies the several computation steps for BTS dimensioning.Starting site data are:

• Offered traffic• Site layout: number of sectors per site, number of TRX per cell• Blocking rate currently taken for BTS on TCH: 2%• Blocking rate currently taken for BTS on SDCCH: 0.1%

3


Contents

> Overall Information

> Dimensioning Detailed Method

> Packet Logical Channels

> BTS Connections

> Terrestrial Link Optimization

4


Overall Information

Cell subscriber repartition (Example)

100

100

100

20

60 100

100

60 60

20

20

20

20

20

20

60

40 20

20

Town

RuralSuburb

Highway

The cellular planning determines the cell distribution per BTS; the traffic per cell is obtained from the average number of mobile stations assumed in each cell, with a fixed average value of traffic per subscriber.For the example of the diagram:

• Traffic is given per cell or per site, in Erlangs; for instance, assuming an average traffic value of 25 mE per subscriber, 2400 subscribers correspond to a traffic value of 60 Erlangs.

• Three types of traffic area are shown:

— a high traffic area with low surface cells: center of a town

— two medium traffic areas: a suburban area and a straight motorway area

— a low traffic area with large surface cells: countryside

5


Overall Information BTS Dimensioning methods

1. First method: detailed understanding

- TCH- PDTCH- SDCCH (BCCH)- TRX

Offered traffic on site

Site layout

TABLES Abis PCM linkPCM circuit NbrSDCCH/8 NbrBCCH NbrTCH NbrTRX NbrAbis Joker DS0 (EDGE)

Abis LAPD TSLAPD Nbr

2. Second method: look-up tables (for voice standard traffic model)

CS - Voice/data traffic (Erlangs)Signaling (Erlangs)

Blocking rate

Site layout

BTS limits

Abis PCM links

Abis LAPD TS

LAPDConcentration

(2G only)

PS - data traffic (bits/s)Abis Joker DS0 (EDGE)

First method: detailed understandingStarting from the site data, and using the Erlang B, a didactic and detailed method is given; it is a step by step analytic method.This method is general, despite the choice of waiting or blocking rate values in the computation completed hereafter.

Second methodComputations of first method are summarized in tables.These tables are of quick and general use for standard BTS dimensioning.

Final checks are doneOn TRX number relating to radio TS number.On BTS load constraints.

6


Overall Information

> BTS Model provisioning• Radio interface dimensioning:

TCH, PDTCH, SDCCH, CCCH, TRX, BTS Type• Abis interface dimensioning:

Traffic and signaling (LAPD) TS and Joker DS0 (EDGE)• BCF units dimensioning:

PCM interface boards (PCMI)Signaling concentration boards (DSC)

• CBCF units dimensioning: PCM interface boards (CPCMI)

Radio interface dimensioning:Three groups of channels:

• traffic channels TCH, PDTCH• dedicated channels SDCCH• common channels CCCH

Abis interface dimensioning:• Radio interface will be defined, as TRX number• Number of traffic TS = 2 x (TRX number)

•

• Number of Joker DS0 depending on the expected MCS distribution within the cell (EDGE), ranging from 0 to 8

• Depending on the product range BTS 18000, S12000 or S8000

( ) ( )integer upperBTS18000 for 9 or 8

number TRXLAPD of Number =

7


Overall Information GSM/GPRS Logical channels on radio interface TSs

FACCH

Frequency correction

Synchronization

Broadcast control

Access request

Subscriber paging

Answer to Access request

Broadcast info

Dedicated Signaling

Sys Info 5, 5bis, 5ter 6 + SMS

Traffic (speech – CS data)

Associated Signaling

BTS

0 1 2 3 4 5 6 7TS

MSFCCH

SCH

BCCH

PCH

AGCH

CBCH

SDCCH

SACCH

TCH

FACCH

SDCCHSACCH

FCCH

SCH

BCCH

RACH

PCH

AGCH

RACH

CBCH

TCH Traffic (speech – CS data)

Associated Signaling

Radio Measurement + SMS

Broadcast info

Dedicated Signaling

M.S. Pre-synchronization

Access request

Subscriber paging

Answer to Access request

MF51 MF26

PDTCH

PACCH

Traffic (PS data)PDTCH

PACCH

Traffic (PS data)

MF52

Associated SignalingAssociated Signaling

Three groups of logical channels:• 1. Traffic channels (TCH; PDTCH), and associated channels (FACCH,

SACCH; PACCH, PTCCH):

• Number computed from Erlang B law, starting from offered traffic, according to the traffic model.

• 2. Dedicated signaling channels (SDCCH, SACCH, CBCH):

• Number computed from Erlang B law, using figures given by the traffic model.

• The CBCH is optionally used; when activated, it uses permanently one SDCCH resource.

• 3. Common channels (CCCH), BCCH and synchronization channels (FCCH, SCH)

• Theoretical studies on message exchanges on radio interface haveshown that one common channel is often sufficient, for low to medium offered traffic on CELL.

• “BCCH combined”: common channel pattern for small capacity cells (O1): Signaling channels SDCCH/SACCH are included in same frame as common channels: Traffic CHannel

Packet Data Traffic CHannelTCHPDTCH

Fast Associated Control CHannelPacket Associated Control ChannelPacket Timing advance Control CHannel

FACCHPACCHPTCCH

Stand-alone Dedicated Control CHannelSDCCHFrequency Control CHannelFCCHSignaling CHannelSCHCommon Control CHannelCCCHSlow Associated Control CHannelSACCHCommon Broadcast CHannelCBCHRandom Access CHannelRACHBroadcast Control CHannelBCCHPaging CHannelPCHAccess Grant CHannelAGCH

8


Overall Information

FR vs. HR TCH

BTS

Abis interface (E1/T1)

0 1 2 3 4 5 6 7TS n

TS 1/0

TS 24/31

16 kbps

TCH/F

2x8 kbps

TCH/H

Um interface

Capacity improvementsthanks to AMR

introduction

0 1 2 3 4 5 6 7TSf0

TS p

4 5 70 1 2 3 6TSf1

But, there can be holes at a time being.A Full Rate call may not be established.

Full Rate blocking rate increases.

AMR Half Rate allows to double the number of calls that could be carried on a AbisPCM. Therefore, AMR HR offers the possibility to have a capacity increase in terms of Erlang with the quality of a FR speech.Indeed, one Full Rate Traffic CHannel (TCH/F) requires one 16 kbps TS on Abisand one complete Radio TS. Whereas, the same resources (the 16 kbps TS on Abisand the Radio TS) can be shared by two Half Rate Traffic CHannels (TCH/H).The Nortel BSS does only provide Half Rate Traffic Channel with AMR introduction:

• Adaptative multi-rate Half rate Traffic CHannel (TCH/AHS)• Adaptative multi-rate Full rate Traffic CHannel (TCH/AFS)

9


Overall Information

BTS Product range: cell layout

8 TRXs8 TRXs

8 TRXs 8 TRXs

8 TRXs

Omni Bi sectorial Tri sectorial

8 TRXs

For BSC12000: 24 TRXs max per site

16 TRXs16 TRXs

16 TRXs 16 TRXs

16 TRXs

Omni Bi sectorial Tri sectorial

16 TRXs

For BSC3000: 48 TRXs max per site (V15.1) with BTS18000

The Diagrams show the max. number of TRX which can be installed per cell, on one site managed by a BTS.Note that in the case of a BSC3000, a max of 48 TRXs per site is defined only with the introduction of the BTS 18000 and in a S161616 config.Reminder: for high traffic densities, the solution is to create multi-sectorial sites, instead of increasing the number of omni-sectorial sites of reduced coverage, which would result in:

• Higher installation cost• Difficulties to find sites

Currently, the most used configurations are:• Omni-sectorial layout for low traffic sites• Tri-sectorial layout for medium and high density urban sites• Bi-sectorial layout for roads

10


Overall Information Full Range Family

e-cell

Outdoor Microcellular coverage34.5 liters

S8006 StreetDeployableS8002 GSM-RS8000 Indoor S8000 Outdoor

S2000H

Integrated self contained cell-siteCommon package Indoor/OutdoorNo fans, natural convection

S12000 Indoor

S12000 Outdoor

Highest capacityLowest foot printUp to 12 TRXsper cabinet

S8000 Outdoor and Indoor• 8 TRXs per cabinet and up to 3 (with BSC 2G) or 6 (with BSC e3) cabinets• DRX architecture: 1 (e)TRX = 1 (e)DRX + 1 ((H)e)PA• Compact BCF (or CBCF)= CMCF and CPCMI boards

S8002• 2 TRXs outdoor BTS (O2) designed for railway applications (R-GSM band)• Environmental performances equal or better than current S8000• Re-using common S8000 equipment: CBCF, DRX, PA, RX splitter, rectifiers• User compartment (6 U)

S8006• 6 TRXs outdoor BTS designed for installation along streets and roads without

requirement for building permits (O6, S222, S33 and S42)• Environmental performances equal or better than current S8000• Diversity radio path as standard• Re-using common S8000 equipment: CBCF, DRX, PA, RX splitter, rectifiers

S2000H&L• 2 TRXs outdoor/indoor BTS in 1 cabinet, expandable to 4 TRXs with an additional

cabinet• Small BCF (or SBCF) = 1 SMCF + 1 SPCMI boards• Internal antenna for S2000L (optional)

e-cell• 2 TRXs BTS in 1 cabinet, expandable to 4 TRXs with an additional cabinet• 1 antenna (integrated or external)

S12000 Outdoor and Indoor• 12 TRXs per cabinet and up to 3 (with BSC 2G) or 4 (with BSC e3) cabinets• DRX architecture: 1 (e)TRX = 1 (e)DRX + 1 ((H)e)PA• CBCF with CMCF and CPCMI boards (for up to 3 cabinets) or XCBCF with CMCF

Phase 3 and 4 CPCMI boards (for 4 cabinets)

11


Overall Information

Full Range FamilyBTS 18000 OutdoorBTS 18000 Indoor

BTS 18020 Outdoor:• Fully Integrated self contained cell-site:

• 18 TRXs (DRX + PA) in a single cabinet (16 TRXs limitation with BSC3000 in V15.1).

• Rectifiers, battery back-up, cooling and heating and 220 Vac main (or 2 x 110 Vac live)

• Optimized size versus capacity ratio : Cabinet size 150 x 135 x 70 cm• PA TX Power: 30 W (1800/1900) / 40 W (850/900) / 60 W (900 HPRM)• Extended operating temperature range: -40 °C to +50 °C• Max consumption : Total for cabinet : 6642 VA ( with heater on : 9442 VA and with heater on and batteries in charge : 11234 VA )• Cabinet weight: when fully equipped = 500 kg.

BTS 18010 Indoor:• Compact packaging:

• 18 TRX (DRX + PA) in each cabinet. (Divided in 6 RM’s)

• New BCF integrated in the main cabinet and up to 3 radio cabinets.

• Modular and flexible configuration: from S666, or O18 or S99 in 1 cabinet and up to S161616 in 3 cabinets (with a BSC3000) or S888 in 2 cabinets (with a BSC 12000)• Dimensions: Height : 175 cm Width : 60 cm Depth : 60 cm• PA TX Power: 30 W 30 W (1800/1900) / 40 W (850/900) / 60 W (900 HPRM)• Max Consumption : 5123 W• Extended operating temperature range: -5 °C to +45 °C• Cabinet weight: when fully equipped =300 kg

Nortel Networks has also developed the BTS 18000 Combo (indoor/outdoor) which is a UMTS/GSM BTS, and the BTS 18020 MCPA which is an outdoor 1900 GSM BTS with a MCPA cabinet for the coupling system.

12


nortel.com/training

Lesson or Module Title

Lesson or Module # or Module # –Lesson #

nortel.com/training

Dimensioning Detailed Method

This chapter gives all the computation steps needed to evaluate:• The number of traffic channels TCH in a cell.• The number of signaling channels SDCCH in a cell.• The number of TRX per cell.• The total number of time slots on Abis link (including signaling and EDGE DS0 TS).• The number of boards inside the BCF.

13



Traffic channels reminder

AiTi

26 frames = 120 ms

T0 A0T0 T0 T0 T0 T0 T0 T0 T0 T0 T0 T0T1 T1 T1 T1 T1 T1 T1 T1 T1 T1 T1 T1 A1 time

Half Rate - Downlink & Uplink

T : TCH(FR) A : SACCH : IDLETi : TCH (HR)

sub-channelno. i

Ai : SACCHsub-channelno. i

26 frames = 120 ms

Full Rate - Downlink & Uplink

timeT AT T T T T T T T T T TT T T T T T T T T T T T

Full rate speech transmissionWhen a Mobile Station is in communication mode, speech is coded every 20 ms in blocks. These blocks are coded in 8 half-bursts, whose information quantity is equivalent to 4 entire bursts. Then, one burst has to be delivered every 4.615 ms.So, in 26 frames lasting 120 ms, 24 bursts are used for speech transmission. One burst is used for an SACCH. The last one in the sequence is an idle burst. During this burst, the mobile is not idle, but it uses this time to monitor the neighboring cell frequencies.

Half rate speech transmissionWhen the half rate speech transmission is in use, the 26 frames of a given time slot can be separated between two users, since only 12 coded speech bursts are used per user.So, in 26 frames lasting 120 ms, the odd burst numbers are restricted to one user, and the other numbers are for the other user. SACCH bursts are in the 13th and 26th positions. In this case, the monitoring is more frequent.

4.75 kbpsAMR 4k755.9 kbpsAMR 5k96.7 kbpsAMR 6k710.2 kbpsAMR 10k25.6 kbpsHR12.2 kbpsEFR13 kbpsFR

Source coding rate

14



Number of traffic channels in a cell

Erlang ‘B’Loss

Formula

Erlang ‘B’Loss

Formula/2

X

Number of

subscribers

Subscriber

activity

blocking rate

Number of TCH/F resources

+ Number of TCH TS

Percentage

of HR calls

Number of TCH/H resources

XPercentage

of FR calls

X

blocking rate

.planned

cell traffic

planned

cell traffic

Subscriber activity: traffic per subscriber at busy hour = 25 mE (example).Number of subscribers = 1700 (example). Then planned traffic in the cell including the 1700 subscribers = 42.5 Erlangs (example).With only Full Rate calls:Number of necessary resources with a blocking rate of 2%, obtained from ErlangB table: n = 53.Conclusion: TCH channels = 53 for 42.5 Erlangs cell and blocking rate = 2%.

With 20% Half Rate calls:Planned traffic in the cell for Full Rate calls: 0.8x42.5 = 34 Erlangs.Number of necessary Full Rate resources with a blocking rate of 2%, obtained from Erlang B table: n1 = 44.Planned traffic in the cell for Half Rate calls: 0.2x42.5 = 8.5 Erlangs.Number of necessary Half Rate resources with a blocking rate of 2%, obtained from Erlang B table: n2 = 15.Conclusion: TCH/F Channels = 44 + 15/2 = 52 for 42.5 Erlangs cell and blocking rate = 2%.

Another approach consists in dimensioning the number of TCH TS only considering Full Rate TCH and then calculating the capacity increase in terms of Erlang with p% of Half Rate allocations.53 Full Rate resources correspond to 2x53 = 106 Half Rate resources; With a blocking rate of 2%, the Erlang B table gives a traffic of 93.8 Erlangs that is to say a gain of 120%.

15



Dedicated signaling channels reminder

A : SACCH D : SDCCH : IDLE

51 frames = 235 ms

A5 A6 A7 A0

A4

D7D6D5D4D3D2D1D0

D7D6D5D4D3D2D1D0A1 A2 A3

time

Uplink

51 frames = 235 ms

A1 A2 A3A0D7D6D5D4D3D2D1D0

A5 A6 A7A4D7D6D5D4D3D2D1D0

time

Downlink

The dedicated channels are combined into two multi-frames of 51 frames. In the uplink and the downlink directions, the configuration is almost the same one, only shifted by 15 frames.The dedicated channels combination broadcasts a group of 8 SDCCH frames (2 groups of 4 consecutive SDCCH frames), each of them is associated to 4 consecutive SACCH frames. Each different group is used by a different dedicated communication. The multi-frame configuration is shown on the above figure.So 8 users can use the same physical channel simultaneously, and the different communications associated to their SACCH signaling are spread on a cycle of 102 frames (2 51-multi-frames). In such a multiplexing cycle, 6 frames are unused (idleTS).

16



BCCH Combined reminder

R R

R R D2

D2

D1

D1

D0

D0A1

A3

A0

A2R

R

R

R

D3

D3

51 frames = 235 ms

time

Uplink

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

R

A : SACCH D : SDCCH : IDLEB : BCCHS : SCHF : FCCH : AGCH/PCHC R : RACH

A3A2

A1D3D2

D3D2

D1

D1

D0

D0 FSFSFSC CC FSBFS

FSFSFSC CC FSBFS

51 frames = 235 ms

A0

time

Downlink

In the case of a low capacity cell, it is possible to combine on the same physical channel some dedicated channels with some common control channels. Their configuration is done on 2x51 frames and is indicated in the SI type 3.This combination contains all the channels of dedicated and common combinations: FCCH, SCH, BCCH, PCH, AGCH, SDCCH, SACCH and RACH.

Downlink wayFrom a common control combination, FCCH, SCH and BCCH keep theirconfiguration (FCCH+SCH: 0, 10, 20, 30 and 40; BCCH: 2 to 5) for both multi-frames.PCH and AGCH are still dynamically configured but only on the bursts: 6-9 (except when extended BCCH are used), 12-15 and 16-19, for both multi-frames.On the bursts left, 4 blocks of 4 SDCCH TSs, each of them associated with a SACCH block of 4 TSs, and one idle TS at the end of each multi-frame. Each different group is used by a different sub-channel.

Uplink way On 102 frames, 27 RACH frames are kept and the other ones are replaced by 4 blocks of 4 SDCCH TSs, each of them associated with a block of 4 SACCH TSs.

17



Number of SDCCH in a cell

planned celltraffic (ATCH)

ASDCCH

Number

of SDCCH resources

blocking rate

•• 8 Number

of SDCCHTime slots

Erlang‘B’Loss

Formula

X100

x

call attempts/second

location update rate…

mean SDCCH occupancy time

Traffic model at X%

Since 1 SDCCH TS carries up to 8 SDCCH channels, we divide by 8 the number of resources obtained from Erlang B table.If ATCH = 42.5 Erl, ASDCCH = 28% * 42.5 = 11.9 ErlSo the number of SDCCH resources = 24 for a blocking rate of 0.1%.

=> number of SDCCH TS = 24/8 = 3 SDCCH TSRemark: if the number of TCH TS necessary is ≤ 7, then, the BCCH combined configuration can be used if the number of SDCCH resources is ≤ 4.Caution: for a given (TCH, SDCCH) configuration, an increase of the Half Rate traffic requires a new dimensioning of the SDCCH resources.

Example:• Dimensioning for Full Rate only:

ATCH = 42.5 Erl gives NTCH = 53 for a BrTCH = 2%

Therefore, ASDCCH = 11.9 Erl requiring NSDCCH = 24 (3 SDCCH TS) for aBrSDCCH = 0.1%

• Dimensioning for full Half Rate:N’TCH = 2x53 = 106 gives A’TCH = 93.8 Erl for a Br’TCH = 2%

Therefore, A’SDCCH = 0.28x93.8 = 26.3 Erl requiring N’SDCCH = 44 (6 SDCCH TS) for a Br’SDCCH = 0.1%

18


Packet Logical Channels

Multi-frame structure

0 1

Radio Blocks

Cycle of 52 TDMA frames divided in:♦ 12 radio blocks B0-B11 (of 4 consecutive

frames)♦ 4 idle frames (X)

Idle frames

TDMA Frame 0 1 2 3 4 5 6 7 8 9 1011 1213141516171819 20212223 242526 27282930313233 3435363738 3940 4142434445464748 495051

Block B 0 B 1 B 2 0 B 3 B 4 B 5 1 B 6 B 7 B 8 2 B 9 B 10 B 11 3

2 3 4 5 6 7 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7

GPRS Time Slot (PDCH)TDMA Frame

= 4.615 ms

The packet channels carry either RLC data blocks or RLC/MAC control blocks (except PRACH and PTCCH UL, which use an access burst instead of normal bursts). Each of these radio blocks are mapped after channel coding and interleaving onto 4 radio TS (called radio blocks because they carry logical radio blocks).

The mapping in time of the packet logical channels carried by the same PDCH is defined by a multi-frame structure. The multi-frame structure for PDCH consists in a cycle of 52 successive TDMA frames, divided into 12 blocks (of 4 TS each) and 4 idle frames according to the above drawing.The multiplexing of the packet channels on a PDCH is not fixed like in the GSM system. It is managed by some parameters and the following block order: B0, B6, B3, B9, B1, B7, B4, B10, B2, B8, B5, B11. For example, if there are 4 PBCCH blocks in the cell, those will be carried by the blocks B0, B6, B3 and B9 (on the same TS indicated in System Information 13 on BCCH).

The idle frames are used by the MS for signal measurements and BSIC decoding on the SCH of neighboring cells (idle 1 and 3) or for TA update (sending an access burst on PTCCH UL in idle 0 or 2 and receiving an RLC/MAC control block on PTCCH DL in idle 0 and 2 of 2 successive multi-frames = 4 TS in total).

19


Packet Logical Channels

PDTCH Allocation

TS0 TS1 TS2 TS3 TS4 TS6TS5 TS7




TDMA2TDMA3

TDMA4

Combined GSM/GPRS TSConfiguration TCH/PDTCH

GPRS TS (PDTCH: packet switched)

TDMA1

GSM TS (TCH:circuit switched)

The TS configuration is declared for each TS at the OMC-R. Some TS are reserved for the GSM system only (circuit switched TS): TCH,some others are reserved for the GPRS only (packet switched TS: PDTCH),some others TS can be used either as TCH or PDTCH on demand.

The possible configurations for the packet switched channels (PDTCH) are:• PDTCH • PCCCH/PDTCH• PBCCH/PCCCH• PBCCH/PCCCH/PDTCH

These configuration will result in different packet channels multiplexing on the same PDTCH (for more details, see the multi-frame at 52 TS).

20



How many TRX per cell?

Take theupperinteger

multipleof 8

Number of CCCHBetween 1 (TS 0) and 4 radio time slots(TS 0/2/4/6)

÷8

+Number of SDCCHradio time slots

Number of TCH radiotime slots

Total radio time

slots

Number of TRX

Number of PDTCH radiotime slots

CCCH ruleNumber of CCCH radio time slots = 1 per cell.In some cases (microcell, dual band), we may need more than 1 CCCH: up to 4 in total (TS0, 2, 4, 6) as specified in the GSM recommendations. The addition of CCCH TS will depend on the traffic model, the LAC repartition and the environment.2 CCCH TS may be necessary in a single layer cell if, with 1 CCCH TS, the number of TRX per cell is > 6 and the offered traffic per LAC is > 1200 Erls.In a multi layer cell, a second CCCH TS may be necessary if, with 1 CCCH TS, the number of TRX per cell > 5.In our example: Number of TCH radio time slots = 53 (example: cell with 1700 subscribers).Number of SDCCH/8 radio time slots = 3.Total number of radio time slots: 53 + 3 + 2(CCCH) = 58.Number of TRX (8 radio TS per TRX): 58/8 = 8 TRXs.Exercise: In this configuration, what will be the distribution between SDCCH and TCH for full Full Rate? For full Half Rate?

Remark: if the cell is extended, the number of TRX is obtained by dividing the total number of radio TS by 4.

21



How many traffic Abis time slots?

TRXDimensioning

/ 8*2

Total Number of

radio timeslots

number

of TRXnumber of Abistraffictimeslots (64 kbps)

/ 4

2 PCM TS at 64 kbps

8 radio TS carrying 16 HR TCH

64 kbps 64 kbps

Air interface

8 radio TS carrying 8 FR TCH

Abis interface

8 radio TS carrying FR & HR TCH

A PCM TS supports up to 8 half rate traffic channels with a switching matrix at 8 kbps (half rate speech). Concentration from 4 time slots on radio interface towards 1 time slot on Abis interface is performed by BTS.

1 TRX handles 8 radio TS:number of traffic time slots on Abis/Ater = (number of TRX) x 2For the chosen example (8 TRXs):

• Number of traffic TS on Abis and Ater interfaces (8 x 2) = 16 TSNote: 16 time slots on Abis PCM link correspond to 64 Full Rate TCH traffic channels up to 128 Half Rate TCH traffic channels on radio interface.

4 full rate traffic channels are supported by: 4 TS

(on 4 radio channels)1 TS (4x16 kbit/s)(on one PCM link)

1 TS (4x16 kbit/s) (on one PCM link)

4 TS (4x64 kbit/s)

Radio interface Abis interface Ater interface A interface

8 half rate traffic channels are supported by: 4 TS

(on 4 radio channels)1 TS (8x8 kbit/s)

(on one PCM link)2 TS (8x16 kbit/s) (on one PCM link)

8 TS (8x64 kbit/s)

Radio interface Abis interface Ater interface A interface

22


LAPD Frame Reminder

FCS : Frame Check Sequence SAPI : Service Access Point Identifier (0, 1, 3, 62)F : Flag TEI : Terminal Equipment Identifier

0 to 260 octets

FCS Control AddressF

N (R) N (S) TEI SAPI

Information F

LAPD

Start offrame

End offrame

On Abis interface for each BSC and related BTS terminal port (TEI), three types of links may be activated depending on the SAPI parameter value:The Radio Signaling Link:

• Radio resource management procedures SAPI = 0

• Short messages, point to point SAPI = 3

The Operation and Maintenance Link: O&M procedures SAPI = 62.

LAPD messages on Abis:• OML: software download, channel configuration, notification (event report)

• RSL: paging, HO command, channel requirement

On Agprs, between BSC and PCU, same OML SAPI number = 62 is used for radio configuration. RSL SAPI number = 0 is used for allocation of GPRS TS. An extra link exists: GSL(GPRS Radio Signaling Link) using SAPI number = 1 for communication between BTS and PCU for TBF (Temporary Block Flow) related messages.

23


Abis Interface Protocols

RSL = Radio Signaling Link

OML = Operation and Maintenance Link

GSL = GPRS Radio Signaling Link

RSM = Radio Subsystem Management

O&M = Operation and Maintenance

RSM O&MRSM O&M O&M

Level 1 layer

RSL OML

TRXBCF

Level 3 layer

LAPDLevel 2 layer

BTS side BSC side

GSLRSL OMLGSL

This interface located between BTS and BSC has these features:• Partly normalized• No inter-operability (currently) proprietary

It is organized in three levels:• Level 1 PCM transmission (E1 or T1):

— Speech:– Conveyed in timeslots at 4 (full rate) to 8 (half rate) x 16 kbps (remote

transcoders)— Data:

– Conveyed in timeslots at 4 x 16 kbps– The initial user rate (CS), which can be 300, 1200, 1200/75, 2400, 4800

9600 or 14400 bps is adjusted to 16 kbps.– For Packet Switch data, 9.05, 13.4 kbps (GPRS CS1 and CS2), 8.8 and 11.2

kbps (EDGE MCS1 and MCS2) channels are each using a 16 kbps timeslot. For all other PS data rates, more than one 16 kbps timeslot are used.

• Level 2 LAPD protocol: Standard HDLC procedure:— RSL = Radio Signaling Link— GSL = GPRS Radio Signaling Link— OML = Operation and Maintenance Link

• Level 3 application protocols:— RSM = Radio Subsystem Management— O&M = Operation and Maintenance procedure

24



Concentrated LAPD with CBCF

CMCF

CPCMI

SwitchingMatrix

8 DRXs

SignalingTS

BSC

Abis

FP1 FP2 FP3 FP4 FP5 FP6 FP7 FP8

LAPDconcentrationUp to 8 DRXs(+ CBCF)

1 internal TS(concentrated LAPD)

CMCF boardCore unit of the CBCF manages the switching matrix, the synchronization, concentration and routing tasks.

Remark: With the introduction of half rate, the number of LAPD messages per TRX, increases. Nevertheless, considering the actual proportion of AMR mobiles in a network, one LAPD for 8 TRX might be sufficient.

In V12.4, DRX, eDRX and DRX-ND3 are all treated and displayed as DRX. In V14.3, eDRX becomes identifiable, while DRX and DRX-ND3 remain un-identifiable. In V15.0, each equipment type is identified, processed and treated independently.This implementation reduces the total cost of ownership for Nortel equipment and is then a benefit for Maintenance and Provisioning process. From V15, CMCF phase 1 and phase 2 are not fully compatible anymore from a feature point a view.The CMCF phase 1 / phase 2 differentiation permits the operator to deploy V15 system release on BTS in the best way as some V15 features are not fully supported by CMCF phase 1 or cannot be activated on phase 1 / phase 2 duplex BTS.

25



Abis PCM dimensioning without EDGE

LAPDdimensioningEngineering Rule

Total 64 kbps TS on Abis land lines

Nbr of LAPDfrom TRX+ BCF

Nbr of ABISTraffic TS

Nbr ofconcentrated LAPD

E1 PCM

•• 31

Number of E1 PCM = upper integer value

T1 PCM

••

24

+

Number of T1 PCM = upper integer value

Reminder: TS on Abis carry traffic time slots and signaling LAPD time slots solely.TRX number:

• TRX number has been previously obtained starting from radio TS number

• Example continued: 64 radio TS, then 8 TRXs

Number of Abis traffic TS = (number of TRX) x 2:• Example continued (8 x 2) = 16 TS on Abis

LAPD dimensioning (see previous page):• One concentrated LAPD on Abis processes signaling for 8 TRXs

• Example continued:8 TRXs ⇒1 LAPD TS on Abis

Total number of Abis TS:• Example continued:

(TS for traffic = 16) + (TS for LAPD = 1) = 17 TS

E1 PCM link (32 TS. TS0 never available: used for link synchronization): 31 TS available.T1 PCM link: 24 TS available.Example continued: 1 E1 PCM link necessary for 17 TS

1 T1 PCM link necessary for 17 TS

26



S12000/S8000

To be dimensioned

CBCF

PrivatePCM bus

CMCF

BSC

Switching

CMCF

DRX

CPCMI

CPCMI

CPCMIPCM

Interface

Control,Signal.Concentr.SynchronizationManagement

S8000 if the CBCF is used: CPCMI and CMCF (1+1).S12000 with CBCF: CPCMI and CMCF (1+1).

27



CBCF Units dimensioning

CBCFdimensioning rules

Number of Abis PCM

Number of CPCMI boards

Number of CPCMI = Upper Integer[number of Abis PCM / 2]

ExternalPCM

CPCMI

CBCFS8000/S12000

InternalPCM

Available Resources:

Rules:• One CPCMI board has been designed to handle two PCM links of Abis

interface.• Example continued:

1 PCM link 1 CPCMI board

S8000 S12000

CMCF 2 2

CPCMI 3 3

28



BCF Unit for BTS 18000

IFMICM

SPM

The BCF for the BTS 18000 is composed of the following cards:• IFM + ICM + SPM

The backplane where they are connected is called IBP. • IFM : The Interface Module provides the following access for the ICM• ICM : The Interface Control Module is designed to manage the whole BTS site in simplex configuration. It is the equivalent of the CMCF and CPCMI modules of the S8000 or S12000.• SPM : The Spare Module (SPM) is reserved for future use. It may be designed to manage the whole site network packetization for example (or RLC/MAC in the BTS).

29



BCF Unit for BTS 18000

IFM board

ICM board

IFM board:The IFM is only used in the BTS18000 base cabinet. It is not present in the extension cabinets. The IFM is composed of a single passive board with connections on the IBP and on the front panel. The IFM provides connectivity and secondary protection on the PCM links.Maximum number per cabinet: 2.Ext Abis connector: E1/T1 links to Abis interfaceShared Abis connector: E1/T1 links to ICM board

ICM board:The ICM is only used in the BTS18000 base cabinet. It is not present in the extension cabinets. It is designed tomanage the whole BTS18000 site in simplex or redundant mode.Redundancy can optionally be introduced using two ICMs in the digital rack. In such a mode, called duplex, there is one active ICM and one passive ICM

30


nortel.com/training



nortel.com/training

EDGE Dimensioning Detailed Method

7 New Coding Schemes (MCS2, MCS3 and MCS5 to MCS9) are implemented with EDGE. They permit to increase significantly the peak radio throughput (up to 59.2 kbps with MCS9).For data circuit channels using MCS3 and greater, more than one 16 kbps TS is required. Therefore, in order to fully benefit from these new Coding Schemes, an extension of the Abis resources is requested. Moreover, a specific hardware on BTS side must be implemented for the BTS to be fully EDGE compatible.To configure EDGE on a network, several steps must be followed. The purpose of these steps are to define the number of additional TS (called DS0) that must be configured on the Abis interface to fully benefit from the new coding schemes. Then,Abis (and Agprs) interface dimensioning must be modified accordingly to take into account additional DS0. Finally, BTS hardware must be checked to ensure a full EDGE compatibility. An eye must be kept as well on the BSC3000 and PCU dimensioning.

First step to perform is a radio interface analysis to obtain an MCS distribution at each position of the cell. Then, using this MCS distribution, additional DS0 TS can be computed. Radio Site Mask and Abis PCM dimensioning must be modified accordingly to the additional DS0 number, and BTS architecture must be checked.

Let’s have a look at all these steps in the following slides.

31



Introduction: Methodology for EDGE Dimensioning

Radio interface analysis

Throughput

Joker dimensioningon Abis

Number of joker to be configured

BTS hardware provisioning

HW Upgrades

Abis Interface dimensioning

PCM#,Radio site Mask

Agprs Interface dimensioning

PCM#Upgrades

BSC/PCU engineeringUpgrades,

Dimensioning

In section 6

In sections 5 and 6

First Step: Radio interfaceBased on radio condition and network design (cell radius, C/I,…) the expected radio TS throughput, the MCS distribution and the average BLER values can be computed. Second Step: DS0 joker on AbisThe second step consists in determining the required number of joker DS0 to be configured on Abis to support the higher throughput per TS. This number of DS0 is obtained from the MCS distribution provided by the radio analysis.Third Step: Abis backhaul dimensioningThis additional number of DS0 joker must be taken into account in the radio site mask definition and in the Abis PCM number computation.Fourth step: BTS hardware compatibility:BTS/DRX imposes constraint on the ability to enable EDGE on one cell/site. Additional limitation can be set on the maximum number of joker DS0 that can be configured per TDMA.Fifth step: Agprs dimensioning.Agprs interface should be re-dimensioned to add capacity for the joker TS.Sixth step: BSC/PCU dimensioning.BSC3000 and PCU will likely require an upgrade due to the increased number of DS0 & PCM (Abis and Agprs). Note that there is no EDGE impact on engineering rules on Gb and Core Packet.

32



First Step: Radio Interface Analysiscell range

Offered throughput

0

Excellent QoS Poor QoS

Max

Throughput varies with : BLERBLER varies with : C/I and Eb/NoFor each (C/I, Eb/No), offered throuhput can be predicted at each position on the cell

1

10

100

-10 0 10 20 30

C/(I+N) (dB)

BLE

R (%

)

MCS1MCS2MCS3MCS4MCS5MCS6MCS7MCS8MCS9

BLER = f (C/(I+N))TU 50, 1900 MHz, without Frequency Hopping, without IR

860 688 516 344 172 0 172 344 516 688 860860

688

516

344

172

0

172

344

516

688

860

55

55

55

55

50

50

50

50

45

45

45

45

45

40

40

40

40

40

40

35

35

35

35

35

3530

30

30

30

30

3030

30

25

25

25

25

2020

2020

Cumulative Averaged Throughput

AT

The purpose of this step is to obtain the expected radio TS throughput through the MCS distribution (equivalent to throughput distribution) within the cell, depending on its range:

• C/I (frequency plan dependant) & Eb/No (environment dependant) distributions are first computed on the cell. The result provides C/(N+I) distribution over the cell.• BLER distribution f[C/(I+N)] on cell is then deduced for each MCS using R&D simulations. Indeed, BLER distribution depends on radio conditions and estimations between them have been obtained through software signal processing simulator at air-interference layer where transmitter, receiver, interference andmultipath channels were modelled.• Throughput distribution on cell is deduced from BLER distribution for each MCS. Following formula is used to calculate effective throughput per TS (at RLC/MAC level) according to the BLER:

EffectiveThroughput = MaxThroughput_MCS x (1-BLER)

Maximum Throughput per TS according to the MCS. *MCS1 and MCS4 are not implemented in V15.1

Finally, having throughput value per TS at each position of the cell, mean throughput per TS is obtained by integrating data throughput over the covered area.

MCS1* MCS2 MCS3 MCS4* MCS5 MCS6 MCS7 MCS8 MCS9 8.8kbps 11.2kbps 14.8kbps 17.6kbps 22.4kbps 29.6kbps 44.8kbps 54.4kbps 59.2kbps

33


EDGE Dimensioning Detailed Method Example of an Urban MCS Usage Distribution

Distance (km)

Throughput / TS

(kbps)MCS usage

(%)Mean Throughput / TS

calculation 0.00 59.200 MCS-9 0.0370.03 59.200 0.2960.06 59.200 0.5920.09 59.200 0.8880.12 54.340 MCS-8 1.0870.15 53.707 1.3430.17 52.393 1.5720.20 50.273 1.7600.23 47.347 1.8940.26 43.771 1.9700.29 39.637 1.9820.32 35.290 1.9410.35 31.804 MCS-7 1.9080.38 28.686 1.8650.41 25.575 1.7900.44 22.488 1.6870.47 19.989 MCS-6 1.5990.50 18.369 1.5610.52 16.741 1.5070.55 15.155 1.4400.58 13.660 0.674

Mean Throughput/TS (kbps): 29.391

% Users % Users Cumulative Mean BLER when used BLER at cell edgeMCS-1 0.0 100.0 0.0 14.4MCS-2 0.0 100.0 0.0 19.7MCS-3 0.0 100.0 0.0 29.7MCS-4 0.0 100.0 0.0 45.2MCS-5 0.0 100.0 0.0 41.3MCS-6 39.9 100.0 42.6 53.9MCS-7 27.0 60.1 40.1 75.7MCS-8 30.0 33.1 17.0 84.6MCS-9 3.1 3.1 0.0 100.0

Mean BLER 32.9

MCS9 to MCS6 8-PSK modulation are only used

Hypothesis:Assuming a cell radius of 580 m, C/I = 12 dB, in Downlink 1800/1900 MHz and in TU3 Km/h no IR

1. BLER distribution for each MCS using R&D simulations

2. Throughput distribution on cell for each MCSdeduced from BLER distribution ; MCS distribution over the cell

3. Average theoretical throughput = 29.4 kbps / TS in DL

In this example, it can be seen from the BLER distribution table that only MCS 6 to 9 are used. These results are computed through signal processing simulators depending on C/I, cell radius, and TU3 environment.MCS 9 will be used only by MS having very good radio conditions, i.e. MS close to the BTS. With a uniform user repartition within the cell, 3.1% of the users will benefit from MCS 9 (users being located from 0 to 0.09 km). Users located at cell edge will use MCS 6 and the minimum available throughput at this cell edge will be of 13.66 kbps.Throughput distribution on cell is deduced from BLER distribution for each MCS. Mean throughput per TS at each position of the cell is equal to the MaxThroughput_MCS x (1-BLER).Finally, mean throughput per TS is obtained by integrating data throughput over the covered area and is equal to 29.4 kbps.Note that MCS thresholds are optimised by the Link Adaptation function (graph presented on the following slide).

34


EDGE Dimensioning Detailed Method Example of an Urban EDGE Data Throughput Distribution per TS

Maximum data Throughput vs cell position

010203040506070

0.000.200.400.60

Cell Position

Max

imum

Dat

a Th

roug

hput

MCS-1MCS-2MCS-3MCS-4MCS-5MCS-6MCS-7MCS-8MCS-9LA

Link Adaptation sets thresholds between 2 different MCS

Depending on the MCS distribution over the cell, the Link Adaptation function sets MCS to be used at each position on the cell.Actual real throughput varies with the number of aggregated TS (additional configured DS0) per MS. This computation is to be seen in coming slides.

35


EDGE Dimensioning Detailed Method Example of a Rural MCS Usage Distribution

MCS7, MCS6 and MCS5 8-PSK modulation are mainly used

GMSK modulation is used atcell edge in DL (high BLER so low MCS)

Distance (km)

Throughput / TS

(kbps)MCS usage

(%)0.00 40.3 MCS-70.24 40.30.48 40.30.73 40.30.97 40.31.21 39.31.45 37.81.69 36.21.93 33.72.18 30.72.42 28.1 MCS-62.66 27.22.90 25.63.14 23.93.38 21.23.63 18.7 MCS-53.87 17.34.11 15.44.35 13.54.59 9.3 MCS-24.84 8.8


Rural 1900 MHz % UsersMCS-1 0.0MCS-2 14.4MCS-3 0.0MCS-4 0.0MCS-5 33.0MCS-6 30.0MCS-7 22.6MCS-8 0.0MCS-9 0.0

Mean Throughput/TS (kbps): 22.3Minimum Data Throughput/TS (kbps): 8.8

In this example of a rural site, MCS-2 must be used at cell edge. This is due to the size of the cell, 4.84 km. The data throughput per TS is 8.8 kbps at this cell edge, and mean data throughput per TS is 22.3 kbps.Note that both 8-PSK and GMSK modulations are used, the latter being used only at cell edge.

36


EDGE Dimensioning Detailed Method Second Step: Dimensioning of DS0 Joker on Abis

> Main TS: 16k TS used for voice, data circuit and GPRS dedicated to one radio TS

> Joker TS: each TDMA is associated to a set of 64k TS (DS0) on Abis• each 64k TS is divided into 16k TS, dedicated to EDGE• dynamically shared on a TDMA basis

radio frameAbis

main

joker

joker

Main & Joker TS Definition

Each joker frame indicates its associated main TS

Every radio TS (voice or GPRS) is mapped statically on one 16 k bearer (1/4 of DS0) on the Abis interface. Since V15.0, new EDGE coding schemes are managed up to MCS9 (59.2 kbps). So the current Abis (and Agprs) interface, based on 16 kbps TS, has to be enhanced in order to manage this new throughput. Nortel has implemented a dynamic solution based on "main+joker TS", which allow the operator to define:

• A classical set of 16 kbps Abis TS (called Main TS) used in order to manage circuit switch calls and part of the packet data bandwidth

• A number of Abis TS used for EDGE only by all radio TS of one TRX, called Joker TS. The 64k granularity for joker TS is due to the 64k switching matrix of the BTS

Each radio frame is managed on Abis by:• One main TS• n joker TS, dynamically shared• Each frame on a joker TS indicates its associated main TS at each occurrence

37


EDGE Dimensioning Detailed Method Second Step: Dimensioning of DS0 Joker on Abis

8.8

11.2

14.8

17.6

22.4

29.6

44.8

54.4

59.2

0.0 16.0 32.0 48.0 64.0 80.0

Required Bandwidth (kbps)

MCS1

MCS3

MCS5

MCS7

MCS9

EDGE Data To Backhaul Requirements

PayloadControl fieldAdditional CRCSTART & STOP patternRLC/MAC Hdr + FBI/EUnused Required Bandwidth (kbps)

MAIN Joker1 Joker4Joker3Joker2

The total number of required Joker TS (1/4 of DS0) can be computed from the MCS distribution provided by the radio analysis

4 Joker TS at 16 kbps

= 1 Joker DS0 at 64 kbps

Joker TS are dynamically shared on a TDMA basis. Every 20 ms, the allocator will adjust the bandwidth on Abis to the MS requirements. A number of joker DS0 (between 0 to 8) must be provisioned for every EDGE TDMA. This number of DS0 joker can be computed from the MCS distribution provided by the radio analysis.

The following formulas provide the statistical number of joker required as a function of the EDGE number of TS and the number of joker required per TS• 16k Joker TS dimensioning: Nb_of_Joker_per_EDGE_TS*Nb_of_EDGE_TS• 64k Joker DS0: round_up(Nb_of_16k_Joker/4)

Following table provides the number of additional 16k DS0 for one radio TS depending on the MCS selected:

38


EDGE Dimensioning Detailed Method Second Step: Dimensioning of DS0 Joker on AbisExample

> Example for a TDMA with 4 PDTCH and following assumptions about radio environment: DL, cell radius = 580m, 1800/1900 MHz with IR, TU3

> 16k joker TS dimensioning:Nb_of_Joker_per_EDGE_TS*Nb_of_EDGE_TS

> 64K joker DS0: round_up(Nb_of_16k_Joker/4)MCS % Users Joker 1/4 DS0

Requirement MCS1 0.0 0MCS2 0.0 0MCS3 0.0 1MCS4 0.0 1MCS5 0.0 1MCS6 4.9 2MCS7 49.5 3MCS8 27.5 4MCS9 18.1 4

Mean 16k Joker perEDGE TS 3.407

% of users per MCS is provided by radio analysis (first step)

• Number of 16k Joker TS = 3.407 x 4 = 13.6 Joker TS

• Number of 64k Joker DS0 = 13.6 / 4 = 3.4Round_up (3.4) = 4 Joker DS0

A TDMA with 4 PDTCH would therefore require 4 DS0 Joker configured on the Abis interface in order to fully benefit from the available radio throughput

These 2 formulas provide the statistical number of 64k joker DS0 required on Abisas a function of the EDGE number of TS (PDTCH) and the number of 16k joker per EDGE TS.In the above example, if a 4+1 MS close to the site requires MCS-9 on all PDTCH, the allocator will allocate 4 TS with MCS-9.If only 3 DS0 are configured instead of 4, the 4+1 MS will only use 3 TS with MCS-9 and 1 TS with MCS-2 (corresponding to a normal GPRS TS). The average TS throughput is therefore decreased.

39



Third Step: Abis Interface Dimensioning

> Radio Site Mask for BTS configured with EDGE must be updatedto take into account additional Joker DS0:

Abis TS = 2 x TRX + DS0 Jokers + LAPD TS

> PDTCH and Jokers TS for EDGE must be declared for all the different concerned TDMA and for all the cells of a site

Additional PCM may be required

The introduction of joker TS induces some impacts on the PCM dimensioning:• without joker TS, one TDMA uses on Abis 2 DS0. The maximum number of TDMA per PCM is therefore:

o E1 PCM (30 DS0): 15 TDMA

o T1 PCM (23 DS0): 11 TDMA

• with 4 joker TS, one TDMA uses on Abis 2+4 = 6 DS0, which are all configured on one PCM, so the maximum number of TDMA per PCM is:

o E1 PCM (30 DS0): 5 TDMA, which use 5*6=30 DS0, so no DS0 remains available

o T1 PCM (23 DS0): 3 TDMA, which use 3*6=18 DS0, so 5 DS0 can beallocated to small TDMA (for example 2 TDMA without joker)

• As the maximum number of PCM per site is 6, joker TS induce some limitationin terms of number of TDMA per site. Moreover, it would not be possible to declare a full EDGE capacity for all the TDMA of the site

40



Third Step: Abis Interface Dimensioning - Example

> Hypothesis: 1 tri-sectorial BTS, single band, 3 TRX per sector, 4 PDTCH and 2 EDGE TDMA per sector, 1 E1 Abis PCM, up to MCS9, 3DS0 Jocker/TDMA.

• Before EDGE activation3 TRX, 3 cells 3 x 3 = 9 TRX for the whole BTS1 TRX = 2 TS on Abis 9 x 2 = 18 TS on Abis for traffic9 TRX > 8 TRX therefore 1 Primary (RDV TS) and 2 secondary LAPD

18 TS for traffic + 2 TS for signaling

• After EDGE activation4 PDTCH TS per cell and 3 joker DS0 per EDGE TDMA3 TRX, 3 cells 3 x 3 = 9 TRX for the whole BTS1 TRX = 2 TS on Abis 9 x 2 = 18 TS on Abis for traffic3 joker DS0 per EDGE TDMA & 2 EDGE TDMA/sect 2 x 3 x 3 = 18 Joker DS0 on Abis9 TRX > 8 TRX therefore 1 Primary (RDV TS) and 2 secondary LAPD

18 TS for traffic + 2 TS for signaling + 18 TS (DS0)

41



Third Step: Abis PCM dimensioning

LAPDdimensioningEngineering Rule

Total 64 kbps TS on Abis land lines

Nbr of LAPDfrom TRX+ BCF

Nbr of JokerTS for EDGE

Nbr of LAPD TS

E1 PCM

•• 31

Number of E1 PCM = upper integer value

T1 PCM

••

24

+

Nbr of ABISTraffic TS

Number of T1 PCM = upper integer value

With EDGE activated on a network, additional DS0 TS required on Abis must be taken into account on the PCM computation.

Note that EDGE is only available with BSC3000. As BSC3000 can support a high number of LAPD channels, there is no more need to concentrate them (to be seen on coming section).

42



Fourth Step: BTS Hardware Provisioning

8E-cell10BTS 18000

8CBCF CMCF phase II6CBCF CMCF phase I6BCF new GTW PROM2BCF old GTW PROM

2S2000 H/L2CSW DCU4

Max number of DS0 per TRXType of site

GPRS + EDGEeCellGPRS + EDGEeDRX + (H)ePA

GPRSeDRX + legacy PAGPRSDRX-ND3GPRSDRXGPRSDCU4NoneDCU2

Optimum data capabilityTRX

BTS Hardware constraints table TRX capability table

Both chains of the site must have the same level of hardwareBoth eDRX & (H)ePA are required to support EDGE

Each type of site (BCF, CBCF, CSWM…) is able to connect a given number of DS0 to one TRX.As an example, the BSC can configure one TDMA with 6 DS0 only if the site is:• a BCF equipped with new GTW PROM (old GTW PROM does not support any Edge TDMA configuration)• a CBCF equipped with CMCF phase I• a CBCF equipped with CMCF phase II• a CBCF equipped with 2 CMCF phase I and II• an e-cell.In other cases, the TDMA is not configured.The BTS 18000 is able to configure 1 TDMA with 10 DS0 (2 DS0 main + 8 DS0jocker).One mandatory rule is to have in the BTS the same level of site hardware (BCF, CSWM…) for both chains.If this rule is not verified, the board having the most constraining limitation will provide the EDGE capability of the site (CMCF Ph 1 + CMCF Ph 2 : 6 DS0 instead of 8)In V15, the BTS H/W configuration can be audited by the operator through new EDGE Data Display commands available at OMC-R.

43


BSC Location in relation to BTS Sites

The BSC is the center of gravity of BTS sites

BTS

BTS

BTS

BTS

BTSBTS

BTS

The BSC has a strong concentrationeffect when Abis links are underused

TCU

BSCMSC

The BTS must be connected to the MSC.One way to make the connection is to connect each BTS to the MSC with a separate point to point link. This is generally not acceptable due to prohibitive costs. Another way to make the BTS to MSC connection is to use a BSC as a remote concentrator to facilitate the sharing of a high capacity line among several terminals.Furthermore Abis links represent a substantial part of the operational costs of a PLMN knowing that a lot of BTS are used in a network and that each BTS site requires a relatively small number of circuits and PCM redundancy can be used for a better quality of service.The BSC3000 can switch up to 4056 DS0 on Abis/Agprs/Ater interfaces. This switching capacity (provided by the SRT8K module in the BSC3000 Interface Node) becomes a significant limiting factor with EDGE penetration.

44


BTS Connections

Example of BTS Connections

Airinterface

Abisinterface

Starconnection

Chainconnection

Loopconnection

(single multi-drop)

MS

(full multi-drop)

Hub & Spokeconnection

The chained or looped BTS configurations (Drop and Insert) optimize the use of E1 and T1 PCM time slot (TS) resources.The 64 kbps time slots for speech and signaling do not fill the 2.048 Mbps E1 PCM or 1.544 Mbps T1 PCM links.Links may be under-used in a star configuration.BTSs are chained to fill the links.Chained or looped configurations allow the use of remaining time slots for otherBTSs, thus reducing the number of E1 or T1 PCM links.

45


Terrestrial Link Optimization by Drop and Insert

The system sees:

The system sees:

The chain configuration The loop configuration

BSC BTS BTS BTS

BTS

BTS

BTSBSC

BSC

BSC

BTS BTS BTS

BTS

BTS

BTS

When BTSs are chained together, they must not exceed ten. But NORTEL guarantees a good functioning of the chain with up to 6 BTSs. The failure of any component involved in transmission may affect security.For a chained connection, the availability of one BTS depends not only on those above it but also on the links between those above BTSs.So the chain is closed and the farthest BTS of the BSC is directly connected to the BSC. That is the loop configuration.In the looped configuration, PCM redundancy is N+1.The parameter bscSitePcmList (btsSiteManager logical object) provides the list of connections [bscPortNumber ~ btsPortNumber], between a BTS and its managing BSC. This can explain why the BSC does not see the intermediate BTS in a chain or in a loop.

46


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Dimensioning Look-up Tables forStandard Traffic Model at28% Erlang signaling

These tables are a summary of the detailed method results of the previous chapter, using a traffic model with 28% dedicated signaling and with

• A blocking rate on traffic (TCH) equals to 2%

• A blocking rate on signaling (SDCCH) equals to 0.1%

47


Dimensioning Look-up TablesOffered traffic (Erlangs) & Abis interface:omnisectorial sites

22342631196.65106.40O 16

22322631116.5898.65O 15

21302631036.4990.88O 14

2128253966.4784.10O 13

2126252896.4477.34O 12

1124252816.3369.65O 11

1122242746.2962.94O 10

1120242666.1555.33O 9

1117142585.9747.76O 8

1115132515.8841.19O 7

1113131445.7834.68O 6

1111131365.4727.34O 5

119121295.2621.04O 4

117121214.6814.04O 3

115111144.108.20O 2

113101*72.942.94O 1

T1 PCME1 PCMTotal PCMTime slots

Number ofLAPD TSSDCCH/8CCCHTCH/FE/TRXErlangsConfig.

PCM E1 (31 TS) / PCM T1 (24 TS) Blocking factor for traffic = 2.0% 8 TRXs/LAPD* Combined BCCH

These tables are a summary of the detailed method results of the previous chapter, using a traffic model with 28% dedicated signaling.

48


Dimensioning Look-up Tables

Carried Erlangs according to HR allocation penetration

218190171155143133124118111107103118O 16

2021761581441331231141081039995110O 15

189163148134124115106101969289103O 14

173150136124113105979287848195O 13

15913812511310496908580787588O 12

1441251121029487807772706780O 11

130113102928478736965636173O 10

1149990817469646057555365O 9

1038981736662575451494759O 8

887669625652484543414051O 7

756558524744403836343344O 6

605146413835323028272636O 5

463936322927252322212029O 4

322724222018171615141421O 3

19.516.314.312.811.610.79.79.08.58.27.914O 2

6.45.04.33.73.22.92.72.52.32.22.26O 1

100%90%80%70%60%50%40%30%20%10%0%Number ofTCH/FConfig.

The above table presents some simulation results, linked to HR and FR allocation inter-working. Inputs of these simulations are:

• HR allocation duration: Erlang B law, average = 25 seconds

• FR allocation duration: Erlang B law, average = 35 seconds

Reminder: without HR channel, the normal allocation duration is around 40 seconds, but due to HR ⇔ FR handover, this duration is reduced.During this simulations, the number of SDCCH TS is kept constant for each configuration whatever the HR percentage.

This table shows carried traffic and not offered traffic, the number of traffic TS is different from previous table, for these reasons Erlang numbers should not be compared.

49


Dimensioning Look-up Tables

Carried Erlangs according to HR allocation penetration

0

50

100

150

200

250

0% 10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

% of HR allocation

Erla

ng

O1

O4

O8

O12

O16

50


Dimensioning Look-up TablesOffered traffic (Erlangs) & Abis interface: bisectorial sites

PCM E1 (31 TS) / PCM T1 (24 TS) Blocking factor for traffic = 2.0% 8TRXs/LAPD* Combined BCCH

336842x62x32x1196.652x106.40S 1616

336442x62x32x1116.582x98.65S 1515

326042x62x32x1036.492x90.88S 1414

325642x52x32x966.472x84.10S 1313

325132x52x22x896.442x77.34S 1212

224732x52x22x816.332x69.65S 1111

224332x42x22x746.292x62.94S 1010

223932x42x22x666.152x55.33S 99

223422x42x22x585.972x47.76S 88

213022x32x22x515.882x41.19S 77

212622x32x12x445.782x34.68S 66

112222x32x12x365.472x27.34S 55

111712x22x12x295.262x21.04S 44

111312x22x12x214.682x14.04S 33

11912x12x12x144.102x8.20S 22

11512x02x1*2x72.942x2.94S 11



51


Dimensioning Look-up TablesOffered traffic (Erlangs) & Abis interface: trisectorial sites

PCM E1 (31 TS) / PCM T1 (24 TS) Blocking factor for traffic = 2.0% 8 TRXs/LAPD* Combined BCCH

5410263x63x33x1196.653x106.40S 161616

449663x63x33x1116.583x98.65S 151515

439063x63x33x1036.493x90.88S 141414

438353x53x33x966.473x84.10S 131313

437753x53x23x896.443x77.34S 121212

337153x53x23x816.333x69.65S 111111

336443x43x23x746.293x62.94S 101010

325843x43x23x666.153x55.33S 999

325133x43x23x585.973x47.76S 888

224533x33x23x515.883x41.19S 777

223933x33x13x445.783x34.68S 666

223333x33x13x365.473x27.34S 555

2126-272-33x23x13x295.263x21.04S 444

1120-212-33x23x13x214.683x14.04S 333

111313x13x13x144.103x8.20S 222

11713x03x1*3x72.943x2.94S 111



These tables give immediately the number of TRX and PCM time slots on Abisinterface.Case of omni-directional sites (one cell) or multi-sectorial sites (several cells):

• Starting with total offered traffic in Erlangs as input data in the table, on the same line are given: Number of TRX, number of LAPD TS, total number of PCM time slots, number of PCM boards.

NoteLAPD for multi-sectorial sites:

• One or several LAPD time slots are dedicated per sector, instead of grouping the LAPD time slots on the site.• Exception for low or medium traffic multi-sectorial sites: signaling is grouped as indicated in tables, to save LAPD time slots.

Note• Check that TRX number is in compliance with:

Total number of radio channels (TCH + CCCH + SDCCH/8) ≤ (number of TRX) x 8

• Check BTS load constraint (BCF dimensioning rules)

Note• Sxyz (x ≠ y ≠ z)

• For dimensioning, consider Sxyz as three omni-directional sites: Ox, Oy, Oz.

52


Summary of the BTS Dimensioning

SDCCH offered Traffic

SDCCH resources

Br = 0.1%

/ 8

Number of Abis traffic TS+ Input

Output

Site Layout Number of LAPD TSEng’g rule

Estimated number of subscribers in

the cell

Br = 2%

TCH offered Traffic

Number of DSC

Number of (C)PCMI

/ 31 (or 24)

Number of PCM on Abis

At least1 TS for CCCH

SDCCH TS

subs. activity(25 mE)

x28%

x

Estimated half rate penetration (p/100)x

TCH HR

xEstimated full rate penetration (100-p)/100

TCH TS+

TCH FR

/2

Estimated PS data traffic in the cell

PDTCH

/8

X2

Number of TRX

+

X2

TRX from other cellsof the same BTS

/2Number of DS0 TS

53


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Review Exercises

54


Review ExercisesExercice 1

1. Assumptions: S12000 Indoor product range- Traffic per subscriber = 25 mE- Blocking rate on traffic = 2%- Blocking rate on Signaling = 0.1%

2. Find out number:- n of TRX- CPCMI boards

3. Find out the capacity increase in term of Erlang with 100% HR allocations (same numberof TRX as in 2.). Do not forget to correctly dimension the resources needed for SDCCH.

Note:- Use Detailed method- Use Look-up tables

BTS

S12000

Indoor

On2500 Subscribers

OMNISECTORIAL BTS

1. Dimensioning Detailed Method

2. Summary Table

3. Summary Table for 100% HR calls:

TRX TCH BCCH SDCCH/8 LAPD PCM TS E1 T1 PCMI

TRX TCH BCCH SDCCH/8 LAPD Erlangs

55



1. Assumptions: S12000 product range- Traffic per subscriber = 25 mE- Full rate mobiles (no AMR or HR)- Blocking rate on traffic = 2%- Blocking rate on signaling = 0.1%

2. Find out number (using look-up tables) :- TRX per cell- CPCMI boards

3. Find out the new configuration of the BTS with 50% of subscribers using HR channels

S12000

1350Subscribers

1900Subscribers

2500Subscribers

Trisectorial BTS

Summary table by using look-up tables

TRX TCH BCCH SDCCH/8 LAPD PCM TS E1 T1 PCMI

56



1. Assumptions: BTS18000 product range- Replaces both BTS S12000 Ind and Out computed

previously- Total subscribers: 2500+ (1350+1900+2500)

shared equally in each cell of BTS 18000- Traffic per subscriber = 25 mE- Full rate mobiles (no AMR or HR)- Blocking rate on traffic = 2%- Blocking rate on signaling = 0.1%

2. Find out number (using look-up tables) :- TRX per cell- IFM and ICM boards


BTS18000

nSubscribers

nSubscribers

nSubscribers

Trisectorial BTS

Summary table by using look-up tables

TRX TCH BCCH SDCCH/8 LAPD PCM TS E1 T1 IFM ICM

1


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Section 4

BSC/TCU 12000 Dimensioning

Restriction: AMR (Adaptive Multi Rate) is not compatible with BSC 12000.

2


Objectives

> Upon completion of this section, the student will be able to :

• Calculate the number of BSC 12000 necessary to manage the BTSs

• For each BSC 12000, calculate:• Number of SICD8V boards• Number of BSCB boards• Number of DDTI boards• Number of CCS7 boards

The dimensioning method is developed:Starting from the sites featuresDealing with the hardware and software limits of BSC boardsTaking into account signaling capacity on LAPD and CCS7 links

Dimensioning rules are carried out and their use is explained.

RemarksIn the BSC dimensioning, we have to consider 2 types of signaling: LAPD (Abis + Ater + Agprs) and CCS7 (Ater)BSC 12000 type depends only on the number of: - SICD8V

- BSCBand on the offered traffic from the BTS.

3


Contents

> Overall Information

> SICD8V Computation

> DDTI Computation

> TCU Capacity

> Final Step

4

Student notes

5


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Overall Information

6


MMU-IDE

ECI B

To/From OMC-R

O&M/A bus O&M/B bus

Chain A Chain B

To/From TCU/MSCTo/From BTS

CONTROL

EQUIPMENT

External Loops

CPU-MPU SUP2

SICD8VSICX

CPU-BIFP

CCS7

CPU-BIFP

CPU-MPU

SICD8V SICXCCS7

RCB

CPU-OMU- IDE

TSCB DDTIALA BSCB

ECI A

SLS2

RCB

SCSI busIDE bus

SLS2 MMU-IDE

CPU-OMU- IDE

SCSI busIDE bus

SUP2

ConstantType dependant To be dimensioned

Kit HC100

BSC 12000 Architecture

The elements to dimension are:• CCS7 boards for CCS7 signaling

• SICD8V boards for LAPD signaling

• DDTI boards for PCMs

• BSCB boards for LAPD concentration

HC100 Kit (hardware) =• new MMU-IDE

• new OMU-IDE

• new interface IDE (before: interface SCSI)

• new SLS2

• new SUP2

RemarkThe kit increases the resistance to overload but does not increase itself the capacity of the BSC. In order to increase the BSC capacity, especially for tough traffic model (like “short calls” or “high mobility”) a software patch is necessary, available from V11.03. This patch can not be implemented without the HC100 kit.

7


MSC

- CCS7 TS (2, 4 or 6) - LAPD TS (One or more on Abis; one on Ater and Agprs)

AAter

4

1

BTS

BTS

1

Abis

16

16

1

1

BSC 12000

SICD8V

TCUup to

12 Or 14

BTS dimensioning BSC dimensioning

TSCB

BSCB

CCS7

CCS7DDTI

TCU#1

Agprs PCU

1

Dimensioning Elements

Dimensioning BSC 12000 consists in determining its hardware and software configurations:

• Taking into account as specifications: data supplied by the sites and BTS organization

• Using dedicated BSC rules and limits

The elements to define are:• Number of CCS7 boards

• Number of SICD8V boards

• Number of BSCB boards (if needed)

• Number of DDTI boards

• Number of A PCM links

• Number of Agprs PCM links

• Number of Ater PCM links

• Number of TCUs

8


Dimensioning ElementsGPRS impact

MSC - Mobile Switching CentreVLR - Visitor Location RegisterHLR - Home Location RegisterBSS - Base Station SubsystemEIR - Equipment Identity Register

PCUSN - Packet Control Unit Support NodePSPDN - Packet Switched Public Data NetworkSGSN - Serving GPRS Support NodeGGSN - Gateway GPRS Support Node

BSC

PSPDN

HLR

MSC

AMAP-D

VLRPSTN/ISDN

SGSN GGSN

Ater

BTS

PCUSN

SMSC EIR

TCU

Agprs

Abis

12 PCMMAX

GPRS entails no BSC capacity decrease in terms of processing. In other words, the processing power of boards is not a limiting factor for GPRS dimensioning. Only the PCM connectivity (Abis + Ater + Agprs) and the circuit switching capacity of the BSC have to be taken into account for GSM and GPRS network engineering.Note that BSC/TCU 12000 are not compliant with V15. Therefore, EDGE cannot be implemented on BSS networks based on such equipments.

9


Maximum limitation

Control cabinet: Boards list (per chain)

MPU/BIFP boards *1SICD8V boardsCCS7 boardsOMU boardsSICX boardsSUP boardsMMU boardSLS board

Equipment cabinet: Boards list

ECI boardsSWC boardsSWE boardsMSW boardsRCB boardsDDTI boardsTSCB boardsBSCB boards *2ALA board

2x12x1

2x1/2x22x1/2x2

2x110 to 24

20/41

2x12x1

2x1/2x22x1/2x2

2x210 to 24

20/61

2x12x1

2x1/2x22x1/2x2

2x310 to 24

20/91

2x12x12x22x22x4

10 to 242121

2x12x12x22x22x5

10 to 242

121

BSC type (Erlangs) Type 1 (250) Type 2 (500) Type 3 (750) Type 4 (1000) Type 5 (1200)

21111111

22211111

33211111

34211111

35311111

BSC type (Erlangs) Type 1 (250) Type 2 (500) Type 3 (750) Type 4 (1000) Type 5 (1200)

BSC 12000 Product Range

This table gives the board configuration for each available BSC type:• CCS7 boards: one board can process 2 CCS7 links

• SICD8V boards: one board can process up to 64 TRXs

• TSCB/BSCB boards: one board can process 15 I/O

• DDTI boards: to interface Abis PCM links and Ater PCM links; each board handles 2 PCM links

*1 Always 1 MPU board + 1 or 2 BIFP board(s) according to the BSC type.*2 The figures are given (in both cases) considering that one board is needed for redundancy purpose.

10


BSC Load, Software and Hardware Limits

type 1 type 2 type 3 type 4 type 5

Sites per BSC *1 Hard 27 59 91 123 137TRXs per BSC Soft 64 128 192 256 320TCUs per BSC with E1 Soft 12 12 12 12 12TCUs per BSC with T1 Soft 14 14 14 14 14E1 Ater Terrestrial Circuits Soft 1440 1440 1440 1440 1440T1 Ater Terrestrial Circuits Soft 1288 1288 1288 1288 1288TCU per BSC with E1 or T1 soft 1 1 1 1 1E1 or T1 Agprs PCM links soft 12 12 12 12 12E1 Agprs Terrestrial Circuits Soft 1440 1440 1440 1440 1440T1 Agprs Terrestrial Circuits Soft 1104 1104 1104 1104 1104Total PCMs Hard 48 48 48 48 48Cells per BSC Hard 64 120 160 160 160Erlangs Soft 250 500 750 1000 1200

BSC 12000Limits

This table summarizes the limitation rules used to determine the different components of a BSC and then to choose its type.The main limitation rules for BSC 12000 dimensioning are:

• Rule 1: No more than 64 TRXs per SICD8V.

• Rule 2: One SICD8V manages up to 8 LAPD ports (concentrated or not).

• Rule 3: No more than 8 TRXs per LAPD TS delivered by the BTS (BCF limitation).

• Rule 4: CCS7 links per BSC 12000:

— 2 for BSC type 1

— 4 for BSC type 2, 3, 4

— 6 for BSC type 5

• One CCS7 board handles 2 CCS7 links on A interface. Around one CCS7 link per 200 Erlangs of traffic TCH. Two links must be provided at least (load sharing pair).

• Rule 5: One DDTI board handles 2 PCM links on Abis, Ater and Agprs interfaces.

• Rule 6: No more than 15 TEI per SICD8V port (with BSCB boards).

Reminder on TCU: The maximum number of TCU in the table includes one redundant TCU.*1 The maximum number of sites per BSC corresponds to the maximum number of LAPD TS that a BSC can receive on Abis interface. Consequently, this maximum value is obtained for the maximum number of BSCB boards (with 1 redundant) and if each site delivers a single TS (Smallest configuration). Two LAPD ports are reserved : one for TCUs and one for PCU.

11


BSC Dimensioning Method

Siteaddition

Σ

LAPD Nb (Abis)

BSCType(s)

CCS7 Nb

DDTI Nb

BSC limits

LAPD Nb (Ater)

1

n

Siteelements

BTS BSC

SICD8VComputationWith BSCB

boards

DDTIComputation

max offeredtraffic

BSCChoice

BSC blocking rate

SICD8V Nb

1

TCUNumber

TRX Nb

BSCB Nb

TRX Nb

max offeredtraffic

TSCB

LAPD Nb (Agprs)

PCMAterDim.

PCM Nb (Abis)

PCM Nb(Ater)

PCM Nb (Agprs)**

BSCnumber

The whole BSC provisioning process is made up of the steps described hereafter.1. Site computation

The goal of this step is to determine the number of BSC. It is an iterative process done until we have grouped the sites per BSC.Results have been obtained previously for each site (BTS dimensioning). The computation now, consists in finding out for all sites:

• Offered traffic: adding Erlangs of each site

• Cell number: adding number of cells of each site

• TRX number: adding number of TRX of each site

• LAPD TS number on Abis and Agprs interfaces

• Number of PCM links on Abis and Agprs interfaces; for BTS connection to BSC, the different possibilities must be taken into account according to PCM link save (and cost save) star connection, chain connection (single multi-drop), or loop connection (full multi-drop).

The values obtained above are compared with those of the summary table.2. SICD8V computation

The number of SICD8V boards is obtained, using number of LAPD channel as a starting data, and then computation is done using rules 1, 2 and 6 on previous page.The output will be to determine the number of SICD8V boards taking into account their load limits. BSCB boards, when necessary allow to concentrate LAPD signaling up to the optimum load of the SICD8V boards in order to minimize their number.

12

3. DDTI computationThis step determines the number of DDTI boards according to the need of PCM links for traffic TS, CCS7 TS, LAPD TS and X.25 TS.

4. BSC choiceThis step is the final process and will determine the type of BSC to be used. All influent parameters are considered, without forgetting the CCS7 board(s).

13


Site Computation

BSC limitsAdding

forall sites

LAPD number(SICD8V & BSCB)Abis & Agprs number(DDTI)BSC traffic (CCS7)(~ offered traffic)

Number of cells

Number of TRX

Number of Abis

Number of LAPD

Max. Offered traffic

Site Computation

Number of sites

BTSdimensioning

BSC dimensioning

1 BSC enough?

BSC dimensioning

Yes

Sites Splitting

No

The influent parameters of each site are taken into account to allow other computations. The values of each site must be added, with respect to the limitations of the summary table.

1. Cell number (examples)• add 1 for each omni-directional site • add 3 for each tri-sectorial site

• add 2 for each bi-sectorial site • add n for each n-sectorial site

2. TRX numberThe number of TRX is the cumulative number for all the cells. This number was obtained previously for each cell by the BTS dimensioning.

3. PCM link number on Abis interfaceThis number of PCM links is maximal in case of star configuration (at least 1 PCM per BTS). The number of PCM necessary to connect each BTS to the BSC is determined during the BTS dimensioning. If we use drop and insert, 2 configurations are possible:

• Single “drop and insert”: only the number of PCM links of the first site is taken into account.

• Chained “drop and insert”: only the number of PCM links of the first site and of the last one are taken into account.

The drop and insert configuration is often determined during the BSC dimensioning.

14

4. LAPD numberThe number of LAPD channels on Abis interface is the cumulative number of LAPD TS obtained in the BTS dimensioning for all sites. LAPD TS on Ater from TCU are concentrated to one single LAPD portLAPD TS on Agprs are provisioned as one per PCM link.

5. Offered trafficMaximum traffic in Erlangs offered by all the sites to the BSC. We consider that this offered traffic is the maximum offered traffic that all the sites can manage together for the required QoS.

6. BSC limitsThe BSC limits to be taken into account (summary table) are:

• Maximum number of sites, cells and TRXs managed by a BSC

• Maximum number of boards of each type

• Maximum offered traffic

If the site computation results do not exceed the BSC limits, 1 BSC is sufficient (able to manage all the sites) and we just have to dimension it. In reverse case, site splitting must be performed and another BSC must be added. Finally, each BSC of the network must be dimensioned.

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SICD8V Computation

16


SICD8V ComputationLoad constraints on LAPD and SICD8V without BSCB boards

n1 + n2 + n3 + n4 + n5 + n6 + n7 + n8 < 64

SICD8VLAPD1

LAPD8

n 1

n 8

TRX BSCBTS

Multibus II

MUX

MUX

Software limit

8 TRXs max / BTS LAPD TS

DSC/CMCF

This diagram translates the rules concerning the number of TRX managed by the BSC through SICD8V board.

• One SICD8V board can manage 64 TRXs at most (software limitation).

• One SICD8V board has 8 LAPD ports.

• Remember: the BTS is able to concentrate the signaling for up to 8 TRXs onto one single LAPD TS.

Remarks• By convention, the TCU concentrated LAPD TS (delivered by the TSCB board)

is always processed by the SICD8V 0 port 3 (fourth port).

• If we do not use BSCB boards, the SICD8V software limit is virtual because we will never cross the 64 TRXs value (on each of the 8 ports, we have at most 8 TRXs: DSC limitation).

17


SICD8V ComputationBTS LAPD Concentration by BSCB boards

LAPD

LAPD

SICD8V

LAPD

LAPD

LAPD

LAPD

LAPD

LAPD

BSCBBSCB

TSCB

BSCB

BTS-LAPDConcentration

by BSCB:15 TEI max

Mul

tibus

II

DDTI

RCB

TSCB

External PCM

SwitchingMatrix

12

112

TCU-LAPDConcentration

Transcoding

NRZHDB3B8ZS

LAPD delivered by a BTS:at most 8 TRXs

8 TRXs max(w/o BSCB)15 TEI max (w BSCB)

up to14->1

x 4

This feature aims to concentrate LAPD links from different BTS sites on the same SICD8V port.It allows to manage up to 138 sites (with redundancy) or 147 sites (without redundancy) on a BSC 12000 type 5.This is performed thanks to signaling concentration from the BTS on a BTS Signaling Concentration Board BSCB. These additional BSCB boards are particularly useful for microcellular configurations where a lot of sites are necessary to use the total capacity of the BSC 12000. The usage of these boards is optional and the operator has the possibility to add them when required.

BSC levelWithout this feature, the number of sites managed by a BSC is limited by the number of SICD8V ports (39 is the maximum with 5 SICD8V boards).One BSCB has 15 ports which are configured in this way: 4 ports concentrated to 1, this being done three times.

ConfigurationThe BSC 12000 is equipped with 2 TSCB (1+1) and up to 12 BSCB (11+1). The two TSCB boards are reserved for the Ater interface. In the same cabinet, an extra shelf contains the supplementary BSCB boards (up to 12 BSCB) needed for the LAPD concentration on the Abis interface.

18

Engineering Rules: Max. number of sites according to the number of Abis / BSCB boards.Example: with redundancy of BSCB boards:

RedundancyA N+1 redundancy mechanism is provided in the BSC software meaning that the dimensioning must take into account that an additional board is needed for redundancy purposes.

13812Type 5

12312Type 4

919Type 3

596Type 2274Type 1

Max. number of sitesNumber of BSCBBSC 12000

19


SICD8V Computation

15 TEIs max / LAPD port

SICD8VLAPD1

LAPD8

BSCB :12 in, 3 out

ni TRX

n1 MUX

CMCF

Software Limit (TRX)

Σ ni < 64

Multibus II

TSCB :

14 in, 1 out

FromTCUs

FromBTSs

FromPCU

For BTS LAPDDirect connection is possible from BTS LAPD TS to LAPD port.Using BSCB boards, the limitation on each port of the SICD8V board is 8 TRXsand 15 TEI maximum.This TRX/TEI limitation regulates the concentration of the LAPD TS by the BSCB boards.Recommendation: If a BTS delivers several LAPD TS and if BSCB boards are used, the signaling carried by each LAPD TS shall be connected to different LAPD ports, otherwise the configuration could lead to serious operational problems. In other words, if BSCB boards are used in the BSC 12000, a BSCB board shall not concentrate together LAPD TS delivered by the same BTS.For TCU LAPD TSCB board is used to concentrate up to 14 TCU LAPD links.For PCU LAPD Direct connection is made from one PCU LAPD TS to one LAPD port.

20


SICD8V Computation

* verify that there exists a repartition of the LAPDs onto the SICD8V boards including the TCU LAPD, the PCUs LAPDs & verify the number of TEI per LAPD port

Software Rule:

Number of TRX / 64

Hardware Rule:

Number of LAPD links / 8(concentrated + non concentrated by BSCB)

N1

N2

Max* (N1, N2)N Number of

SICD8V boards

R1

R2

Overview

To define the number of SICD8V boards:• Use hardware rule: one SICD8V board for up to 8 LAPD links

• Check the load limit for SICD8V board: software rule related to TRX number

• Check that there is no SICD8V port with more than 8 TRXs (Rule 3).

Note: add one LAPD channel (and only one) to take into account TCU management:

• On Ater interface, one LAPD channel is necessary per TCU.

• Each BSC 12000 can manage:

—up to 12 TCU with E1 Ater PCM links

—up to 14 TCU with T1 Ater PCM links

• The LAPD channels on Ater interface are connected to only one LAPD channel incoming SICD8V board, through TSCB board and interface boards DDTI and RCB in BSC.

• The concentration of LAPD channels on Abis interface through BSCB allows the BSC 12000 to manage more sites (up to 138 instead of 39).

21

Example 1: 4 S888R1: (4 sites x 24 TRXs) / 64 = 2 SICD8VR2: (4 sites x 3 LAPD + 1 for TCU) / 8 = 2 SICD8VSoftware and hardware rules give the same results

Example 2: 10 S333R1: (10 x 3 x 3) / 64 = 2 SICD8VR2: (10 x 3 + 1) / 8 = 4 SICD8VWe take the result provided by the hardware rule.

Example 3: 10 S121212R1: (10 x 3 x 12) / 64 = 5.625 SICD8VR2: (10 x 5 + 1) / 8 = 6.37 SICD8VWhat is the conclusion?

22


SICD8V ComputationExercise

S332O2O2O2

O1O2O4O2

O2O2O2O2

S888

O8

O8

O4

S444

BSCB

SICD8V

ExerciseGive the errors that have been done on this configuration of a BSC 12000 type 1.Propose one possible solution using the minimum number of SICD8V and BSCB boards.

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DDTI Computation

24


DDTI Computation

Max. total CS traffic in the cells managed by the BSC

BSC blocking rate(0.1%)

Total number of traffic channels on Aterinterface

Total numberof traffic TS on Aterinterface

— 4 ••

Terrestrial CircuitComputation

• Agprs traffic TS

Max. total PS traffic in the cells managed by the BSC

Total numberof traffic TS on Agprsinterface

Terrestrial CircuitComputation — 4 •

•

Total number of traffic channels on Agprsinterface

• Ater traffic TS

Traffic on BSC = S traffic on the BTS.For a given BSC blocking rate, tables of Erlang B law give the number of resources on Ater (terrestrial circuits).For DATA PS traffic, the addition of all the TS coming from BTSs determine the number of necessary TS on Agprs.Dynamic Agprs increases the user throughput from 15% to 80% depending on the cells traffic unbalance and the user profile.Using Dynamic Agprs to reduce the number of Agprs PCM is possible (gain between 15% and 50%)Example for a BSC with planned traffic of 150 Erlangs and blocking rate of 0.1%:

• Tables give: 183 resources: 183/4 = 46; i.e. 46 traffic TS on Ater PCM links

To terrestrial circuits for traffic you must add:• CCS7 TS for signaling between BSC and MSC (Ater and A PCM links)

• LAPD TS on Ater for signaling between BSC and TCU (Ater PCM link)

• X.25 for O&M traffic transportation towards OMC-R at A interface

• LAPD TS on Agprs for signaling between BSC and PCU (Agprs PCM link)

Note0.1% is the recommended value for blocking rate at A interface for terrestrial circuit computation.

25


DDTI Computation

LAPD on Ater 1 LAPD TS on each Ater PCM

1 LAPD TS on each Agprs PCMLAPD on Agprs

There is one LAPD TS on each Ater PCM link (OML for TCU supervision and downloading).

There is one LAPD TS on each Agprs PCM link (OML for PCU supervision and downloading, RSL and GSL).

26


DDTI ComputationCCS7 Signaling link dimensioning on Ater interface

BSC 12000

2 links for BSC type 1

4 links for BSC type 2, 3, 4

6 links for BSC type 5

1 CCS7 board manages 2 CCS7 links (TS)

The various procedures running between NSS and BSS are using CCS7 signaling. One CCS7 link is conveyed through a PCM TS at 64 kbps.However, for redundancy purposes, CCS7 links must work by pair on a load sharing basis (if real redundancy is observed).A BSC 12000 needs up to 6 CCS7 links.In the dimensioning procedure, we deduce the number of CCS7 boards needed from the type of the determined BSC 12000, whereas the SICD8V boards number is involved in the BSC type determination.For BSC 12000, this is possible because the BSC type can be determine so far (without the number of DDTI board).We can also estimate the type of the BSC 12000 according to the offered traffic, the number of sites and cells, the number of TRXs and the number of SICD8V boards. And then check that this assumption was correct in terms of CCS7 management.Note: If the number of Ater links is less than the CCS7 TS number, the use of a second CCS7 redundant link on the same Ater link will not be considered as a full redundancy.Approximately: 1 CCS7 load sharing pair for 200 to 300 Erl offered traffic (depending on traffic model), if we use full redundancy. At this level of the BSC 12000 dimensioning, the BSC type is estimated from the offered traffic only.

27


DDTI ComputationX.25

X.25

1+1 Redundant TS per BSC on the Ater Interface

This connection for O&M traffic transportation towards OMC-R is optional

An X.25 link is used for O&M transportation towards the OMC-R at Ater and A interfaces, when a direct connection between the OMC-R and the BSCs is not possible (X.25 network).In this case, 2 TSs (1 + 1 redundant) shall be provisioned per BSC for X.25 signaling, and these 2 TSs shall be preferably carried by 2 different PCM links.

28


DDTI ComputationAter PCM Link computation

Take the uppermultiple of 30

numberof E1 PCM

on Ater(+ 1 if spare TCU)

E1 PCM

T1 PCM

One TS for TCU LAPD

Number of traffic

Time slots (64 kbps)

2TS for X.25optional

2 TS, 4 TS or 6 TS for CCS7signaling

+Totalnumber

of Ater time slots

Take the uppermultiple of 30 ÷ 30

One TS for TCU LAPD


numberof T1 PCM

on Ater(+ 1 if spare TCU)

Do not forget to add a supplementary Ater PCM link if you provision a spare TCU

Ater definition: one LAPD TS is sufficient and mandatory on each Ater PCM link for intra-signaling between BSC and TCU; then:

• For E1 PCM link: with TS0 dedicated to PCM link management and synchronization, then 30 TSs are available for traffic and CCS7 TSs (and X.25 if this option is used).

• For T1 PCM link: then 23 TSs are available for traffic and CCS7 TSs (and X.25 if this option is used).

Example (continued from previous pages) (150 Erlangs BSC):• Number of traffic TSs on Ater: 46

• Number of CCS7 TSs on Ater: 2 (1 + 1)

• Total number of TSs on Ater: 48

• For E1 PCM: 48/30 Þ 2 Ater PCM links

• For T1 PCM: 48/23 Þ 3 Ater PCM links

NoteThis dimensioning example does not take into account X.25 TSs for O&M traffic transportation towards OMC-R at A interface.

Do not forget to add a supplementary Ater PCM link if you provision a spare TCU.

29


DDTI ComputationAgprs PCM Link computation

Total number oftraffic channels

on Agprs interface— 4 •

•

Number of E1 PCM links

on Agprs

Total number of traffic Time Slots

on Agprs



Number of T1 PCM links

on Agprs

E1 PCM

T1 PCM

One TS for TCU LAPD

One TS for TCU LAPD

Number of GPRS information channels• Number of data channels on the PCUSN/BSC = 480 CICs.

Number of Agprs PCM links• 480 CICs need 120 DS0 on the Agprs interface, i.e. 4 E1 PCMs (or 6 T1) for

traffic handling.

• Let 5 E1 (or 7 T1) be the number of Agprs PCMs required (with LAPD additional DS0).

30


DDTI ComputationCheck

Software limits

Number of DDTI boards

OK if lower than 24

+

AbisPCM linksAterPCM links ÷ 2

AgprsPCM links

1.DDTI boards are the direct BSC 12000 interface to all BSC external PCM links: Abis and Ater PCM links must be added.2.Then according to the DDTI implementation, the number of DDTI boards is immediately obtained:

1 DDTI board for 2 PCM links.

3.• Check of the DDTI implementation in BSC 12000 (table of limits).• The maximum number of DDTI boards equals 24 for BSC 12000.

• Note: The DDTI computation results compliance with software limits is represented on the overview diagram by the OK signal.

• The number of DDTI boards is between 10 and 24 independently on the type of the BSC 12000 the number of DDTI boards needed does not decide for the BSC type, and it will finally never be lower than 10.

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TCU Capacity

32


TCU CapacityE1 PCM Links

TCUMSC (A interface)

BSC (Ater interface)

120 full rate traffic channels

16 kbps

1 TCU per Ater PCM link

1 TS = 1*(64 kbps “A Law” channel)

1 TS = 64 kbps

One TCU manages one PCM link on Ater interface, so the number of TCU equals the number of PCM links on Ater interface. One TCU is generally used for redundancy, so:

Number of TCU = number of PCM links on Ater interface

(include the spare TCU if a spare Ater PCM link was provisioned)

The TCU main function is reminded:• On Ater interface, a TS of the PCM link carries 4 encoded full rate speech/data

samples.

• On A interface, a TS of the PCM link carries only one of these samples.

Reminder• On each A interface E1 PCM link, 31 TSs are available at most (TS0 is

reserved for PCM link management and synchronization). If we add 1 LAPD TS per Ater PCM, the maximum capacity of each PCM on Ater interface (without CCS7 TS) is 30 TS. So 1 TCU can manage at most 30 x 4 = 120 full rate communications.

• One BSC 12000 can manage up to 12 TCU (redundancy included).

33


TCU CapacityT1 PCM Links

TCUMSC (A interface)

BSC (Ater interface)

92 full rate traffic channels

16 kbps

1 TCU per Ater PCM link

1 TS = 1 * (64 kbps “µ Law” channel)

1 TS = 64 kbps

One TCU manages one PCM link on Ater interface, so the number of TCU equals the number of PCM links on Ater interface. One TCU is generally used for redundancy, so:

Number of TCU = number of PCM links on Ater interface

(include the spare TCU if a spare Ater PCM link was provisioned)

The TCU main function is recalled:• On Ater interface, a TS of the PCM link carries 4 encoded full rate speech/data

samples.

• On A interface, a TS of the PCM link carries only one of these samples.

Reminder• On each A interface T1 PCM link, 24 TSs are available at most. If we add 1

LAPD TS per Ater PCM, the maximum capacity of each PCM on Ater interface (without CCS7 TS) is 23 TSs. So 1 TCU can manage at most 23 x 4 = 92 full rate communications.

• One BSC 12000 can manage up to 14 TCU (redundancy included).

34


TCU CapacityA interface PCM computation

(Full rate)Number of E1 PCM on Ater

Number of E1 PCMon A interface

x 4

Number of T1 PCM on Ater

Number of T1 PCM on A interface

x 4(Full rate)

The number of PCM links on A interface is directly obtained from the number of Ater PCM links.Each TS on A PCM link (64 kbps rate) carries one single speech or data communication channel (speech is sampled at 8 kHz and each sample is coded onto 8 bits) whereas on Ater interface, a communication channel has a rate of 16 kbps.

35


TCU CapacityAter and A interface E1 PCM capacity: look-up table

These values do not take into account X.25 TS and consider CCS7 TS are working by pair

Full rate traffic channels (BSC 12000)blocking rate = 0.1%

Traffic Load(in Erlangs)

E1 PCM Links(BSC-TCU)

E1 PCM Links(TCU-MSC)

8619530041452964476087698511011218

1234567891011

48121620242832364044

Full rate traffic channels; blocking rate = 0.1%This table summarizes the detailed calculations described on the two above diagrams.Other such tables can be established for other blocking rate values, in the same manner.Example 1 - 100 Erlangs BSC offered traffic; BSC blocking rate = 0.1%

• Result given directly by the table:

—2 E1 PCM links on Ater interface

—8 E1 PCM links on A interface

• Detailed calculation:

—from Erlang B tables: number of resources = 128

—for full rate traffic channels (division by 4): 128/4 = 32 traffic channels on Ater interface

—for a 100 Erlangs BSC: 2 CCS7 TSs only are necessary; therefore, adding two TSs gives 34 TS on Ater interface

—number of PCM links on Ater interface: 34/30 Þ 2 (as previously found)

—number of PCM links on A interface: 2 x 4 = 8 (as previously found)

Note: 1 LAPD TS is taken into account on Ater link (30 TS instead of 31) for management of each TCU.

36

Example 2 - Given a BSC with one E1 PCM link on Ater interface; BSC blocking rate = 0.1%

• Result given directly by the table: 86 Erlangs offered traffic.


— CCS7 TSs on Ater: 2 CCS7 TSs are necessary

— LAPD TSs on Ater: one TS is reserved on each Ater link for TCU management then: number of Ater TSs (one link): 31 - 1 (LAPD) = 30 TS

— number of traffic TSs: 30 - 2 (CCS7) = 28 TS

— number of terrestrial circuits: 28 x 4 = 112 TS

— from Erlang B tables: offered traffic » 86 Erlangs (as obtained previously)

37


TCU CapacityAter and A interface T1 PCM capacity: look-up table

These values do not take into account X.25 TS and consider CCS7 TS are working by pair

Full rate traffic channels (BSC 12000)blocking rate = 0.1%

Traffic Load(in Erlangs)

T1 PCM Links(BSC-TCU)

T1 PCM Links(TCU-MSC)

61144229308395483571659748837919100810981187

1234567891011121314

48121620242832364044485256

Full rate traffic channels; blocking rate = 0.1%This table summarizes the detailed calculations described on the two above diagrams.Other such tables can be established for other blocking rate values, in the same manner.Example 1 - 100 Erlangs BSC offered traffic; BSC blocking rate = 0.1%

• Result given directly by the table:

—2 T1 PCM links on Ater interface

—8 T1 PCM links on A interface


—from Erlang B tables: number of resources = 128

—for full rate traffic channels (division by 4): 128/4 = 32 traffic channels on Ater interface

—for a 100 Erlangs BSC: 2 CCS7 TSs only are necessary for redundancy purpose; therefore, adding 2 TSs gives 34 TS on Ater interface

—number of PCM links on Ater interface: 34/23 Þ 2 (as previously found)

—number of PCM links on A interface: 2 x 4 = 8 (as previously found)

Note: 1 LAPD TS is taken into account on Ater link (23 TS instead of 24) for management of each TCU.

38

Example 2 - Given a BSC with one T1 PCM link on Ater interface; BSC blocking rate = 0.1%

• Result given directly by the table: 61 Erlangs offered traffic


— CCS7 TSs on Ater: 2 CCS7 TSs are necessary

— LAPD TS on Ater: one TS is reserved on each Ater link for TCU management then:number of Ater TSs (one link): 24 - 1 (LAPD) = 23 TSs

— number of traffic TSs: 23 - 2 (CCS7) = 21 TSs

— number of terrestrial circuits: 21 x 4 = 84 TSs

— from Erlang B tables: offered traffic » 61 Erlangs (as obtained previously)

39


Final StepOverall diagram

OK

Number of BSCB (if used)

Number of SICD8V

Offered traffic BSC 12000TypeNumber of cells

Number of sites

Number of TRXs

Type 1

Type 2

Type 3

Type 4

Type 5

An overall diagram summarizes the main data involved in the definition of BSC type:

• Number of boards (SICD8V, TSCB, BSCB, CCS7, DDTI)

• Offered traffic

All site dependent elements of the BSC 12000 have been defined, according to:• The definition rules

• And the limits of the BSC load (software and hardware limit table)

When these site elements are in compliance with these rules and limits, the OK signal on the diagram is right.Confirmation of the BSC type choice is given by the BSC 12000 product range table.

40

Student notes

1


nortel.com/training

Section 5

BSC3000/TCU3000 Dimensioning

Remark: AMR (Adaptative Multi Rate) and EDGE are only supported by BSC3000/TCU3000.

2


Objectives

> Upon completion of this section, the student will be able to :

• provision a BSC3000 cabinet and a TCU3000 cabinet by defining the number of:• TMU modules in the Control Node of a BSC3000 cabinet• LSA-RC in the Interface Node of a BSC3000 cabinet• LSA-RC in one of both Transcoding Nodes of a TCU3000

cabinet• TRM modules in one of both Transcoding Nodes of a TCU3000

cabinet

3


Contents

> BSC3000 and TCU3000 Generic Architecture> BSC12000HC and BSC3000 Comparison> TCU12000 and TCU3000 Comparison> BSC3000 Provisioning> BSC3000 and TCU3000 Configurations> BSC3000 Provisioning Example> TCU3000 Provisioning Example> BSC3000 Dimensioning> BSC3000 and TCU3000 Configurations> Case Study: BSC12000/BSC3000 Replacement

4


TCU12000 (30 shelves)

BSC12000HC (6 cabinets )

BSC3000 vs BSC12000HC

BSC3000 and TCU3000 (2 cabinets)

600_120600_1201000_205Floor load (kg/m2_ lb/ft²)540/11881620/3564570/1254Weight (kg/lb)

W: 156/61 D: 60/23 H: 200/78

W: 468/183 D: 60/23 H: 200/78

W: 96/37 D: 60/23 H: 220/86Cabinet dimension (cm/in)

1.75.12.0Power consumption (kW)126037803200A circuits48/48144/144126/168E1/T1 links

61816SS7 links40120567LAPD links138414500BTS160480600Cells3209601000TRX

120036003000ErlangFor one BSC12000HCFor three BSC12000HC For one BSC3000Maximum values

BSC12000HC and BSC3000 Comparison

Flexibility: there will be no predefined and limited number of configurations as for the BSC 12000HC.A set of product configurations fitting closely the needs of a given customer, in terms of processing, signaling, PCM connectivity can be delivered, given that these configurations remain within the minimum and maximum product configurations.For example, if a 2000 Erlang BSC with the same PCM and signaling connectivity is delivered to two customers having networks with different traffic profiles, the number of TMUs in each BSC can be different, say 8 TMUs for one and 10 for the other. A BSC3000 of maximum capacity is ‘equivalent’ to three BSC 12000.

The BSC3000 can switch up to 2268 DS0 on Abis/Agprs/Ater interfaces. This switching capacity (provided by the SRT8K module in the BSC3000 Interface Node) might become a significant limiting factor with EDGE penetration if DS512 option is not used to increase the switching capacity.

5


600_120600_1201000_205Floor load (kg/m2_ lb/ft²)

283/6238490/18690570/1254Weight (kg/lb)

W: 78/30 D: 60/23 H: 200/78

W: 78/30 D: 60/23H: 200/78

W: 96/37 D: 60/23 H: 220/86

Cabinet dimension (cm/in)

1302.0Power consumption (kW)

120 for E1 links92 for T1 links

3600 for E1 links2760 for T1 links3200A-circuits for E1/T1 links

4+1120+3030+103 for E1 links38+132 for T1 linksAter + A for E1/T1 links

For one TCU 12000For thirty TCU 12000For one TCU3000Maximum values of

TCU 12000 (30 shelves)

BSC 12000HC (6 cabinets)

TCU3000 vs TCU 12000

BSC3000 and TCU3000 (2 cabinets)

TCU 12000 and TCU3000 Comparison

6


BSC3000 and TCU3000 Generic Architecture

OMUOAM

ATM SW

InterfaceNode (1)

TranscodingNode (1 or 2)

ControlNode (1) OMU

OAMMMS

ATM SW TMU

TrafficManagement

TMU

TrafficManagement

MMS

Private

TRM

CEMCEM

LSA RC

TRMLSA RCCEM

CEM

LSA RC

LSA RC

ATM RM

8K RM

8K RM

Shared

ATM RM

TRM

LSA RC

TMU

TrafficManagement

To be dimensioned

5 to 14Per BSC

2 to 10Per transc.node

2 to 6Per BSC1to 4 PerTransc.node

The BSC3000 is composed of the Control Node and the Interface Node. The TCU3000 is composed of the Transcoding Node.Control Node main functionalities are:

• Management of OAM for the C-Node, I-Node and T-Node

• Traffic management towards the BTSs and MSC

• BTS supervision, Transcoding Node supervision

• OMC-R link management

• Failure detection and processing

• HandOver procedures

• BSS configuration and software management

• BSS performance counter management

• ATM Management

Interface Node main functionalities are:• I-Node OAM management

• Switch management and Timeswitch control

• PCM interface

• ATM Management

Transcoding Node main functionalities are:• T-Node OAM management

• Switch management and call processing

• BSC Access

• Carrier Maintenance

7


ATM SW

OAM OMU

N + P + 2

1 + 1

1 + 1

TMU

TrafficManagement

300 E

Control andSwitchingChain BPassive

Control andSwitchingChain AActive

1 - BSC3000 versus BSC12000

BSC3000 Provisioning

The redundancy concept of the BSC3000/TCU3000 is different from the 2G BSC/TCU: the two redundant chains do not exist any more. But, there is a per module or per card (LSA) redundancy.Except for the TMU module for which an N+P redundancy is implemented, all the modules are 1+1 redundant. The entire Call Processing of the BSC3000 is based on the TMU module. The TMU dimensioning is based on the estimated traffic load (maximum 300 Erlang per TMU). The BSC3000 estimated traffic is calculated by taking into account the sum of each cell traffic (based on the number of TRX per cell). The BSC3000 estimates itself the number of TMU needed to reach the capacity required by the Site/Cells/TRX configured by the OMC. If the calculated number of TMUs is less than the installed TMUs, then the BSC notifies to OMC via Load Balancing Anomaly how many TMUs are needed in order to reach the required capacity.Due to the fact that there are no more fix configurations (like type1...5 in case of BSC 12000), the OMC-R only verifies the maximum dimensioning of the BSC3000.

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2 - Number of TMUs: N+P+2– N is the minimum number of TMUs needed for no loss of processing capacity.

– P is the minimum number of TMUs needed for redundancy.

– 2 is the number needed for SS7 processing

10+2+29+2+28+2+27+2+26+2+25+1+2TOTAL222222SS7: 2222221P1098765N

3000Erlang

2700Erlang

2400Erlang

2100Erlang

1800Erlang

1500Erlang

Capacity

Number of TMUs

BSC3000 Provisioning

In order to have a well balanced processing load between TMUs, two mechanisms have been implemented:

• The BSC3000 makes a site distribution per Cell Group using a special algorithm so that a number of equally charged Cell Groups can be obtained:

—a Cell Group is a logical entity containing several sites,

—all the Cells and the TRXs belonging to one site are in the same Cell Group.

• The Cell Groups are then distributed over the existing TMUs. A TMU is capable of managing up to 16 Cell Groups (8 active and 8 passive). The active Cell Groups from one TMU will have their passive instance on another TMU.

Concerning TMU redundancy, let us define the following: • N is the minimum number of TMUs needed for no loss of processing capacity

this is the minimum number of TMUs needed to run all the active processes (Fault Tolerance).

• P is the minimum number of TMUs needed for current redundancy

• 2 TMUs are needed for processing of SS7 signaling

Taking into account these considerations, the BSC3000 capacity can be defined.

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BSC3000 Provisioning3 - Abis LAPD channels

LAPD link Dimensioning:

• Up to 567 LAPD channels per BSC3000

• 62 LAPDs per TMU module (2 for TCU LAPDs)

• Engineering recommendation = 60 BTS LAPDs per TMU

• Dependence between the number of TMUs and LAPDs:

Total number of TMUsGSM Object 1 2 3 4 5 6 7 128 9 10 11

LAPD Channel (Abis) Not standard 120 180 240 300 300 360 420 480

13 14

540 567

LAPD link dimensioning:Up to 567 LAPD channels can be configured at the BSC3000 level.62 LAPD (Abis, Agprs, Ater) can be handled by each TMU module (2 are reserved for TCU LAPDs).The 60 LAPDs per TMU used for BTSs must be split between active and passive resources (passive resources being used for redundancy only). The dependence between the number of TMUs and LAPDs that can be handled by the BSC3000 is presented in the table.The BSC3000 engineering recommendation is 40 BTS LAPDs per TMU: this engineering margin will provide enough processing capacity on the TMU or the GPRS LAPDs.

10


BSC3000 Provisioning4 – Maximum number of TRXs

Total number of TMUsGSM Object 1 2 3 4 5 6 7 128 9 10 11

TRX for 0.1% blocking rate Not standard 360 540 720 900 900 1000 1000 1000

13 14

1000 1000

TRX for 2% blocking rate Not standard 200 300 500 600 700 800 900400 500 1000

LAPD link dimensioning:Up to 567 LAPD channels can be configured at the BSC3000 level.62 LAPD (Abis, Agprs, Ater) can be handled by each TMU module (2 are reserved for TCU LAPDs).The 60 LAPDs per TMU used for BTSs must be split between active and passive resources (passive resources being used for redundancy only). The dependence between the number of TMUs and LAPDs that can be handled by the BSC3000 is presented in the table.The BSC3000 engineering recommendation is 40 BTS LAPDs per TMU: this engineering margin will provide enough processing capacity on the TMU or the GPRS LAPDs.

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BSC3000 Provisioning5 - GPRS impact

MSC - Mobile Switching CentreVLR - Visitor Location RegisterHLR - Home Location RegisterBSS - Base Station SubsystemEIR - Equipment Identity Register

PCUSN - Packet Control Unit Support NodePSPDN - Packet Switched Public Data NetworkSGSN - Serving GPRS Support NodeGGSN - Gateway GPRS Support Node

BSC3000

PSPDN

HLR

MSC

AMAP-D

VLRPSTN/ISDN

SGSN GGSN

Ater

BTS

PCUSN

SMSC EIR

TCU3000

Agprs

Abis

24 PCMMAX

GPRS entails no BSC capacity decrease in terms of processing. In other words, the processing power of the TMU and of the other processing boards is not a limiting factor for GPRS dimensioning. Only the PCM connectivity (Abis + Ater + Agprs) and the circuit switching capacity of the BSC3000 have to be taken into account for GSM and GPRS network engineering.In urban areas, the BSC3000 has enough available PCMs so that the GPRS introduction can be done without any PCM dimensioning constraints.For example a maximum capacity BSC3000 managing a BSS network made mainly of S444 BTSs, will need around 90 E1 PCMs for Abis and Ater, out of 126. Therefore, whatever the GPRS profile is, there will be enough additional PCMs available for Agprs.In rural areas (BTS S111 & S222), all PCMs might be used for voice service only. The introduction of GPRS can then impact the BSC3000 capacity in terms of number of managed BTSs and TRXs.The maximum circuit switching capacity of the BSC3000 (2268 64-kbps circuits) shall be taken into account in the dimensioning of a voice + GPRS network.The switching capacity is not a limitation for voice-only and for low-speed GPRS and EDGE services (CS1/CS2 and MCS1/MCS2).

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For high-speed data services (GPRS CS3/CS4 and EDGE MCS3 to MCS9), since the radio time-slots carrying those services require more circuits on Abisand Agprs (2 to 5 times more than for voice and low-speed packet data), the BSC3000 switching capacity limit can be reached for some networkconfigurations, especially for high data penetration (for example 8 radio TS per cell for GPRS). From release V15 and further, the DS512 option can be used on the BSC3000. As explained in coming slides, this option enables the BSC3000 to switch much more TS, the switching capacity of BSC3000 being no more a limiting factor (even if EDGE is activated on the network).The impact on BSC3000 capacity in terms of the number of managed TRX has to be determined on a case-by-case basis, according to the network configuration.As for EDGE, the configuration and activation of this feature on BSS is based on a UNIX program installed at the OMC-R. The purpose of this tool is to configure EDGE parameters and/or EDGE backhaul by execution of the MMI command files. This avoids manual operation and turns out to be efficient in order to optimize:

• the operation duration• the configuration errors due to the number of impacted parameters since the NRP is available as a plug-in

Note that EDGE has no impact on TCU3000.Moreover, the number of Agprs PCM that can be connected to a PCUSN is increased in V15 to 24 per BSC3000 (to be compared with 12 in V14). A PCUSN12 must be then upgraded to a PCUSN24.

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BSC3000 Provisioning6 - AMR impact

TCU BSC BTS

Ater Interface Abis Interface

TS i

TS 1/0

TS 24/31

TS j

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

AMR HR TCH (TCH/AHS)

FR TCH (TCH/FS or TCH/EFS) AMR FR TCH (TCH/AFS6.7, TCH/AFS5.9 or TCH/AFS4.75)

8 kbps channel carrying supplementary information in downlink, padding in uplink.

TS 24/31

TS m

TS 1/0

TS n

TS p

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

0 1 2 3 4 5 6 7

8 kbps channel carrying supplementary information (in uplink and in downlink).AMR FR TCH (TCH/AFS10.2)

A Interface

Each TS on A PCM link (64 kbps rate) carries one single speech or data communication channel (speech is sampled at 8 kHz and each sample is coded onto 8 bits) whereas on Ater/Abis interface, a communication channel has a rate of 8 or 16 kbps: refer to the above slide for more details.

BSS Capacity• Abis PCM: AMR Half Rate allows to double the number of calls that could be

carried on an Abis PCM.

• BSC3000 capacity: The introduction of AMR services on BSC induces:

— handovers between half rate and full rate TCH, in order to adapt the radio link to radio conditions

— more complex algorithms for TMG mechanisms and channel allocations

• thus the BSC load of an AMR call is greater than the load induced by a non AMR call. Therefore according to HR AMR penetration, the BSC configuration (number of cells by BSC, number of TRX by BSC, LAC size…) has to be studied.

• TCU3000 capacity: AMR services induce more complexity on TCU, leading to some capacity reduction compared to EFR or to FR calls.

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BSC3000 and TCU3000 Configurations

Nbr of BTS (≤ 500)BSC configuration:TMU number( 5 to 14)LSA number (2 to 6)

Nbr of Cells (≤ 600)

Nbr of PCMs (≤ 126/168)

Nbr of LAPD (≤ 567)

Nbr of TRX (≤ 1000)

TrafficModel

TMU / TRMredundancyN+P+2 / N+1

Loadlimits

Nbr of SS7 links (≤ 16)

Nbr of Erlangs (≤ 3000)

TCU configuration:TRM number (2 to 10)LSA number (1 to 4)

(Abis +Ater + Agprs)

Number of (PDTCH/4 + CIC/4 + TRX*2 + Joker DS0 if EDGE) ≤2268 (8K RM module)

1 - Overview

The different limits to be taken into account within the provisioning model are classified into hardware, software and load limits.Main hardware limits come from:

• the number of TMU and TRM modules• the number of LSA modules per node

Main software limits are given by:• the number of TRX (1000)• the number of cells (600)• there is no limit in terms of cells per TMU, but taking into account that a cell must have at least one TRX, we can deduce that the limit of cells per TMU is equal to the TRX limit per TMU• the maximum number of sites (500); the number of sites per BSC3000 will be reduced in the case of 2 or 3 LAPDs per site

Main load limits are:• the number of LAPD channels per TMU module (62)• the number of TRXs per LAPD channel (8)

Note that in V15 an optional kit can be used to increase the switching capacity to 4056

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BSC3000 and TCU3000 Configurations

BSC blocking rate

BSC

SS7 numberLSA number

BSC limits

LAPD number < 567(Ater + Abis + Agprs)

1

n

Abis PCM Nb

Siteelements

LSAComputation

(Ater Nb)

BSC3000Model

BTS BSC

TCUNumber

BSCnumber

Real traffic

CS PCM TS Nb

TMUnumber

TRX number

TMUComputation

SiteComputation

Σ

2 - Proposed system

• Step 1 - Determine the offered traffic: Abis PCM links, GPRS/EDGE cells,GPRS/EDGE TS, Total offered traffic (GSM + GPRS/EDGE).

• Step 2 - Determine the real traffic that will be managed by the BSC, = (Traffic intensity per subscriber) x (number of subscribers).

• Step 3 - Determine the number of information channels on the Ater interface: the (GSM voice channels needed between the BSC and the TCU) by using Erlang B formula, = ErlangB_Inv_N (traffic, blocking rate).

• Step 4 - Determine the number of Ater PCM links: convert the number of voice channels into traffic DS0s and PCM links on the Ater.

• Step 5 - Determine the number of GPRS/EDGE data channels needed between the BSC and the PCUSN.

• Step 6 - Determine the number of Agprs PCM links.

• Step 7 - Determine the total number of PCM links needed.

• Step 8 - Convert the number of PCMs into LSA RC modules: an LSA supports 21 E1 type PCMs (resp. 28 for T1 type).

• Step 9 - Convert the number of total offered traffic into TMU modules.

• Step 10 - Check the dimensioning of the 8K RM module.

16


BSC3000 Provisioning Example

BSC limits

Addingfor

all sites

LAPD number on AbisAbis number(LSA RC)BSC traffic (CCS7)(~ offered traffic)

Number of cells

Number of TRX

Number of Abis

Number of LAPD

Max. Offered traffic

Site Computation

Number of sites

BTSdimensioning

BSC dimensioning

1 BSC3000Enough?

BSC3000 dimensioning

Yes

No

Site Splitting

1 - Site computation

ExampleSite input: number of BTS S444 (S8000 CBCF) handled by the BSC = 40.

#SITEs = 40#CELLs = 120 #TRXs = 480#PCMs = 40 (star configuration) if no EDGE, 80 if EDGE with 4 PDTCH & 4 DS0 per cell#GPRS/EDGE cells = 120#GPRS/EDGE TSs = 480 (4 GPRS/EDGE TS per cell)#Abis LAPDs = 120

Step 1 - Offered traffic:maximum offered traffic: #Erl (GSM) = 2106 Erl (2% blocking rate)total offered traffic #Erl (virtual traffic) 40 x 63 Erl = 2520 Erl (Including GPRS/EDGE TSs)

Step 2 - Real traffic:number of mobile subscribers (Ksubs) = 100traffic intensity per subscriber (mErl/subs) = 20 real traffic intensity = 100 x 20 = 2000 Erlrealistic (or real) capacity on the BSC3000 = 2000 Erl

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BSC3000 Provisioning Example2 - Ater PCM TS computation

Erlang Law

Real offered traffic in the cells managed by the BSCBSC blocking rate

(0.1%)

Total number of traffic channels on Ater interface(maximum 3112)

Total number of traffic TS on Ater interface

— 4 ••

HR penetration Traffic on BSCNumber of traffic TS on Abis interface

Number of traffic TS on Ater interface

Step 3 - Number of information channels:• number of voice channels for offered traffic on the TCU/BSC = 2200 CICs

(0.1% blocking rate)

Number of CICs • The maximum number of CICs supported by the BSC3000 is 3112.

• This number corresponds to 3000 Erlang at 0.1% blocking rate on the A interface.

• In fact the limit of 3000 Erl per BSC3000 comes from this limitation.

Remark:The introduction of HR induces an increase of the traffic in a given cell. Therefore, the traffic on the BTSs and on the BSC also increases. But, the number of needed traffic TS on Abis interface remains unchanged whereas the number of traffic TS on Ater interface grows.EDGE has no impact on Ater PCM computation.

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BSC3000 Provisioning Example3 - Ater PCM link computation


on AterNumber of traffic Time Slots

(64 kbps)

TSs for CCS7 signaling(200 Erl / SS7 link + 1

for redundancy)

+TotalNumberof Ater Time Slots




on Ater

LAPD TS Assumed number (2 per LSA module)

E1 PCM

T1 PCM

Step 4 - Number of Ater PCM links• 2200 CICs need 550 DS0 on the Ater interface, i.e. 19 E1 PCM (or 24 T1) for

traffic handling.

• Let 19 E1/24 T1 be the number of Ater PCMs required (with SS7 and LAPD additional DS0).

SS7 links Dimensioning • Up to 2 SS7 links are supported by each TMU module.

• Up to 16 SS7 channels can be handled by a BSC3000.

• According to the real time capacity limitation of the TMU moduleit is recommended not to create more SS7 channels than TMUs.

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BSC3000 Provisioning Example4 - Agprs PCM link computation

Total number oftraffic channels on Agprs interface

— 4 ••


on Agprs

Total number of traffic Time Slots

on Agprs




on Agprs

E1 PCM

T1 PCM

Step 5 - Number of GPRS information channels• number of data channels on the PCUSN/BSC = 480 CICs

Step 6 - Number of Agprs PCM links• 480 CICs need 120 DS0 on the Agprs interface, i.e. 4 E1 PCMs (or 6 T1) for

traffic handling

As maximum number of PCM on Agprs is 24 in V15 (remains 12 in V14), without dynamic Agprs, the maximum number of Gprs TS is:

• 24*4*30 = 2880 for E1 (one TS is reserved for LapD on each PCM link)

• 24*4*23 = 2208 for T1 (one TS is reserved for LapD on each PCM link)

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BSC3000 Provisioning Example4 – Dynamic Agprs Principles – GPRS Principles

> Target: optimize Agprs PCM use, according to GPRS traffic sharing among cells

> Benefits: minimize the number of AGPRS links, orimprove the available cell bandwidth

under heterogeneous traffic distribution (when combined with Time Slot Sharing)

> How: on demand, on a Agprs PCM basis• the PCU computes the AGPRS load of each cell and triggers reconfiguration procedures in order

to exchange ONE 16k AGPRS TS from the least to the most loaded cell• the BSC performs the reconfiguration, according to the PCU request

Cell A Cell BAGPRSPCM

Dynamic Agprs feature optimizes Agprs resources on Agprs interface according to the GPRS traffic among cells.The PCU computes the Agprs load on each cell and reconfigures Agprs TS from the least loaded cell to the most loaded one in order to increase its available bandwidth.This process is done every second and on a per Agprs PCM basis.Note that only one 16k Agprs TS is reconfigured from one cell to another every second.

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BSC3000 Provisioning Example4 – Dynamic Agprs Principles – EDGE Principles> Same Target & Benefits: move the Agprs resource

towards the cells that require it the most !

> How:• the PCU computes the AGPRS load of each cell and triggers reconfiguration procedures in

order to exchange up to 8 JOKER AGPRS 16k TS (2 DS0) from one cell (e.g. the least loaded cell) to the most loaded cell (or only 1 MAIN 16k TS from one cell to another one)

• the BSC performs the reconfiguration, according to the PCU request• the PCU selects the type of TS (Main or Joker TS) that should be removed from the selected

cell or added to the most loaded cell

Cell A Cell BAGPRSPCM

Main or Joker TS

removed ?Main or Joker TS added ?

Up to 2 DS0 Joker in one shot

The principle of Dynamic Agprs Interface with EDGE is the as with GPRS: to give more bandwidth to the most loaded cells, and take this bandwidth out from the least loaded cells. Process done every second, on a per Agprs PCM basis.

All combinations are possible:1 Main TS Cell B -> 1 Main TS Cell A (same as GPRS)1 Main TS Cell B -> 1 Joker TS Cell AUp to 8 Joker TS (2 Joker DS0) Cell B -> up to 8 Joker TS (2 Joker DS0) Cell A1 Joker TS Cell B -> 1 Main TS Cell A

The number of jokers is controlled by the parameter “JokerPerMainTarget”.If JokerPerMainTarget is “x” and there are already nPDCH & n*x Jokers connected, 1 Main TS is selected by the PCU instead of Joker TS.

Engineering rule:JokerPerMainTarget parameter value should be equal to or less than the number of provisionned Abis DS0 joker.

22


BSC3000 Provisioning Example4 – Guideline for Agprs PCM link computation

The following formula provides the maximum number of cells that can be configured per Agprs PCM depending on the PCM type (T1 or E1), the compression rate to be implemented (should be kept below 70%) and the value of the JokerToMainRatioparameter:

( ) ( )JPMTnNbCell

pdtch +−≤

17.0192

( ) ( )JPMTnNbCell

pdtch +−≤

17.01120

T1 case, 70% compression rate E1 case, 70% compression rate

With:

• 92 16 kbps Agprs data TS on 1 T1 Agprs PCM [25 - 1 (sync) - 1 (Lapd TS)] x 4 = 23 x 4 Agprs data TS

• npdtch number of PDTCH configured on the cell

• JPMT JokerPerMainTarget, equal to Abis DS0 Joker

With:

• 120 16 kbps Agprs data TS on 1 E1 Agprs PCM [32 - 1 (sync) - 1 (Lapd TS)] x 4 = 30 x 4 Agprs data TS

• npdtch number of PDTCH configured on the cell

• JPMT JokerPerMainTarget, equal to Abis DS0 Joker

Agprs interface dimensioning must be done according to:• the number of DS0 needed for GPRS & EDGE TS (PDTCH and Jokers TS),• the compression rate of the dynamic Agprs feature (if activated),• the number of Lapd TS needed (one per Agprs PCM)

Example: 4 PDTCH and 4 DS0 on Abis per cell• T1 case, 60% compression, max number of cells that can be configured per Agprs PCM:

• E1 case, 60% compression, max number of cells that can be configured per Agprs PCM:

Note that compression rate should be kept below 70% to guaranty a sufficient reactivity when a new user starts a TBF in a cell where few resources are allocated on Agprs

( )( ) ( ) 11

4146.011244

≤⇒+−

−≤ NbCellNbCell

( )( ) ( ) 15

4146.0111324

≤⇒+−

−−≤ NbCellNbCell

23


BSC3000 Provisioning Example5 - Number of LSA RC modules

Number of PCM linkson Agprs

+Number of PCM linkson Abis

Assumed number of PCM links on Ater

Total number of PCM links

Nbr of LSAsGSM Objects

Not standardTotal PCM (E1) 21 42 63 84 105 126 HC

≤ 15 ≤ 36 ≤ 57 ≤ 78 ≤ 99 ≤ 120 HC≤ 12 ≤ 12 ≤ 12 ≤ 12 ≤ 12 ≤ 12 HC≥ 1 ≥ 1 ≥ 1 ≥ 1 ≥ 1 ≥ 1 HC

Total PCM (T1) 28 56 84 112 140 168 HC≤ 22 ≤ 50 ≤ 78 ≤ 106 ≤ 134 ≤ 162 HC≤ 12 ≤ 12 ≤ 12 ≤ 12 ≤ 12 ≤ 12 HC≥ 1 ≥ 1 ≥ 1 ≥ 1 ≥ 1 ≥ 1 HC

Nature of rule6

- Ater PCM

- Abis PCM

51 2 3 4

- Agprs PCM

- Agprs PCM- Abis PCM

- Ater PCM

Number of LSA RCmodules(1 to 6)



E1 PCM

T1 PCM

Step 7 - Total number of PCM links• Number of PCMs on the Ater interface: 19 E1 PCM (24 T1)

• Number of PCMs on the Abis: 40 E1 PCM (80 T1 – if no daisy chain config)

• Number of PCMs on the Agprs: 4 E1 PCM (6 T1)

Step 8 - LSA RC modules needed due to port capacity• (19 + 40 + 4) / 21 = 3, then 3 LSAs E1 are needed on the BSC

• (24 + 80 + 6) / 28 = 4, then 4 LSAs T1 are needed on the BSC

PCM Dimensioning depends on the PCM type (E1/T1) and LSA modulesprovisioned

• No. of PCMs = 21 * No. of LSAs (E1)

• No. of PCMs = 28 * No. of LSAs (T1)

This means a maximum of 126 E1 or 168 T1 ports per BSC3000 (Abis/Ater/Agprs). From these ports, 6 are reserved for Ater links (synchronizing ports).

24



Virtual offered traffic (GSM + GPRS)

÷ 300 Number N of TMU modules

Number Pof TMU modulesfor redundancy

Total number N + P + 2of TMU modules

(Active + passive processes

+ redundancy)

2 for SS7 processing

Nbr of LAPD (≤ 567)(Abis +Ater + Agprs) ÷ 60

TRX number÷ 100

10+2+29+2+28+2+27+2+26+2+25+1+2TOTAL222222SS7: 2222221P1098765N

3000Erlang

2700Erlang

2400Erlang

2100Erlang

1800Erlang

1500Erlang

Capacity

Number of TMUs

6 - Number of TMUs

Step 9 - TMUs needed due to offered capacity2520 Erl are offered on the Abis side (total installed radio traffic). i.e. (2520 / 300),N = 9 then 13 TMUs are needed due to TMU real-time capacity limitation (N+P+2 redundancy&SS7 mandatory).

TMU real-time capacityMain assumption: one TMU (redundant or not) can handle 300 Erl as offered traffic (different types of Call Profile will generate different TMU processor loads).Offered traffic induces additional non-payload signaling load, which is unfortunately computed by TMU modules. That is why, the offered traffic will be always taken into account for BSC3000 dimensioning, from the processing capacity point of view.

TRX DimensioningMaximum number on TRXs supported by the BSC3000 is 1000 (software and hardware limitation).Maximum number of TRXs per TMU: 300 Erlang divided by the number of Erlangper TRX, depends on the considered blocking rate. One Cell TRX at 2% blocking rate can handle around 3 Erl, which means 100 TRXs/TMU.

25



Number of Abis TSs(64 kbps)

+Number of Ater TSs(64 kbps)

Number of Agprs TSs(64 kbps)

If number of TSs > 2268(> 4056 in V15 with DS512)

2 BSC3000

Total number of switched TSs (DS0)≤ 2268 (8K-RM module)

≤ 4056 (in V15, with DS512 option)

Traffic only

7 - 8K RM maximum capacity

Step 10 - 8K-RM module limitation• 4056 DS0s is the number of traffic TSs a 8K-RM can switch

• this implies a new condition:

number of TRXs < [4056 – (No of CICs/4) –(No of PDTCH/4)]/2

• check the 8K-RM capacity: [(2200 + 480) / 4 + 480 x 2) = 1630 lower than 4056, thus one BSC is sufficient

This example shows that one BSC3000 can process the proposed traffic• E1 case: BSC3000 with 3 LSAs and 9+2 TMUs

• T1 case: BSC3000 with 4 LSAs and 9+2 TMUs

In V15.0, the DS512 option aims to increase the capacity of SRT8K module used in the BSC3000 Interface Node up to 4056 DS0. Thanks to this option, the switching capacity of the BSC3000 is no more a limiting factor.

26


EDGE Impacts on BSC3000

1. Connectivity impact on BSC3000Additional PCM for Abis and Agprs interfaces => New LSA board may be needed (maximum of 6 LSA corresponding to 126 E1 PCM or 168 T1 PCM)Constraint: in V15.0 maximum number of Agprs PCM / BSC is 24. (previously 12 in V14.3)

2. Increase of switching capacity with the DS512 option, available in V15 onlyThe switching capacity goes from 2268 DS0 to 4056 DS0 with DS512 upgrade: Max8kRM > [2*NbTRX + ( x / 4) + Y + Z]With,

Max 8kRM = 4056 with DS512 option2268 without DS512 option

x : nbr of CIC, on the A interface, <= 3112Y : nbr of DS0 used on Agprs interface (excluding LAPD DS0)Z : sum of joker DS0 configured on Abis interface.

=> No significant impact on other boards (E.g. TMU)

In V14, the BSC3000 can switch up to 2268 DS0 on Abis, Agprs and Aterinterfaces. This capacity can be a limiting factor, especially if EDGE is activated (more DS0 to be switched with the same BSS configuration).To increase the BSC3000 switching capacity, 4 DS512 links (optical fibers) are connected between each CEM and each 8k-RM board in BSC3000 front panel. With theses connections, the total number of DS0 that can be switched is increased to 4056.DS512 links are “plug and play”, they can be hot inserted while the BSC3000 is online. A new parameter is introduced at the OMC-R: bscHighSwitchingCapacity to allow the DS512 option management.With the DS512 option, no check on switching capacity is to be performed because the switching matrix limit can not be reached (in E1 case 126 PCM * 31 DS0 < 4060 DS0 or in T1 case 168 PCM * 24 DS0 < 4060 DS0).Note that DS512 option is available in V15 even if EDGE is not activated.

27


TCU3000 Provisioning Example1 - Overview

Number of Ater PCM links

Number of LSA RC modules

Number of actives TRMs(up to nine)

Number of A CIC traffic channels

Number of TCU nodes(one or two)

No EDGE impact on TCU Dimensioning

Step 1 - Number of actives TRM modules.

Step 2 - Number of TCU nodes.

Step 3 - Number of Ater PCM links.

Step 4 - Number of TCU LAPD channels.

28


TCU3000 Provisioning Example2 - Number of TRM

Number of actives TRMs

(up to nine/node)

÷ 72Number of FR/EFRtraffic channels

Number of TCU nodes(one or two)

÷ 60Number of AMR traffic channels

÷ 48Number of EFR + TTY

traffic channels

+ : 3

* Nearest greater integer

*

*

*

Step 1 - Number of active TRM modulesEach TRM is made of 3 “archipelagos”whose capacity is dependant on codec type. One archipelago is associated to only one type of codec.FR/EFR codec: archipelago capacity is 72 circuitsAMR codec: archipelago capacity is 60 circuitsEFR + TTY codec: archipelago capacity is 48 circuitsThe TRM number is calculated according to a variable capacity, which is from 144 to 216 circuits per TRM, depending on type of vocoder.

Step 2 - Number of TCU nodesThe TCU can manage up to nine active TRMs plus one redundant: this gives the maximum capacity in terms of circuits of 1944 per Transcoding Node.

One TCU node can be connected to only one BSC3000, so that up to two BSC3000 can be connected to a TCU3000 cabinet (containing two TCU nodes).Due to TCU cabinet power supply redundancy, it is no longer necessary to connect one BSC to two different TCU3000 cabinets.To reach 3000 Erlang we have to install two TCU nodes.

29


TCU3000 Provisioning Example

÷ 21 (E1)or

÷ 28 (T1)

Number of LSA RC modules

Number of Ater PCM

Number of A PCM

Number of Ater traffic channels ÷ 31 (E1)

or÷ 24 (T1)Number of SS7 channels

+Number of A PCM

+

3 - Number of LSA RC modules

Step 3 - Number of Ater PCM links = 19 E1 (or 24 T1).

PCM Dimensioning depends on the PCM type (E1/T1) and LSA modulesprovisioned:

• Number of E1 PCMs = 21 * number of LSAs

• Number of T1 PCMs = 28 * number of LSAs

• This means a maximum of 84 E1 or 112 T1 ports per BSC3000 (Ater/A); of these ports, 6 are reserved for A interface links (synchronizing ports).

SS7 dimensioning (A interface) is one TS for 200 ERL for worst case traffic model.

30


TCU3000 Provisioning Example4 - Number of Ater LAPDs

Number of LSA RC modules Number of Ater LAPDs

Number of TCU3000 Nodes/BSCNumber of LSA RC

modules1 2 3 4 5 6 7 8

Number of LAPD DS0 2 4 6 8 10 12 14 16

1 2

X 2

Step 4 - Number of TCU LAPD channels between the BSC3000 and the TCU3000• Two LAPD channels per LSA RC module are dynamically reserved for TCU

Call Processing signaling, and TCU O&M signaling.

Check that the number of LAPD channels is compatible with the number of free Ater TSs. (see the slide BSC3000 Provisioning Example / Number of PCM links).

31


BSC3000 Dimensioning

4/65/77/107/1010/14Agprs E1/T1

26/3426/3426/3426/3411/15Ater E1/T1

40/4650/6270/7093/124105/139Abis E1/T1

44566LSA

121212126TMU

480600630750600Nb of TRXs30003000300030001300BSC capacity (Erl)

205070125200Nb of BTSsS888S444S333S222S111BTS Configuration

Typical examples

The BSC3000 offers flexibility for network engineering, because it has only one dimensioning factor in most network configurations, which is the capacity in Erlang.The other factors, such as the number of BTSs, cells, TRXs, PCMs, LAPD links, etc., will not be limiting in most cases.This table gives some dimensioning examples for the BSC3000 according to the type of BTS sites. The figures in red are the dimensioning factors for the BSC. With the exception of a pure S111 BTS configuration, the only dimensioning factor is the maximum Erlang capacity (3000 E). If the network consists of 100% S111 BTSs, the maximum number of cells (600) supported by a BSC3000 is reached before the maximum Erlang capacity. In S111 and S222 cases, Abis concentration is assumed.

32


BSC3000 and TCU3000 Configurations1 - Min and Max configurations

163SS7 links3100620A interface circuits (BSC3000)1900200A interface circuits (TCU3000)

84/11221/28E1/T1 PCM (TCU3000)126/16842/56E1/T1 PCM (BSC3000)

567120LAPD links600360Cells500120BTS

1000360TRX3000600Erlang

MaxMinBSC3000 and TCU3000 dimensioning

This table gives the dimensioning factors for the BSC3000 & TCU3000 in minimum and maximum configurations.BSC configuration:

• The minimum configuration is a 600 E, which translates to 5 TMUs (2+1 for redundancy + 2 for SS7) and 2 LSAs (42 E1 or 56 T1 PCMs).

• The maximum configuration is a 3000 E, which translates to 14 TMUs (10+2 for redundancy + 2 for SS7) and 6 LSAs (126 E1 or 168 T1 PCMs); the TCU function will require two Transcoding nodes.

Between these two configurations, all configurations can be offered, nevertheless some product engineering rules are defined to avoid inconsistency between the number of TMUs and the number of LSAs.TCU configuration:

• The minimum configuration is a 200 E TCU3000, which translates, in the case of Enhanced Full Rate, to 2 TRM modules (1+1 redundant) and 1 LSA (21 E1 or 28 T1 PCMs).

• The maximum configuration is a 2000 E: up to 11 TRMs (10+1 redundant) and 4 LSAs in each of the 2 nodes of a TCU cabinet. The TCU3000 cabinet can be connected to the same BSC or to 2 different BSCs.

Note: The TCU3000 can have a maximum of 12 TRMs modules if required.Between these minimum and maximum configurations, all configurations can be offered. Nevertheless, in the TCU3000 the number of TRMs and the number of LSAs are directly related to the required A interface capacity.

33


BSC3000 and TCU3000 Configurations2 - BSC3000 and TCU3000 typical examples

84/112Nb of E1/T1

4LSA9+1TRM

1800ETCU3000126/168105/14063/84Nb of E1/T1

567480300Nb of LAPD653LSA

10+21+1

8+21+1

5+1 1+1

TMU traffic TMU SS7

3000E2400E1500EBSC3000

34


BSC12000/BSC3000 Replacement Exercise

20% Drop&Insert => Abis PCMs235413358Busy Hour Erlang (on A/Ater)

Number of SitesNumber of CellsNumber of LAPD TSTraffic Radio (2%)Number of TRXs

22825O1161710S2281214S333

TotalBSC 3BSC 2BSC 1

Ater LAPD

SS7

Agprs int. Traffic

Ater int. (Traffic + SS7)

A int. Traffic (0.1%)

T1 PCMsE1 PCMsDS0Preliminary computation

LSA RCTRMTCU3000 modules8K-RMLSA RCTMU

T1E1BSC3000 modules

The three 2G BSCs with around 2300 Erlang installed in radio, and carrying around 1000 Erlang on the A interface, will be replaced by BSC3000, connected to TCU3000.For LAC dimensioning, the engineering recommendation is not to exceed 40 000 subscribers per LAC. In our case 1000 Erlang are generated by 40 000 subscribers (at 25 merl/subscriber) so the entire BSC3000 could be ‘under’ one LAC.For GPRS and EDGE dimensioning, the engineering recommendation is to provision 4 PDTCH per cell.

1


nortel.com/training

Section 6

PCU Dimensioning

2


PCUSN

Dimensioning Methodology

> Calculate the radio rate

> Choose the Coding Scheme

> PCUSN dimensioning

At the beginning, we'll start by calculating the rate necessary on the radio interface. We will see that this calculation can be made by two - more or less complex - ways. Then, environment analysis makes it possible to choose coding to be used in the network.The dimensioning of the PCUSN is rather automatic. All depends on the preceding parameters: radio rate and Coding Scheme.The PCUSN dimensioning rules are identical in V15.0 as compared with previous release. The same hardware configurations are supported.Even if Gb interface is not impacted by EDGE introduction from an engineering point of view, it should be ensured that sufficient capacity is available when several EDGE users are downloading data with MCS9 and 4 TS (up to 236 kpbs/sub).

3


Dimensioning MethodologyRadio Rate

Coding Scheme

Number of Radio TS

Number of Agprs TS

Number of Agprs links=

Number of PCM links=

Number of SPMs

Number of PCUSNs

÷÷ 4

÷ 30

÷ 6, 12 or 24

Example*:We have 100 cells and we need 30 Kbps per cell using CS-2.

SPM: Signal Processing Module

30 kbps

CS-2# 12 kbps

per radio TS3 Ts x 100 = 300

75 Agprs TS

(=2.5)We need 3 PCM links

=3 SPMs

1 PCUSN

÷

÷4

÷30

÷6, 12 or 24

* Attention: This example is not exact! It is here for pedagogical purposes.

Number of cells

4


Calculate the Radio Rate

2 methods:

Guaranteed throughput

Capacity

Guaranteed throughput:This method is applicable when the capacity is not a significant factor but quality or ability to exchange a given amount of data during a limited time.

Capacity:The method of capacity is a little more complex. It is, of course, applied at the BH of the network. We will detail this method in the pages which follow.

5



Radio Rate = Data to down/Upload

Time

Example: The carrier will allow the user to download 1 Mbits in 1 minute→ R = 17.5 Kbits/s

Guaranteed throughput

6



1. Make a traffic analysis

2. Determine the subscriber categories

3. Traffic Modeling

4. Calculate the mean throughput at the BH

Capacity

7


Calculate the Radio RateCapacity Method 1/4

File Sizeper transaction

in Kbytes

Information Service & E-commerce

UL

E-mail (without attachment)

E-mail (with attachments)

Web Access (no file downloading)

Web Access (file downloading)

0.7Simple Messaging

0.3

2.7

4

12

204

612

180

8

680

10

0.3UL

UL

UL

UL

UL

DL

DL

DL

DL

DL

DLstatistics from the UK for 2000

1. Traffic analysis 2. Subscriber categories3. Traffic Modeling4. BH Throughput

8



Active Data Terminalsin X’s network (k units) BH

Business 1038

Consumer 20132

Field Service 1028

Telemetry 323

Total 221


Capacity Method 2/4

9



BusinessFile Size

per transaction

Number oftransactions

at BHin Kbytes

Information Services & E-commerceUL 0.300

DL 2.700

E-mail (without attachments)UL 4.000

DL 12.000

E-mail (with attachments)UL 204.000

DL 612.000

Web Access (no file downloading)UL 8.000

DL 180.000

Web Access (file downloading)UL 10.000

DL 680.000

1.95

0.98

0.24

0.19

0.05


UL


DL

Example of GPRS Call Profile: Business, 2001


GPRS and EDGE call profiles include for each type of subscriber (Business, Consumer, Field Service and Telemetry) the types of service used and the description of the amount of traffic each service generates.

10



BH peak bit/s (max UL,DL) sigma

Business 10 1857 3.00Consumer 20 986 2.00

Field Service 10 326 4.00Telemetry 3 2 20.00Network 20 503 bit/s (max UL/DL)

Subscribers’repartition

38/221132/22128/22123/221

Average throughput per subscriber according to GPRS Busy Hours

0,0

400,0

800,0

1200,0

1600,0

2000,0

0 2 4 6 810 12 14 16 18 20 22

hours

Ave

rage

bit/

s pe

r sub

s

Total (max UL, DL)BusinessConsumerTelemetryField Service

Impact of Different Busy Hours on Average Throughput per Subscriber


The last parameter to take into account is the subscriber Busy Hour.If we assume that the GPRS (EDGE) traffic profile is gaussian like, we have a sigma and a peak time (Busy Hour) for each category. Using the number of active GPRS (EDGE) subscribers per category (deduced from marketing inputs) as coefficients, it is possible to compute an average throughput per subscriber at each time of the day (curve “Total(max UL, DL)”). Its peak value is the average throughput per subscriber at Network Busy Hour.

Thus, according to GPRS Busy Hour, the average traffic per subscriber can be very different (almost double). If the busy hour is different for each subscriber, then the average throughput per subscriber is reduced.The Busy Hour is largely determined by Operator Tariffing and subscribers behavior. It has to be considered carefully.

11



Rate in the cell = Rate per subscriber x number of subscribers per cell

Cell 1Cell 2

Cell 3

And at the End

12


Choosing the Coding Scheme

GPRS / EDGE product performance measured through BLock Error Rate:

BLER = f(C, C/I, CS, environment type)

Real user throughputof 1 GPRS/EDGE time slot

GPRS/EDGE time slot requirements in the cell

Average throughput required in the cell

(traffic modeling output)

Methodology

GPRS/EDGE radio interface dimensioning consists in evaluating the number of timeslots required to deal with the amount of data to be carried by the network during busy hour. Radio dimensioning is done cell by cell.Particular care must be given to radio interface dimensioning because radio interface is the bottle-neck of the network. Indeed spectral resource is scarce and expensive. Operators have to minimize it as much as possible.Due to necessary retransmissions on the radio interface, actual user throughput is lower than offered throughput.Radio interface dimensioning is the most critical task in the process of dimensioning a GPRS network.Please refer to section 3 “BTS Dimensioning” slides 29 to 42 for EDGE Dimensioning Detailed Method.

13


Choosing the Coding Scheme

> BLER and Effective User Throughput Parameters> BLER = f (environment type, C/I, Eb/No, CS) > Effective user throughput = g (BLER, Max Throughput)

Simulation of user throughput

0

2

4

6

8

10

12

14

9 10 11 12 13 14C/I (dB)

(Kbi

ts/s

)

CS-1

CS-2

CS-3

CS-4

BLock Error Rate varies as a function of:• the type of environment (TU3, TU50, HT130, RA250...) and the use of

frequency hopping

• the experimented level of interference quantified by C/I

• the experimented coverage quantified by Eb/No

• the implemented Coding Scheme

Effective user throughput is function of the BLER and the maximum throughput, then it depends on all the above parameters.

Consequently, for each couple (C/I, Eb/No), a coding scheme will maximize the effective user throughput. On the example given above:

• CS1 will be optimized for C/I < 9 dB

• CS2 will be optimized for 9 dB ≤ C/I < 11 dB

• CS3 will be optimized for 11 dB ≤ C/I

With a fixed allocation strategy, a coding scheme will be chosen for a cell and allocated whatever its radio conditions. Typically previous results would lead to a CS2 choice.

14


Choosing the Coding SchemeEffective Capacity of One TS at Application Layer

Coding Scheme CS1 CS2 CS3 CS4

Theoretical RLC/MAC User Throughput (kbit/s)

User Throughput at Application layer in kbit/s (without retransmission)

Effective User Throughput at Application layer in kbit/s

(with retransmissions: BLER = 4%)

Effective User Throughput at Application layer in kbit/s

(with retransmissions: BLER = 10%)

8

7.0

6.7

6.3

12 14.4 20

10.6

10.2

12.8 17.9

12.3 17.3

9.5 11.5 16.2

When it is stated that a coding scheme offers a given amount of throughput, it is not raw user throughput. It corresponds actually to the total throughput at RLC/MAC layer including RLC/MAC headers, spare bits and information bits.By keeping only the information bits from the bits flow, the theoretical RLC/MAC user throughput can be computed.However, treatments in the protocol layers between the RLC/MAC layer and the SNDCP layer induce throughput modifications. Consequently, even the previously computed theoretical RLC/MAC user throughput is not totally used for sending user data. For instance, RLC/MAC acknowledgments use part of the information throughput at RLC/MAC layer. Taking into account protocol layers headers and treatments but no block retransmission leads to the computation of the user throughput at application layer. Block errors induce retransmissions reducing the user throughput. Taking into account the BLER leads to the effective user throughput application layer:

Effective User Throughput = (1 - BLER) * Maximum User Throughput

The effective user throughput at application layer is the useful figure for radio interface dimensioning. It gives the effective capacity of one time slot at application layer.

15


PCUSN DimensioningAgprs Interface Dimensioning on BSC Side

Number of radio time slots handled by the

BSC÷ 120 Number of Agprs PCM

links

Abis PCM linksAgprs PCM links:

• one PCM time slot carries 4 radio time slots• 30 TS per E1 PCM link for traffic• 1 TS per E1 PCM link for signaling• 1 TS per E1 PCM link for synchronization

BSC

Each E1 time slot can either be configured as a LAPD link or accommodate GPRS traffic channels. However, with standard signaling profile and network configuration, 1 LAPD per PCM link on the Agprs interface is estimated to be enough to handle GPRS signaling. Thus, in each E1 PCM digital link, TS0 is used for link synchronization and one time slot is reserved for GPRS signaling, leaving 30 time slots for traffic.Whether CS1 or CS2 is used on the radio interface, one E1 time slot (at 64 kbit/s) conveys 4 radio time slots (at 16 kbit/s). Thus, the number of E1 PCM links to provision on Agprs interface on BSC side is equal to the number of radio time slots handled by the BSC divided by 120 (=4×30).

Dynamic Agprs increases the user throughput (or number of users) from 15% to 80% depending on the cells traffic unbalance and the user profile.Using Dynamic Agprs to reduce the number of Agprs PCM TS is possible (gain between 15% and 50%).

16

Student notes

17


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nortel.com/training

Exercise

18


ExerciseStep 1: Preliminary CalculationsInitial values.Calculations are done during the busy hour of the GPRS network.

Number in millions of subscribers (GSM network):

GPRS penetration rate:

Number of attached GPRS subscribers at busy hour:

Number of active GPRS subscribers at busy hour:

Each active subscriber has one activated PDP context.

Number of BSCs:

Number of cells per BSC:

Homogeneous repartition of subscribers among cells.

E1 T1 (US)

5.76 M 4.416 M

5%

100%

50%

120 BSCs

60 Cells 46 Cells

19


Exercise

Number of GPRS subscribers =

Number of attached GPRS subscribers =

Number of active GPRS subscribers =

Total number of cells in the network =

Number of attached GPRS subscribers per cell =

Number of active GPRS subscribers per cell =

20


Exercise

> The goal of this step is to determine the number of GPRS TS (PDTCH) that is needed in a cell.

> In order to determine it, the calculation should be done with 2 different hypothesis:1) the average throughput per user per cell during the busy hour is

200 bit/s.

2) a guaranteed throughput is used: 1 user, being the only one to transmit in the cell at a given time, should be able to download a file of 1200 kbits (=146.5 kbytes) in less than 60 seconds.

> In a cell, the CS-2 coding scheme is used, with a BLER of 5%, meaning that the application throughput is 10 kbit/s.

> The choice of the TS number will depend on the worse case.

Step 2: Radio Interface Dimensioning

21


Exercise

Hypothesis 1• What is the average throughput in the cell =

• How many TS per cell do we need =

Hypothesis 2• What is the average throughput in the cell =

• How many TS per cell do we need =

Finally, how many TS per cell do we need =

22


Exercise

1) Agprs dimensioning & PCUSN number

Step 3: PCUSN Dimensioning

BSC

Abis PCM links

Agprs PCM links:

• one PCM traffic time slot carries 4 radio time slots

• Number of TS per PCM link for traffic:

• Number of TS per PCM link for signaling and for synchronization:

Agprs PCM links:

E1 T1 (US)

30 TS 23 TS

2 TS 1 TS

23


PCUSN Shelf

1 2 3 40 5 6 7 8 9 10 11 12 13 14 15

E1C/

DS1C

E1AAL

/DS3C

CP

PCUSP12 SPM

E1C/

DS1C

E1C/

DS1C

PCUSP12 SPM

E1AAL

/DS3C

E1C/

DS1C

CP

RRR

PCUSP12 SPM

PCUSP12 SPM

R

A PCUSN is a Nortel Networks Passport 7K equipment.One shelf is composed of the following cards:

• Control Processor card (CP) which manages the shelf

• PCUSP (PCU Server Processor) card which mainly deals with the RLC/MAC protocol toward the BSSs

• E3C cards that make the physical link toward BSSs

• E1C cards that handle the frame relay Gb interface

24


PCUSN Boards

E1CDS1C

BSC1

BSC2

BSCn

MUXE1/E3

orT1/T3

Gb interface (Frame relay)

towards SGSN

backplane

SPM2

PCUSP

SPM1

SPMn

E3/

DS3

SPM2

E1CDS1C

E1CDS1C

E1CDS1C

(n = 6 or 12)

Standard PCUSP is provisioned with either 6 or 12 SPM (signaling processor module).One SPM board is needed per Agprs PCM.From V15.0, the SPM board is not limited to any max defined number of users in transfer (default in V14 was 40 MS).In V14 release, one BSC (either 2G or e3) must have all its Agprs PCM connected on the same PCUSP board. Therefore, the maximum Agprs PCM per BSC that a PCUSN can managed is 12.In V15.0 release, this constraint does not exist anymore: a BSCe3 can have all its Agprs PCM split on two different PCUSP of the PCUSN. This means that the maximum number of Agprs between one BSCe3 and one PCUSN is increased to 24.

25


The PCUSN 12

Termination panel

Agprs multiplexor

12 Agprs PCMs to the BSCs

CP

PCUSP 12 SPM

E1C/

DS1C

E3C/

DS3C

FILLER

FILLER

FILLER

E3C/

DS3C

E1C/

DS1C

E1C/

DS1C

PCUSP 12 SPM

CP

E1C/

DS1C

FILLER

Note : Due to joker on Agprs, the increase of the number of Agprs PCM may require to upgrade PCUSN12 to PCUSN24 or to introduce new PCUSN elements in the network.

26


The PCUSN 24For USA

Agprs multiplexor 1

Termination panel

24 Agprs PCMs to the BSCs

27


The PCUSN 24For Europe and Asia

Agprs multiplexor 2Agprs multiplexor 1

Agprs PCMs to the BSCs

28


Exercise

Number of GPRS radio TS per BSC =

Number of Agprs links per BSC =

Number of PCUs =

Number of SPM boards handling one BSC per PCUSN =

Number of PCUSN =

1 – PCUSN Number

29


Exercise

2) PCUSN board dimensioning

Step 3: PCUSN Dimensioning

A E1C/DS1C board handles 4 ports at:

Due to engineering rules (in case of Frame Relay transport, a 70% margin is usually used), the maximum throughput available per port is:

Meaning that the total throughput for the board (4x) is:

To dimension this type of board, we remember that the average user throughput per cell during the busy hour is 200 bit/s.

E1C DS1C (US)

2 Mb/s 1.536 Mb/s

1.344 Mb/s 1.07 Mb/s

5.376 Mb/s 4.3 Mb/s

For Frame Relay transport, we must take into account the header, specific Frame Relay messages and PCU – SGSN signaling which reduces the throughput of the PCM to around 70% of its nominal value.

30


Exercise

> Number of attached users per PCUSN =

> Number of active users per PCUSN =

> Total throughput needed over Gb interface per PCUSN =

> Number of E1C board per PCUSN =

2 – PCUSN board dimensioning

31


ExerciseSummary

CP :

PCU-SP :

E3C :

E1C :

Ethernet :

Blank :

32

Student notes

1


nortel.com/training

Section 7

BSS Dimensioning Review

2


Contents

> Exercise 1 – Global Example

> Exercise 2 – Global Example

> Exercise 3 – Global Example with EDGE activated

> Case Study

3


Assumptions

Site configuration: Ox and Syyy

Radio interface blocking rate:(TCH): 2%Radio interface blocking rate:(SDCCH): 0.1%A interface blocking rate: 0.1%

E1 PCM linksProblem: define BSC 12000 type, Abis link, Ater link and A link For BTS dimensioning use look-up tables:

BTS1 = OmnisectorialBTS2 = Trisectorial

BSC

n m

BTS1S8000

1900 Sub25 mE 2500

25 mE

100025 mE2500

25 mE

BTS2S12000

Exercise 1 – Global Example

4


62.5250062.5250062.52500247.519001

Abis T1PCMlinks

BTSconfig.

Abis E1PCMlinks

TotalPCM TSLAPDSDCCH/8BCCHTCHTRXErlangsSubscribers

per cellBTS

TCUBSC

12000type

SS7board

AE1/T1 PCMlinks

DDTIboards

AterE1/T1 PCM

linksSICD8VboardsTRX

AbisE1/T1 PCMlinks

Cell(s)Site(s)ErlangsBSC

Exercise 1 (con’t) – Global Example

5


Exercise 2 – Global Example

BTS50

This global example is given to show the impact of limitationsBeware: this example is not a field application

Ox: 400 subscribers (25 mE) Ox: 400 subscribers (25 mE)

Abis

Assumptions: • Radio blocking rate on TCH: 2%; radio blocking rate on SDCCH: 0.1%; A interface

blocking rate: 0.1%; E1 and T1 PCM links• 50 same sites Ox with 400 x 25 mE subscribers

Problem:• Show limitation due to Abis PCM links (number of DDTI boards)• Compute the number of SICD8V and DDTI boards, and then define BSC 12000 variant• Compute the number of SICD8V and DDTI boards, using BSCB boards for Abis

management and Drop and Insert techniques for the BTS (6 BTS per loop)

BTS1

BSC 12000

6


Exercise 3 – Global Example with EDGE

Assumptions: • Urban area, one BSC3000 (2000 Erl)• 51 sites: 20 S222, 10 S333, 10 S444, 10 S888 and 1 S121212• An average of 580 m cell radius is assumed, with TU3 radio environment (C/I = 12 dB)• 2 EDGE TDMA per sector are configured, with 4 PDTCH per EDGE TDMA• Average TS throughput, mean BLER and Mean Joker per EDGE TS are provided in the

Note section (see below). These results come from R&D simulations

Problem:• From tables, what is the mean BLER value on the cell ?• From tables, what is the average DL TS throughput with EDGE ?• What is the number of DS0 Joker that can be provisioned per cell ?• What is the number of Abis PCM (E1 & T1) with and without EDGE ?• What is the number of Agprs PCM (E1 & T1) with EDGE (54% compression rate) ?• What is the BSC3000 dimensioning ? (TMU, LSA, Switching Matrix)• Any influence on the PCUSN dimensioning ?

Distance (km)

Throughput / TS

(kbps)MCS usage

(%)Mean Throughput / TS

calculation 0.00 59.200 MCS-9 0.0370.03 59.200 0.2960.06 59.200 0.5920.09 59.200 0.8880.12 59.064 1.1810.15 57.838 1.4460.17 55.724 1.6720.20 52.726 1.8450.23 48.886 1.9550.26 44.878 MCS-8 2.0200.29 41.510 2.0750.32 38.062 2.0930.35 34.895 2.0940.38 31.833 2.0690.41 29.168 MCS-7 2.0420.44 27.022 2.0270.46 24.945 1.9960.49 23.072 1.9610.52 21.336 1.9200.55 18.442 1.7520.58 15.985 MCS-6 0.789


% Users % Users Cumulative Mean BLER when usedMCS-1 0.0 100.0 0.0MCS-2 0.0 100.0 0.0MCS-3 0.0 100.0 0.0MCS-4 0.0 100.0 0.0MCS-5 0.0 100.0 0.0MCS-6 4.9 100.0 46.0MCS-7 49.5 95.1 47.3MCS-8 27.5 45.6 30.8MCS-9 18.1 18.1 7.3

Mean BLER 35.5

MCS MCS % Distribution

Joker 1/4 DS0 Requirement

MCS1 0.0 0MCS2 0.0 0MCS3 0.0 1MCS4 0.0 1MCS5 0.0 1MCS6 4.9 2MCS7 49.5 3MCS8 27.5 4MCS9 18.1 4

total 100 3.407

7


City A

City B City C

City D City E

12 Szz 12 Szz

8 Szz

8 Szz

8 Szz

8 Szz

12 Szz 12 Szz

7 Szz

8 Szz

7 Szz

8 Szz

8 Szz

8 Szz

7 Szz

7 Szz

130 Sxxx

120 Sxxx 117 Sxxx

59 Sxxx 110 Sxxx

80 Syyy

69 Syyy

46 Syyy

70 Syyy

42 Syyy

Case study

The exercise consists in dimensioning the BSS of a GSM/GPRS network.The network is composed of five regions: BTSs are controlled by 5 BSC/PCUSN locations which are detailed below (a BSC/PCUSN location may have several BSC/PCUSNs):

Assuming that the subscribers are equally distributed on all the cells of a given city or site and using the traffic model of section 2 (25mErl per sub and radio BR at 2% and 50% HR allocation), find the BTS configuration in each BSC/PCUSN location.Compute the traffic in Erlangs in each BSC/PCUSN site.Determine the minimum number and type of BSC3000 in each BSC/PCUSN site. Determine the number of PCUSN in each BSC/PCUSN site assuming 10% of subscribers are GPRS users at 200 bits/s useful throughput and CS2 (100% are attached, 100% are active). Determine the number of TCU cabinets for each BSC/PCUSN site.

183 (110 tri + 46 tri + 27 bi)750000 + 55000 + 20500E (City + rural + roads)128 (59 tri + 42 tri + 27 bi)500000 + 50000 + 18000D (City + rural + roads)

213 (117 tri + 69 tri + 27 bi)100000 + 200000 + 21500C (City + suburbs + roads)

217 (120 tri + 70 tri + 27 bi)1100000 + 83000 + 21000B (City + rural + roads)

242 (130 tri + 80 tri + 32 bi)1200000 + 230000 + 40000A (City + suburbs + roads)

Number of BTSsNumber of subscribersBSC/PCSN locations

8

Student notes

1


nortel.com/training

Section 8

Exercise Solutions

2


Contents

> Exercise Solutions for• Section 2• Section 3• Section 4• Section 5• Section 6• Section 7

3


Exercise

Erlang Law (Section 2)

> How many resources are necessary for an offered traffic of 65Erl with a blocking rate value of 2%?

> What is the maximum offered traffic that 95 resources can manage without exceeding a blocking rate value of 0.1%?

> How many resources are necessary for an offered traffic of 290Erl with a blocking rate value of 0.1%?



Solution

According to the Erlang Tables:65 Erl at 2% ⇒ 77 resources95 resources at 0.1% ⇒ 70.854 Erl at most290 Erl at 0.1% ⇒ 334 resources960 resources at 10% ⇒ 1057.377 Erl at most

1070 resources at 2% ⇒8177.1062=70×

100865.991226.1093

+865.991=A

4


Standard traffic model. Observed figures

Number of observed subscribers = 4000Total call attempts at the busy hour = 4000

Mean TCH occupancy duration per call attempt (traffic) = 90.1 sMean TCH occupancy duration per call attempt (signaling) = 16.72 s

Mean SDCCH occupancy duration per call attempt = 4 sMean SDCCH occupancy duration for Loc./Rout. Area update, Attach/Detach, SMS, Supplementary Services = 4 sCall attempts per subscriber during

the busy hour = 1

100

20

60 100

20 Average number of requests for SDCCH, except those for call attempts, during the BH, for the whole subscribers = 26920

Mean TCH occupancy per call attempt (total) = 106.82 sExercise: ATCH ?

Exercise: ASDCCH ?

Traffic Model (Section 2)

Exercise:Find ATCH and ASDCCH for 1 subscriber at the busy hour.• ATCH = λTCH x TTCH

λTCH = λcall attempts = 1 CA/BHTTCH = 106.82 s = (106.82 / 3600)h = 0.02967 h

ATCH = 1 x 0.02967 = 29.67 mErl• ASDCCH = Σ (λSDCCH-i x TSDCCH-i)

= λSDCCH-call attempts x T SDCCH-call attempts + λothers x T others

λothers = 26920 / 4000 = 6.73 requests per subscriber during BHTSDCCH-call attempts = T others = 4 s = (4 / 3600)h = 0.0011 h

ASDCCH = (6.73 + 1) x 0.0011 = 8.59 mErl• ASDCCH =8.59/29.67 = 28.95% ATCH

5

BTS Dimensioning Exercise (Section 3)Exercise p 3-20.Solution: For full Full Rate:

With 8 TRXs, 64 TS are available. But the total number of radio TS we need is 58 (53 TCH + 3 SDCCH/8 + 2 CCCH).So we have 6 TS in addition.If we use these 6 TS as TS for TCH, we will have: 53 + 6 = 59 TS for TCH.This 59 TS for TCH correspond to 48.7 Erl of TCH (1 resource = 1 TCH andErlang table with blocking rate = 2%).Corresponding SDCCH needed traffic is:

28% x 48.7 = 13.62 Erl => 26 resources SDCCH(blocking rate = 0.1%)

=> 4 TS SDCCH/8Therefore, 3 TS SDCCH/8 are not sufficient to carry the dedicated signaling corresponding to the new traffic.So we cannot add more than 5 TS TCH.Finally, we must split the 6 supplementary TS into 5 TCH and 1 SDCCH/8.Conclusion: 64 TS = 58 TCH + 4 SDCCH/8 + 2 CCCHFor full Half Rate:

With 8 TRXs, 64 TS are available. If we use the 58 TS as TCH, we will have: 58 x 2 = 116 resources for Half Rate TCH correspond to 103.5 Erl of TCH (2 Half Rate resources = 1 TCH TS andErlang table with blocking rate = 2%).Corresponding SDCCH needed traffic is: 28% x 103.5 = 28.98 Erl => 46 resources SDCCH (blocking rate = 0.1%)=> 6 TS SDCCH/8Therefore, the 58 TS cannot be fully used as TCH TS, as 2 SDCCH/8 TS are missing, let us take these 2 SDCCH/8 TS out of the 58 TCH TS and try:64 TS = 56 TCH + 6 SDCCH/8 + 2 CCCH56 TS give 112 resources or 99.62 ERL at 2%28% x 99.62 = 27.89 ERL needing 45 resources at 0.1% or 6 SDCCH/8 TS

Conclusion: 64 TS = 56 TCH + 6 SDCCH/8 + 2 CCCH is correct.

6


Exercise 1

1. Assumptions: S12000 Indoor product range- Traffic per subscriber = 25 mE- Blocking rate on traffic = 2%- Blocking rate on Signaling = 0.1%

2. Find out number:- n of TRX- CPCMI boards

3. Using:- Detailed method- Look-up tables

4. Find out the capacity increase in term of Erlang with 100% HR allocations (same numberof TRX as in 2.). Do not forget to correctly dimension the resources needed for SDCCH.

BTS

S12000

Indoor

On2500 Subscribers

OMNISECTORIAL BTS

BTS Dimensioning exercise (Section 3)

1. Solution in tableOffered traffic = 2500 x 25 mE = 62.5 Erlangs; table gives immediately(for 62.94 Erlangs maximum):

10 TRXs, 74 TCH , 2 CCCH, 4 SDCCH/8, 2 LAPD, 22 PCM TS1 PCMI/E1 board or 1 PCMI/T1 board

2. Solution with detailed computationFrom Erlang B table: TCH number = 74 TSs for 62.5 ErlangsSDCCH computation: use of Erlang B tables starting from the traffic model for which:

• Offered traffic of 62.5 Erlangs needs signaling traffic of 62.5 x (28/100) = 17.5 Erlangs

• Erlang B table at 0.1% gives: SDCCH resources = 32 then SDCCH/8 = 32/8 = 4 TSs

Total number of radio channels (TCH + SDCCH + CCCH): 74 + 4 + 2 = 80Number of TRXs: 80/8 = 10

7

4. S12000 BTS load limits• CPCMI boards:

— Number of PCM links = Nb of TSs / 31 (for E1),= Nb of TSs / 24 (for T1),

— Number of TSs = 2 (LAPD) + 2 x 10 (TRX) = 22 TSs,— Number of PCM link = 1,— 1 CPCMI board is sufficient.

5. Summary table

6. Summary Table for 100% HR calls:

• 10 TRXs deliver 10 x 8 = 80 TSs• HR penetration increases load on SDCCH. Therefore, the previous configuration 74

TCH/F + 2 CCCH + 4 SDCCH, cannot be kept. • Hypothesis: Reduction of the number of TCH TSs to 71 TCH/F.• 71 TCH/F means 142 TCH/H. From Erlang B table, the offered traffic (with a blocking

rate at 2%) corresponding to 142 TCH/H is 128.9Erlangs.• SDCCH computation (using Traffic Model):

— signaling traffic for offered traffic is: 28 x 128.9 / 100 = 36.09 Erlangs— Erlang B table gives: 55 resources or 55/8 = 7 SDCCH TSs

• Finally: 71 TCH/F + 2 CCCH + 7 SDCCH = 80 TSs. From Erlang B table, the offered traffic (with a blocking rate at 2%) corresponding to 142 TCH/H is 128.9 Erlangs.

• Capacity increase in term of Erlang:128.9/62.94 = 204.8%

TRX TCH CCCH SDCCH/8 LAPD PCM TS E1/T1 CPCMI

10 74 2 4 2 22 1 1

TRX TCH CCCH SDCCH/8 LAPD Erlangs

10 71 2 7 2 128.9

8


BTS Dimensioning exercise (Section 3)

Exercise 2

1. Assumptions: S12000 product range- Traffic per subscriber = 25 mE- Full rate mobiles (no AMR or HR)- Blocking rate on traffic = 2%- Blocking rate on signaling = 0.1%

2. Find out number (using look-up tables) :- TRX per cell- CPCMI boards


S12000

1350Subscribers

1900Subscribers

2500Subscribers

Trisectorial BTS

Cell dimensioning:1350 subscribers => Offered traffic = 33.75 Erlangs: table gives (for 34.7 Erlangs):

6 TRXs, 44 TCH, 1 CCCH, 3 SDCCH/8, 1 LAPD, 13 PCM TSs1900 subscribers => Offered traffic = 47.5 Erlangs: table gives (for 47.8 Erlangs):

8 TRXs, 58 TCH, 2 CCCH, 4 SDCCH/8, 1 LAPD, 17 PCM TSs2500 subscribers => Offered traffic = 62.5 Erlangs: table gives (for 62.94 Erlangs):

10 TRXs, 74 TCH, 2 CCCH, 4 SDCCH/8, 2 LAPD, 22 PCM TSs

Site dimensioning:BTS configuration: S6810

52 PCM TSs on Abis give 2 PCM links, so 1 CPCMI board

50% HR introduction:Using table page 3-35 at 50% HR penetration we have:• 35 Erlangs carried (for 33.75 needed) by 5 TRX instead of 6TRX• 52 Erlangs carried (for 47.5 needed) by 7 TRX instead of 8TRX• 62 Erlangs carried (for 62.5 needed) by 8 TRX instead of 10TRX

BTS configuration: is then S578 instead of S6810 we save 4 TRX out of 24 that is to say 16.66%.

9


BSC 12000 Dimensioning exercise (Section 4)

SICD8V# 2

S332O2O2O2

O1O2O4O2

O2O2O2O2

S888

O8

O8

O4

S444

SICD8V

> 8 TRXs

> 8 TRXs

> 8 TRXs

> 8 TRXs

O1O2O2O2

O2O4O2

O2O2O2O2

S888

S444

BSCB

SICD8V# 1

O8

O8

O4

S332

TSCB

TRX

7

8

8

0

8

8

4

0

= 43

One solution could beProposition

BSCB

TEI

11

11

12

0

8

8

5

0

TRX

8

8

4

8

8

0

8

0

= 44

TEI

9

9

5

8

8

0

9

5PCU

Proposition with 1 SICD8V board:Number of LAPD: one LAPD is able to support up to 8 TRXs. So for the S888 we need more 3 LAPDs and for the S444, 2 or 3.One LAPD has to be used for the signaling of the TCU (via the TSCB). This LAPD is missing here.Each SICD8V port is able to manage up to 8 TRXs, but the ports 1, 2, 4 and 8 manages more than 8 TRXs. The SICD8V board is able to manage up to 64 TRXs. In this example there are 87 TRXs. This is not possible. The number of TEI per LAPD port after the BSCB board has to be less or equal to 15. An S332 correspond to 9 TEI and an O2 to 3 TEI. So, on the first concentrated LAPD there are 9 + 3 x 3 = 18 TEIs. It is too much. For GPRS, at least one LAPD has to be used for the signaling of the PCU. This LAPD is missing here.

Solution with 2 SICD8V boards:The SICD8V #1 and SICD8V #2 support:

• No more than 8 TRXs per port

• No more than 15 TEIs per port

The SICD8V #1 supports 43 TRXs (< 64). The SICD8V # 2 supports 44 TRXs (< 64).

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BSC/TCU e3 Dimensioning Case Study (Section 5)

A) With E1 PCMRadio part characteristics:

• Maximum offered traffic (GSM + GPRS)

This is the maximum offered traffic that the sites can handle if they were used for GSM only. Knowing that the max offered traffic for an S333 is 42 Erl, for an S22 it is 16.4 Erl and 2.9 Erlfor an O1.

Max offered traffic = 34 S333 x 42 + 43 S22 x 16.4 + 55 O1 x 2.9 = 2292.7 Erl.

• Real traffic

This is the offered traffic according to the number of subscriber in the cells.

40 000 subscribers x 0.025 Erl/subscriber = 1000 Erl.

• Number of sites = 34 S333 + 43 S22 + 55 O1 = 132 sites.

• Number of cells = 243.

• Number of GPRS cells = 34.

• Number of TRXs = 533.

• Number of GPRS TSs = 4 TSs/cell x (34x3) cells = 408 GPRS TSs.

• Number of Abis LAPDs = 34 S333 x 3 LAPD + 43 S22 x 1 LAPD + 55 O1 x 1 LAPD = 200.

• Number of Abis PCMs = 132 Sites x Drop&Insert ratio (20%) = 106 PCMs.

Ater PCM linksThere must be enough E1 PCM links on Ater to carry the traffic generated by the subscribers with a blocking rate of 0.1%. Moreover Ater also includes SS7 signaling and LAPD signaling.

• Ater traffic TSs: From the Erlang B table we find that 1077 channels are needed to carry 1006 Erlang with a blocking rate of 0.1%. With 4 channels per Ater TS, this makes 1077/4 = 270 TSs.

• Ater SS7 TSs: 1006 Erl / 200 Erl per SS7 TSs = 5 SS7 TSs. Adding 1 for redundancy makes 6 SS7 TSs.

• Ater LAPD TSs: We cannot compute the number of LAPD TSs yet, we need to know the number of LSA modules in the TCU e3. We will just make sure that we have enough available TSs for the LAPD.

• Number of Ater E1 PCM links: (270 traffic TSs + 6 SS7 TSs) / 31 TSs = 276/31 = 9 PCM links. With 9 PCM links we have 279 TSs, which would allow a maximum of 3 LAPD TSswhich will not be enough, we have then to provision 10 PCM links.

11

Agprs PCM links[(34 S333)x(3cells)x(4PDTCH)]/4 Agprs TSs / 30 TSs (available on Agprs) = 102/30 = 3.4 then 4 E1 PCM links

Number of LSA modules (BSC)4 PCMs (Agprs) + 10 PCMs (Ater) + 106 PCMs (Abis) = 120 E1 PCM links.120 PCMs / 21 ports (per LSA) = 6 LSA (max number of LSA in the BSC e3).Remark: 6 more ports are available.

Number of TMU modulesThe maximum offered traffic (virtual traffic) is 2292.7 Erl and one TMU can support 300 Erl. So we need 8 TMUs for the active process. From the configuration table we see that 8 +2 + 2 TMUs are necessary for the passive process, SS7 and for redundancy.

8K RM capacity check.(533TRX)x2 or 1066 traffic TSs (Abis) + 270 TSs (Ater) + 102 TSs (Agprs) =1438 TSs (< 2268).

So the BSC e3 is able to switch all the TSs.

Number of TRM modules1077 traffic channels (Ater) / 216 channels (per TRM) = 5 TRMsAdding 1 for redundancy makes 6 TRMs.One TCU e3 node can have up to 10 TRMs, so one TCU e3 node is enough.

Number of LSA modules (TCU)10 PCMs (Ater) + (1077 + 6 SS7)/31 PCMs (A) = 10 + 35 = 45 E1 PCM links.45 PCMs / 21 ports (per LSA) = 3 LSA modules are required.

Ater LAPDAs three LSA modules are used in the TCU e3, six LAPD TSs are necessary on Ater.

Ater LAPD / PCM check270 PCM TS for traffic plus 6 PCM TS for SS7 plus 6 PCM TS for LAPD make a total of282 PCM TS or 282/31 = 9.1 then 10 PCM links

12

B) With T1 PCMRadio part characteristics

• Maximum offered traffic (GSM + GPRS)

This is the maximum offered traffic that the sites can handle if they were used for GSM only. Knowing that the max offered traffic for an S333 is 42 Erl, for an S22 it is 16.4 Erl and 2.9 Erlfor an O1.

Max offered traffic = 34 S333 x 42 + 43 S22 x 16.4 + 55 O1 x 2.9 = 2292.7 Erl.

• Real traffic

This is the offered traffic according to the number of subscribers in the cells.

40 000 subscribers x 0.025 Erl/subscriber = 1000 Erl.

• Number of sites = 34 S333 + 43 S22 + 55 O1 = 132 sites

• Number of cells = 243.

• Number of GPRS cells = 34.

• Number of TRXs = 533.

• Number of GPRS TS = 4 TS/cell x (34x3) cells = 408 GPRS TSs.

• Number of Abis LAPDs = 34 S333 x 3 LAPD + 43 S22 x 1 LAPD + 55 O1 x 1 LAPD = 200.

• Number of Abis PCMs = 132 Sites x Drop&Insert ratio (20%) = 106 PCMs.

Ater PCMThere must be enough T1 PCM links on Ater to carry the traffic generated by the subscribers with a blocking rate of 0.1%. Moreover Ater also includes SS7 signaling and LAPD signaling.

• Ater traffic TSs: From the Erlang B table we find that 1077 channels are needed to carry 1006 Erlang with a blocking rate of 0.1%. With 4 channels per Ater TS, this makes 1077/4 = 270 DS0.

• Ater SS7 TSs: 1006 Erl / 200 Erl per SS7 TS = 5 SS7 DS0. Adding 1 for redundancy makes 6 SS7 DS0.

• Ater LAPD TSs: We cannot compute the number of LAPD TSs yet, we need to know the number of LSA modules in the TCU e3. We will just make sure that we have enough available TSs for the LAPDs.

• Number of Ater T1 PCM links: (270 traffic TSs + 6 SS7 TSs) / 24 TSs = 276/24 = 12 PCM links. With 12 PCM links we have 288 TSs, which would allow a maximum of 12 LAPD TSswhich will be more than enough.

13

Agprs PCM408/4 Agprs TSs / 23 (available on Agprs) = 4.43 then 5 T1 PCM links

Number of LSA modules (BSC)5 PCMs (Agprs) + 12 PCMs (Ater) + 106 PCMs (Abis) = 123 T1 PCM links123 PCMs / 28 ports (per LSA) = 5 LSA modules (17 ports are free)

Number of TMU modulesThe maximum offered traffic (virtual traffic) is 2292.7 Erl and one TMU module can support 300 Erl. So we need 8 TMUs for the active processes. From the configuration table we see that 8 +2 + 2 TMUs are necessary for the passive processes, SS7 and for redundancy.

8K RM capacity check(533TRX)x2 or 1066 Abis traffic TSs + 270 Ater + 102 Agprs = 1438 < 2268So the BSC e3 is able to switch all the TSs.

Number of TRM modules1077 (Ater traffic channels) / 216 channels per TRM = 5 TRMsAdding 1 for redundancy makes 6 TRMs.One TCU e3 node can have up to 10 TRMs, so one TCU e3 node is sufficient.

Number of LSA modules (TCU)12 PCMs (Ater) + (1077 + 6 SS7)/24 PCMs (A) = 12 + 46 = 58 T1 PCM links58 PCMs / 28 ports (per LSA) = 3 LSA modules are required.

Ater LAPDAs three LSA module are used in the TCU, six LAPD TSs are necessary on Ater.

Ater LAPD checkAter is dimensioned for up to 12 LAPD TSs, so 6 LAPD TSs is correct.

14


BSC12000/BSC3000 Replacement Exercise (Section 5)

10620% Drop&Insert => Abis PCMs

1006235413358Busy Hour Erlang (on A/Ater)

132463749Number of Sites

243787887Number of Cells

200626177Number of LAPD TS

2292662806824Traffic Radio (2%)

533158184191Number of TRXs

5522825O1

43161710S22

3481214S333TotalBSC 3BSC 2BSC 1

4Ater LAPD

6SS7

2234Agprs int. Traffic

129274Ater int. (Traffic + SS7)

45351072A int. Traffic (0.1%)

T1 PCMsE1 PCMsDS0Preliminary computation

33LSA RC

5+15+1TRMTCU3000 modules

1+11+18K-RM

56LSA RC

8+1+18+1+1TMU

T1E1BSC3000 modules

The three BSC12000 with around 2300 Erlang installed in radio and providing around 1000 Erlang on the A interface, will be replaced by:

one BSC3000, with 8 + 2 TMUsconnected to one TCU3000, with 5 + 1 TRMs

15


Exercise (Section 6)

E1 T1

Number of GPRS subscribers = 288000 22080

Number of attached GPRS subscribers = 288000 22080

Number of active GPRS subscribers = 144000 11040

Total number of cells in the network = 7200 5520

Number of attached GPRS subscribers per cell = 40 40

Number of active GPRS subscribers per cell = 20 20

16



> Hypothesis 1• What is the average throughput in the cell = 200 x 20 = 4Kbps• How many TS per cell do we need = one TS

> Hypothesis 2• What is the average throughput in the cell = 1200 / 60 = 20Kbps• How many TS per cell do we need = two TS

> Finally, how many TS per cell do we need = two TS

17



Number of GPRS radio TS per BSC = 2 x 60 = 120

Number of Agprs links per BSC = 120 / 120 = 1

Number of PCUs = 1 x 120 = 120

Number of SPM boards per BSC = one SCM per PCM, one PCM per BSC, then one SCM per BSC

Number of PCUSN = 10 PCUSN12

1 – PCUSN Number

18



2 – PCUSN board dimensioning

Number of attached users per PCUSN = 288000/10 = 28800

Number of active users per PCUSN = 14400

Total throughput needed over Gb interface per PCUSN = 14400 x 200 = 2.88 Mbps

Number of E1C board per PCUSN = one

19



Summary

CP : 1 + 1 (2 x 1 slots)

PCU-SP : 1 + 1 (2 x 2 slots)

E3C : 1 + 1 (2 x 1 slots)

E1C : 1 + 1 (2 x 1 slots)

Ethernet : 1 + 1 (2 x 1 slots)

Blank : (4 slots)

20



Assumptions

Site configuration: Ox and Syyy

Radio interface blocking rate:(TCH): 2%Radio interface blocking rate:(SDCCH): 0.1%A interface blocking rate: 0.1%

E1 PCM linksProblem: define BSC 12000 type, Abis link, Ater link and A link For BTS dimensioning use look-up tables:

BTS1 = OmnisectorialBTS2 = Trisectorial

BSC

n m

BTS1S8000

1900 Sub25 mE

250025 mE

100025 mE

250025 mE

BTS2S12000

1 – Global Example

Solution1. Site computation

Number of TRX (from appropriate tables):• BTS1: site O8 (8 TRXs; 48.7 Erl)

• BTS2: site S101010 (30 TRXs; 191.7 Erl)

We deduce the number of traffic TSs on Abis (twice TRX) = 76 TSs.Number of LAPD are determined using engineering rule (1 LAPD for 8 TRXs): 1 + 4 LAPD TS are necessary on Abis interface.Offered traffic to BSC: 240.4 Erlangs (48.7 + 191.7); according to traffic consideration, a BSC 12000 type 1 may fit.

2. SICD8V computationHardware limitation: (5 Abis LAPD + 1 Ater LAPD) / 8 ≈ 1 SICD8VSoftware limitation: 38 TRXs / 64 ≈ 1 SICD8VSo 1 SICD8V board is sufficient.

21

3. DDTI computation•Number of PCM links on Ater (from appropriate table):

For BSC total offered traffic of 240.4 Erlangs and 0.1% BSC blocking rate (cf. look up tables):

Ater E1 PCM links = 3 => A E1 PCM links = 12•Number of PCM links on Abis interface are given by the look-up table: n = 1 and m = 3 => 4 Abis PCM links•Total number of PCM links connected to the BSC 12000 is:

4 Abis + 3 Ater = 7 PCM links•Number of DDTI boards (1 DDTI for 2 PCM links): 4 DDTI boards•Then 2 TCU shelves (+ 1 redundant) are necessary, corresponding to 1 TCU cabinet.

4. BSC 12000 choiceAs a conclusion, a BSC 12000 type 1 can hold 10 (≥ 4 needed) DDTI, 1 SICD8V board, and can manage 64 (≥ 38) TRXs, 28 (≥ 2) sites, 1440 (≥ 281) terrestrial circuits and 250 Erl (≥ 240.4 Erl). So a BSC 12000 type 1 fits.5. CCS7 computationFor a BSC 12000 type 1, we need 1 CCS7 board.

47.5 (48.7): respectively current and (maximum) offered traffic for the BTS configuration

BSC Erlangs Site(s) Cell(s)Abis

E1/T1 PCM links

TRXSICD8Vboards

AterE1/T1

PCM links

DDTIboards

AE1/T1

PCM links

SS7boards TCU BSC

type

1 240.4BTS1 1 1

38 1 3 4 12 1 3 1BTS2 3 2

BTS Subscribersper cell Erlangs TRX TCH BCCH SDCCH/8 LAPD Total

PCM TS

Abis E1PCMlinks

BTSconfig.

1 1900 47.5 (48.7) 8 59 1 4 1 17 1 1 O8

2500 62.5 (63.9) 10 75 1 4 /

64 3 3 S1010102 2500 62.5 (63.9) 10 75 1 4 /

2500 62.5 (63.9) 10 75 1 4 total : 4

Abis T1PCMlinks

BTS2

BTS1

Ater1

Abis

3

A

TCU1

4

TCU1

4

O8

S101010

BSC12000

CCS7: 1SICD8V: 1DDTI: 10

TCU1

4

A

22



BTS50

This global example is given to show the impact of limitationsBeware: this example is not a field application

Ox: 400 subscribers (25 mE) Ox: 400 subscribers (25 mE)

Abis

Assumptions: • Radio blocking rate on TCH: 2%; radio blocking rate on SDCCH: 0.1%; A interface

blocking rate: 0.1%; E1 and T1 PCM links• 50 same sites Ox with 400 x 25 mE subscribers

Problem:• Show limitation due to Abis PCM links (number of DDTI boards)• Compute the number of SICD8V and DDTI boards, and then define BSC 12000 variant• Compute the number of SICD8V and DDTI boards, using BSCB boards for Abis

management and Drop and Insert techniques for the BTS (6 BTS per loop)

BTS1

BSC 12000

2 – Global Example

Solution1. Site computation

Offered traffic to one BTS: 25 mErl x 400 = 10 ErlNumber of TRX per BTS: look-up tables indicates that 3 TRXs are necessary => O3 sites (14 Erl)Total traffic offered to the BSC 12000: 50 x 14 = 700 Erl ≤ 750 Erl Þ A BSC 12000 type 3 may fitNumber of TRXs managed by the BSC 12000: 50 x 3 = 150 ≤ 192Þ A BSC 12000 type 3 may fit

Number of sites managed by the BSC 12000: 50 ≤ 92Þ A BSC 12000 type 3 may fit

Number of cells managed by the BSC 12000: 50 ≤ 160Þ A BSC 12000 type 3 may fit

23

2. SICD8V computationa) Without BSCB boards

•Number of LAPD TSs (number of SICD8V ports necessary):• Number of LAPD TSs = Number of Abis LAPD TSs + Number of Ater LAPD TSs• Number of Abis LAPD TSs = (Number of LAPD TS for 1 O3 site) x Number of site• Look-up tables gives that 1 O3 site can concentrate all the LAPD signaling on to 1

single LAPD TS on Abis interface.• Number of Abis LAPD TS = 1 x 50 = 50• TSCB board concentrates all the Ater LAPD TSs on to 1 single LAPD TS inside

the BSC 12000 towards SICD8V boards.• Number of Ater LAPD TS = 1 (inside the BSC)• Finally, number of LAPD TS = 50 + 1 = 51

•Number of SICD8V boards:• Software limitation: N1 = Number of TRX / 64 = (3 x 50) / 64 ≅ 3• Hardware limitation: N2 = Number of LAPD TSs / 8 = 51 / 8 ≅ 7• Number of necessary SICD8V boards: Max (N1, N2) = 7

— It is impossible to process this amount of signaling since the maximum number of SICD8V boards possibly hold by a BSC 12000 is 5.

— We have to concentrate the LAPD TSs into the BSCB boards.

b) Introduction of BSCB boards for Abis signaling concentrationThere are 50 LAPD TS on Abis.

•Thanks to the BSCB, we can put 2 O3 onto 1 LAPD port; 2 O3 correspond to 8 TEIsand 6 TRXs, one LAPD port of a SICD8V board can support up to 15 TEIs and up to 8TRXs (after BSCB concentration). So no problem, each BSCB will manage 6 O3.•The maximum number of BSCB boards we may need is the number of BSCB boards needed to concentrate all the sites. Each BSCB board can manage 6 O3 so we need a maximum of 50 / 6 = 9 BSCB boards.•But less BSCB boards may be sufficient.•With 9 BSCB boards, we can concentrate the 50 sites onto 25 LAPD ports•For a BSC 12000 type 3, only 23 inputs are available from the SICD8V boards (3 boards x 8 inputs - 1 input for TCU). So in this case we need more LAPD ports, thenmore SICD8V boards, a BSC 12000 type 4 at least is needed, providing 4 x 8 = 32 LAPD ports.•We can then connect, after BSCB boards, 50 sites onto 25 LAPD ports, and theTCUs onto another one. 26 out of 32 LAPD ports are used, 6 are not used. •We can then save 2 BSCB boards by connecting directly 8 sites [50 – (7 x 6)] onto 8 out of the (6 + 2 x 3) LAPD ports then available.•So we need 4 SICD8V and 7 BSCB boards. Þ A BSC 12000 type 4 may fit.

24

3. DDTI computationa) Without drop and insert:

•Number of DDTI boards = (Number of PCM links) / 2•Number of PCM links = Number of PCM on Abis + Number of PCM on Ater•Number of PCM on Abis = Number of PCM for O3 sites x 50

= 1 x 50 (1 obtains from the look-up tables) = 50

E1 PCM case:Number of PCM on Ater = 7 + 1 redundant (see look up tables)Number of DDTI = (50 + 8) / 2 = 58/2 ≅ 29

T1 PCM case:Number of PCM on Ater = 9 + 1 redundant (see look-up tables)Number of DDTI = (50 + 10) / 2 = 60/2 ≅ 30

Remark: A BSC12000 can hold at most 24 DDTI boards, thus, we have to perform Drop and Insert to reduce the number of PCM links.

b) With drop and insert:Number of TSs per BTS on Abis interface: 2 TSs x 3 DRXs = 6 TSs (traffic) + 1 TS (LAPD) = 7 TSs per BTS

E1 PCM case: we can chain up to 31/7 ≅ 4 BTSs together.•Number of drop and insert loops using this maximum configuration:

50 / 4 = 12 loops of 4 BTSs + 1 chain of 2 BTSs•Number of obtained E1 PCM links to interface by the BSC:

— (12 x 2 + 1) E1 Abis + 8 E1 Ater = 33 PCM — 33/2 = 17 DDTI boards— A BSC 12000 type 4 may fit.

T1 PCM case: we can chain up to 24/7 ≅ 3 BTSs together.•Number of drop and insert loops using this maximum configuration: 50 / 3 = 16 loops of 3 BTSs + 1 chain of 2 BTSs•Number of obtained T1 PCM links to interface by the BSC 12000:

— (16 x 2 + 1) T1 Abis + 10 T1 Ater = 43 PCM — 43/2 = 22 DDTI boards— A BSC 12000 type 4 may fit.

4. CCS7 ComputationAs we need a BSC 12000 type 4, we need 2 CCS7 boards.

25

5. Number of TCUs:•E1 case: TCU number = PCM links number on Ater = 7 (E1) + 1 redundant.

— So we need 8 TCU shelves spread onto 2 TCU cabinets.

•T1 case: TCU number = PCM links number on Ater = 9 (T1) + 1 redundant.— So we need 10 TCU shelves spread onto 3 TCU cabinets.

6. Conclusion

a) E1 PCM case:Limitation tables give that a BSC 12000 type 4:

•can hold 4 (≤ 4) SICD8V, 17 (≤ 24) DDTI boards, 2 (≤ 2) CCS7 boards, 7 (≤ 12) BSCB boards •and can manage 700 Erl (≤ 1000 Erl), 50 (≤ 124) sites, 150 (≤ 256) TRXs and 50(≤ 160) cells

SICD8V boards and DDTI boards needs were limiting factors for the management of 50 sites by 1 single BSC 12000.But drop and insert technique + LAPD concentration by BSCB (and TSCB) boards lead to a BSC 12000 type 4 acceptable solution for this case.

b) T1 PCM case:Limitation tables give that a BSC 12000 type 4:

•can hold 4 (≤ 4) SICD8V, 22 (≤ 24) DDTI boards, 2 (≤ 2) CCS7 boards, 7 (≤ 12) BSCB boards•and manage 700 Erl (≤ 1000 Erl), 50 (≤ 124) sites, 150 (≤ 256) TRXs and 50 (≤ 160) cells

SICD8V boards and DDTI boards needs were limiting factors for the management of 50 sites by 1 single BSC 12000, but Drop and Insert technique + LAPD concentration by BSCB (and TSCB) boards lead to a BSC 12000 type 4acceptable solution for this case.

26


Exercise (Section 7)3 – Global Example with EDGE

Assumptions: • Urban area, one BSCe3 (2000 Erl)• 51 sites: 20 S222, 10 S333, 10 S444, 10 S888 and 1 S121212• An average of 580 m cell radius is assumed, with TU3 radio environment (C/I = 12 dB)• 4 PDTCH per cell are configured on the EDGE TDMA• Average TS throughput, mean BLER and Mean Joker per EDGE TS are provided in the

Note section (see below). These results come from R&D simulations

Problem:• From tables, what is the mean BLER value on the cell ?• From tables, what is the average DL TS throughput with EDGE ?• What is the number of DS0 Joker that can be provisioned per cell ?• What is the number of Abis PCM (E1 & T1) with and without EDGE ?• What is the number of Agprs PCM (E1 & T1) with EDGE (54% compression rate) ?• What is the BSCe3 dimensioning ? (TMU, LSA, Switching Matrix)• Any influence on the PCUSN dimensioning ?

Solution:From tables provided by R&D simulations, Mean BLER value is 35.5 dB and

average DL TS throughput in EDGE is 32.7 kbps.

The number of DS0 depends on the MCS distribution over the cell. Based on this distribution, the number of DS0 joker can be computed using the 2 following formulas:

— joker TS dimensioning: Nb_of_joker_per_EDGE_TS x Nb_of_EDGE_TS

— joker DS0: round_up(Nb_of_16k_joker/4)

From the table we can see that 3.41 joker per EDGE TS are required. With 2 EDGE TDMA per cell and 4 PDTCH per EDGE TDMA configured, joker TS dimensioning is: 3.41 x 2 x 4 = 27.28. Joker DS0 is therefore round_up(27.28 /4) = 7.7 DS0 joker should be provisioned per cell to benefit from the full EDGE throughput enhancement.

27

• For every site the Abis PCM number and the Radio Site Mask should be recomputed to take into account the DS0 joker. Next table summarizes all the results.

Note that a S121212 site with 12 DS0 (4 per cell) can fit on 5 T1 PCM only if entire PCM are available. If one TS is reserved for other purpose, then a sixth T1 PCM should be provisioned.Therefore in the considered network, the T1 Abis PCM number increases from 84 to 136 (E1 Abis PCM from 63 to 94) as shown in the following table:

•Agprs PCM computation:Using following formulas (T1 / E1) to compute the max number of cells that can be configured per Agprs PCM, required number of Agprs PCM can be deduced:

with 0.54 instead of 0.7, 8 instead of npdtch (4 PDTCH x 2 EDGE TDMA) and 4 instead of JPMT.Hence we can configure 5 cells max with T1 PCM and 6 cells max with E1 PCM.With 153 cells, 31 Agprs T1 PCM are required (26 Agprs E1 PCM).Note that before Dynamic Agprs activation with GPRS only, 14 Agprs T1 PCM were required (11 cells configured per Agprs PCM). Indeed:8 PDTCH/cell are 2 Agprs TS. With T1 PCM, 23 TS are available for data, therefore 11 cells can be configured per PCM. With 153 cells, 14 Agprs T1 PCM are required.Same exercise with E1 PCM gives 11 E1 Agprs PCM (15 cells per PCM, 11 Agprs PCM)

Configurations S222 S333 S444 S888 S121212 Total BSCT1 PCM w/o EDGE 1 1 2 3 4 84T1 PCM with EDGE 2 2 3 4 6 136site Number 20 10 10 10 1E1 PCM w/o EDGE 1 1 1 2 3 63E1 PCM with EDGE 2 2 2 3 4 104

( ) ( )JPMTnNbCell

pdtch +−≤

17.0192

( ) ( )JPMTnNbCell

pdtch +−≤

17.01120

Configurations S222 S333 S444 S888 S121212TRX total 6 9 12 24 36LAPD 1 3 3 3 6T1 PCM w/o EDGE 1 1 2 3 4RSM w/o EDGE 12+0 18+2 12+2 16+2 18+5E1 PCM w/o EDGE 1 1 1 2 3RSM w/o EDGE 12+0 18+2 24+2 24+2 24+5Joker DS0 number 24 24 24 24 24T1 PCM with EDGE 2 2 3 4 6RSM with EDGE 18+0 21+2 16+2 18+2 16+5E1 PCM with EDGE 2 2 2 3 4RSM with EDGE 18+0 21+2 24+2 24+2 24+5

28

• BSCe3 Dimensioning:TMU

The BSCe3 is a 2000 Erl one, therefore 11 TMU are required.

Note that EDGE has only an impact on the connectivity requirement (more PCM on Abisand Agprs interfaces) and on the switching matrix (more DS0 to be switched).

LSA• Without EDGE, 84 T1 Abis PCM + 7 T1 Agprs PCM + 28 T1 Ater PCM (2000 Erl) = 119 T1 PCM. Therefore, 119/28 (number of T1 PCM managed by 1 LSA module) gives 5 LSA (63 E1 Abis PCM + 6 E1 Agprs PCM + 22 E1 Ater PCM = 5 LSA)• with EDGE, 136 T1 Abis PCM + 31 T1 Agprs + 28 T1 Ater PCM = 195 T1 PCM. Therefore, 195/28 = 7 LSA modules.

Switching Matrix• without EDGE: Abis: 2 x Nb_of_TRX = 1212 DS0; Agprs: 23 DS0 x 7 PCM = 161 DS0; Ater: 623 DS0 (2492 CIC)So the total number of DS0 switched in the 8k-RM is 1212 + 161 + 623 = 1996 DS0, which is below the engineering limit of 2268 DS0.• With EDGE: Abis: 2 x Nb_of_TRX (1212) + Nb_of_Jokers (153 x 8 = 1224) = 2436 DS0; Agprs: 23 DS0 x 31 PCM = 713 DS0; Ater: 623 DS0 (2492 CIC)So the total number of DS0 switched in the 8k-RM is 2436 + 612 + 713 + 623 = 3772 DS0, which is above the engineering limit of 2268 DS0.Therefore, the upgrade with the DS512 kit is required.

As a conclusion on this BSC3000, 2 LSA and the DS512 kit must be installed prior to EDGE activation.

10+2+29+2+28+2+27+2+26+2+25+1+2TOTAL

222222SS7: 2

222221P

1098765N

3000Erlang

2700Erlang

2400Erlang

2100Erlang

1800Erlang

1500Erlang

Capacity

Number of TMUs

29

• PCUSN Dimensioning:As the number of Agprs increases from 7 to 31 T1 PCM (from 6 to 26 E1 PCM), BSC mapping over PCUSN and the number of PCUSN should need to be reviewed. Eventually, the PCUSN can be upgraded to PCUSN36 (new T1 configuration) or PCUSN32 (new E1 configuration) or .

No impact on Gb interface.

30

Student notes

31


BSS Dimensioning Case Study (Section 7)

City A

City B City C

City D City E

12 Szz 12 Szz

8 Szz

8 Szz

8 Szz

8 Szz

12 Szz 12 Szz

7 Szz

8 Szz

7 Szz

8 Szz

8 Szz

8 Szz

7 Szz

7 Szz

130 Sxxx

120 Sxxx 117 Sxxx

59 Sxxx 110 Sxxx

80 Syyy

69 Syyy

46 Syyy

70 Syyy

42 Syyy

The exercise consists in dimensioning the BSS of a GSM/GPRS/EDGE network.The network is composed of five regions: BTSs are controlled by 5 BSC/PCUSN locations which are detailed below (a BSC/PCUSN location may have several BSC/PCUSNs):

Assuming that the subscribers are equally distributed on all the cells of a given city or site and using the traffic model of section 2 (25mErl per sub and radio BR at 2% and 50% HR allocation), find the BTS configuration in each BSC/PCUSN location.

• Compute the traffic in Erlangs in each BSC/PCUSN site.

• Determine the minimum number and type of BSCe3 in each BSC/PCUSN site.

• Determine the number of PCUSN in each BSC/PCUSN site assuming 10% of subscribers are GPRS users at 200 bits/s useful throughput and CS2 (100% are attached, 50% are active).

• Determine the number of TCU cabinets for each BSC/PCUSN site.

183 (110 tri + 46 tri + 27 bi)750000 + 55000 + 20500E (City + rural + roads)128 (59 tri + 42 tri + 27 bi)500000 + 50000 + 18000D (City + rural + roads)213 (117 tri + 69 tri + 27 bi)100000 + 200000 + 21500C (City + suburbs + roads)217 (120 tri + 70 tri + 27 bi)1100000 + 83000 + 21000B (City + rural + roads)242 (130 tri + 80 tri + 32 bi)1200000 + 230000 + 40000A (City + suburbs + roads)

Number of BTSsNumber of subscribersBSC/PCSN locations

32



Area A (City, suburbs, roads)

242 BTS sites5442 TRXs41562 Erlangs

7 S33City A

8 S33

8 S33

8 S33

8 S33

130 S111111

80 S444

Suburbs

The exercise consists in dimensioning the BSS part of a GSM/GPRS network.1) Area A BTSs configuration

a) City A• Carried voice traffic on the area: 25 mErl x 1200000 = 30000 Erl

• Carried voice traffic by one BTS: According to the assumption that the subscribers are equally distributed on all the cells, 30000 Erl / 130 sites ≈ 230.77 Erl per site or 76.92 Erl per cell

• Number of TRXs per cell for voice : Look-up tables indicates that 10 TRXs (78 Erlcarried) are necessary per cell.

• Carried data traffic per cell is: 10% of 1200000 x 200 / 390 or 61538.5 bits/s, CS2 is used, then one full rate PDTCH carries 9500 bits/s. 61538.5 /9500 = 6.48 PDTCH are necessary, one additional TRX is needed in every cell. Then the BTS type is S111111

b) Suburbs• Carried voice traffic on the area: 25 mErl x 230000 = 5750 Erl

• Carried voice traffic by one BTS: According to the assumption that the subscribers are equally distributed on all the cells, 5750 Erl / 80 sites ≈ 71.87 Erl per site or 23.96 Erlper cell


• Carried data traffic per cell is: 10% of 230000 x 200 / 240 or 19166.67 bits/s, CS2 is used, then one full rate PDTCH carries 9500 bits/s. 19166.67 /9500 = 2.02 PDTCH are necessary, no additional TRX is needed as 3 TS are available out of the 4 TRX. Then the BTS type is S444

33

c) Roads• Carried voice traffic on the area: 25 mErl x 40000 = 1000 Erl

• Carried voice traffic by one BTS: According to the assumption that the subscribers are equally distributed on all the cells, 1000 Erl / 32 sites ≈ 31.25 Erl per site or 15.63 Erl per cell


• Carried data traffic per cell is: 10% of 40000 x 200 / 64 or 12500 bits/s, CS2 is used, then one full rate PDTCH carries 9500 bits/s. 12500 /9500 = 1.32 PDTCH is necessary, no additional TRX is needed as 3 TS are available out of the 3 TRX. Then the BTS type is S33

d) Number of sites: 130 + 80+ 32 = 242 sitese) Number of TRXs: 4290 + 960 + 192 = 5442 TRXsf) Number of cells: 390 + 240 + 64 = 694 cells

34



Other Areas

City A

City B City C

City D City E

12 Szz 12 Szz

8 Szz

8 Szz

8 Szz

8 Szz

12 Szz 12 Szz

7 Szz

8 Szz

7 Szz

8 Szz

8 Szz

8 Szz

7 Szz

7 Szz

130 Sxxx

120 Sxxx 117 Sxxx

59 Sxxx 110 Sxxx

80 Syyy

69 Syyy

46 Syyy

70 Syyy

42 Syyy

2) Other areas BTSs configuration:Area B: 120 S11111 + 70 S222 + 27 S22 = 217 sites, 4962 TRXs, 624 cellsArea C: 117 S101010 + 69 S444 + 27 S22 = 213 sites, 4851 TRXs, 612 cellsArea D: 59 S101010 + 42 S222 + 27 S22 = 128 sites, 2613 TRXs, 357 cellsArea E: 110 S888 + 46 S222 + 27 S222 = 183 sites, 4344 TRXs, 522 cells

3) BSC site carried traffic:Traffic carried by the BTSs at 50% HR allocation are:S111111 = 261 Erl, S101010 = 234 Erl, S888 = 186 Erl, S444 = 81 Erl S222 = 32.1 Erl, S33 = 36 E, and S22 = 21.4 EThe maximum carried traffic for each area is:Area A: 33930 + 6480 + 1152 = 41562 Erl. 14 BSC Area B: 31320 + 2247 + 577.8 = 34144.8 Erl. 12 BSCArea C: 27378 + 5589+ 577.8 = 33544.8 Erl. 12 BSCArea D: 13806 + 1348.2 + 577.8 = 15732 Erl. 6 BSCArea E: 20460 + 1476.6 + 577.8 = 22514.4 Erl. 8 BSC

4) BSC configurations: see Excel sheets

35



Total number of equipmentNumber of BSC/TCU cabinetsNumber of PCU cabinetsNumber of BTS sites

1610452280922212983147498Total

021638/41/422628522434418322514.4Area E

101238/41/422626357261312815732Area D

012436/37/3826212612485121333544.8Area C

012437/38/3926212624496221734144.8Area B

022835/3726314694544224241562Area A

PCUSN12number

PCUSN24number

TCUnumber

PCMAbis

PCMAter

PCMAgprs

BSCNbCellsTRXsSitesErlangsBSC

location

Per BSC Per site

36

Student notes


nortel.com/training

APPENDIX

Erlang B Tables

Erlang Tables

9-1

Erlang Tables

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%

Channels Offered Offered Offered Offered Offered Offered Offered Offered Offered Offered Offered Offered Offered Offered

1 0.000 0.001 0.005 0.010 0.020 0.031 0.042 0.053 0.064 0.075 0.087 0.099 0.111 0.250

2 0.014 0.046 0.105 0.153 0.223 0.282 0.333 0.381 0.427 0.470 0.513 0.555 0.595 1.000

3 0.087 0.194 0.349 0.455 0.602 0.715 0.812 0.899 0.980 1.057 1.131 1.202 1.271 1.930

4 0.235 0.439 0.701 0.869 1.092 1.259 1.399 1.525 1.640 1.748 1.851 1.949 2.045 2.945

5 0.452 0.762 1.132 1.361 1.657 1.875 2.057 2.218 2.366 2.504 2.634 2.760 2.881 4.010

6 0.728 1.146 1.622 1.909 2.276 2.543 2.765 2.960 3.139 3.305 3.462 3.613 3.758 5.109

7 1.054 1.579 2.157 2.501 2.935 3.250 3.510 3.738 3.946 4.139 4.322 4.497 4.666 6.230

8 1.422 2.051 2.730 3.128 3.627 3.987 4.283 4.543 4.779 4.999 5.207 5.405 5.597 7.369

9 1.825 2.558 3.332 3.783 4.345 4.748 5.080 5.370 5.634 5.879 6.111 6.333 6.546 8.522

10 2.260 3.092 3.961 4.461 5.084 5.529 5.896 6.216 6.507 6.776 7.031 7.275 7.510 9.685

11 2.722 3.651 4.610 5.160 5.842 6.328 6.727 7.076 7.393 7.687 7.965 8.231 8.487 10.857

12 3.207 4.231 5.279 5.876 6.615 7.141 7.573 7.950 8.292 8.610 8.910 9.197 9.474 12.036

13 3.713 4.831 5.964 6.607 7.402 7.967 8.430 8.835 9.202 9.543 9.865 10.173 10.470 13.222

14 4.239 5.446 6.663 7.352 8.200 8.804 9.298 9.730 10.121 10.485 10.828 11.157 11.473 14.413

15 4.781 6.077 7.375 8.108 9.010 9.650 10.174 10.633 11.048 11.434 11.799 12.147 12.484 15.608

16 5.339 6.721 8.099 8.875 9.829 10.505 11.059 11.544 11.983 12.390 12.776 13.144 13.500 16.807

17 5.911 7.378 8.834 9.652 10.656 11.368 11.952 12.461 12.923 13.353 13.758 14.147 14.522 18.010

18 6.496 8.046 9.578 10.437 11.491 12.238 12.850 13.385 13.870 14.321 14.747 15.154 15.548 19.216

19 7.093 8.724 10.331 11.230 12.333 13.115 13.755 14.315 14.822 15.294 15.740 16.166 16.579 20.424

20 7.700 9.411 11.092 12.031 13.181 13.997 14.666 15.249 15.779 16.271 16.737 17.183 17.613 21.635

21 8.319 10.108 11.860 12.838 14.036 14.885 15.581 16.189 16.740 17.253 17.738 18.202 18.651 22.848

22 8.946 10.812 12.635 13.651 14.896 15.778 16.501 17.132 17.705 18.238 18.742 19.226 19.693 24.064

23 9.583 11.524 13.417 14.471 15.761 16.676 17.424 18.080 18.674 19.227 19.751 20.252 20.737 25.281

24 10.227 12.243 14.204 15.295 16.631 17.577 18.352 19.031 19.647 20.220 20.761 21.281 21.784 26.499

25 10.880 12.969 14.997 16.125 17.505 18.483 19.284 19.985 20.622 21.214 21.775 22.313 22.833 27.720

26 11.540 13.701 15.795 16.959 18.383 19.392 20.219 20.943 21.600 22.212 22.792 23.347 23.885 28.941

27 12.207 14.439 16.598 17.797 19.265 20.305 21.158 21.904 22.582 23.213 23.811 24.384 24.939 30.164

28 12.880 15.182 17.406 18.640 20.151 21.221 22.099 22.867 23.566 24.216 24.832 25.423 25.995 31.389

29 13.560 15.930 18.218 19.487 21.039 22.140 23.043 23.833 24.552 25.221 25.855 26.464 27.053 32.614

30 14.246 16.684 19.034 20.337 21.932 23.062 23.990 24.802 25.540 26.228 26.881 27.506 28.113 33.840

Erlang Tables

.

9-2

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


31 14.938 17.442 19.855 21.192 22.826 23.986 24.939 25.772 26.531 27.237 27.908 28.550 29.173 35.066

32 15.632 18.204 20.678 22.048 23.724 24.914 25.891 26.746 27.524 28.250 28.937 29.597 30.238 36.295

33 16.335 18.972 21.505 22.910 24.626 25.845 26.843 27.719 28.520 29.262 29.967 30.644 31.302 37.524

34 17.041 19.742 22.337 23.771 25.530 26.775 27.801 28.699 29.515 30.278 30.999 31.694 32.367 38.753

35 17.752 20.518 23.169 24.638 26.434 27.712 28.759 29.675 30.514 31.293 32.032 32.744 33.435 39.986

36 18.469 21.296 24.006 25.508 27.344 28.648 29.719 30.658 31.513 32.312 33.068 33.797 34.503 41.215

37 19.188 22.078 24.846 26.378 28.254 29.585 30.680 31.640 32.515 33.330 34.106 34.850 35.571 42.448

38 19.910 22.865 25.690 27.253 29.167 30.527 31.644 32.623 33.517 34.352 35.142 35.904 36.642 43.681

39 20.638 23.651 26.533 28.129 30.079 31.469 32.607 33.608 34.521 35.373 36.181 36.960 37.716 44.913

40 21.372 24.444 27.381 29.007 30.998 32.411 33.573 34.596 35.526 36.395 37.222 38.016 38.787 46.146

41 22.105 25.239 28.233 29.888 31.916 33.356 34.543 35.585 36.534 37.419 38.264 39.075 39.861 47.382

42 22.844 26.037 29.084 30.772 32.837 34.304 35.512 36.573 37.541 38.447 39.306 40.131 40.935 48.615

43 23.586 26.838 29.939 31.655 33.759 35.252 36.484 37.564 38.552 39.474 40.350 41.194 42.012 49.851

44 24.333 27.642 30.796 32.542 34.683 36.203 37.457 38.556 39.563 40.502 41.395 42.253 43.086 51.087

45 25.080 28.448 31.655 33.432 35.607 37.156 38.429 39.550 40.573 41.529 42.440 43.315 44.164 52.323

46 25.833 29.254 32.518 34.321 36.533 38.107 39.404 40.544 41.587 42.560 43.484 44.377 45.244 53.559

47 26.586 30.066 33.381 35.213 37.463 39.064 40.382 41.541 42.600 43.590 44.532 45.440 46.321 54.795

48 27.344 30.878 34.246 36.108 38.393 40.017 41.357 42.538 43.614 44.621 45.580 46.502 47.401 56.031

49 28.103 31.696 35.112 37.003 39.323 40.974 42.335 43.535 44.628 45.654 46.627 47.567 48.481 57.271

50 28.867 32.513 35.983 37.901 40.255 41.933 43.316 44.532 45.644 46.688 47.678 48.632 49.562 58.507

51 29.631 33.331 36.851 38.799 41.188 42.892 44.297 45.532 46.664 47.721 48.729 49.698 50.645 59.747

52 30.400 34.154 37.725 39.700 42.123 43.852 45.278 46.532 47.680 48.754 49.780 50.766 51.725 60.986

53 31.170 34.977 38.599 40.603 43.061 44.814 46.259 47.535 48.700 49.791 50.830 51.832 52.809 62.222

54 31.942 35.802 39.472 41.504 43.997 45.776 47.242 48.535 49.719 50.827 51.881 52.900 53.892 63.462

55 32.717 36.631 40.352 42.410 44.935 46.738 48.226 49.538 50.739 51.864 52.935 53.968 54.975 64.701

56 33.495 37.460 41.228 43.314 45.876 47.703 49.213 50.544 51.761 52.900 53.989 55.037 56.059 65.941

57 34.273 38.291 42.108 44.223 46.817 48.668 50.200 51.547 52.784 53.940 55.042 56.108 57.145 67.181

58 35.054 39.125 42.990 45.129 47.758 49.633 51.186 52.553 53.806 54.979 56.096 57.176 58.228 68.420

59 35.837 39.959 43.872 46.038 48.702 50.601 52.173 53.558 54.829 56.019 57.153 58.248 59.315 69.663

60 36.623 40.796 44.757 46.950 49.643 51.569 53.163 54.564 55.851 57.058 58.210 59.319 60.401 70.903

Erlang Tables

9-3

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


61 37.409 41.633 45.642 47.862 50.590 52.537 54.149 55.573 56.876 58.097 59.263 60.391 61.488 72.142

62 38.201 42.473 46.527 48.774 51.533 53.508 55.139 56.582 57.902 59.140 60.320 61.462 62.574 73.385

63 38.990 43.313 47.415 49.689 52.480 54.479 56.131 57.591 58.927 60.182 61.380 62.534 63.664 74.625

64 39.785 44.155 48.305 50.603 53.427 55.450 57.121 58.599 59.953 61.225 62.437 63.608 64.750 75.868

65 40.579 45.001 49.196 51.518 54.376 56.420 58.113 59.608 60.978 62.267 63.493 64.683 65.840 77.108

66 41.376 45.846 50.087 52.435 55.326 57.394 59.106 60.620 62.007 63.309 64.553 65.754 66.926 78.351

67 42.174 46.691 50.977 53.353 56.276 58.368 60.098 61.632 63.035 64.352 65.613 66.828 68.015 79.590

68 42.974 47.539 51.870 54.270 57.225 59.341 61.094 62.643 64.063 65.397 66.673 67.903 69.105 80.833

69 43.774 48.390 52.767 55.191 58.177 60.315 62.089 63.655 65.092 66.443 67.732 68.977 70.194 82.076

70 44.577 49.238 53.663 56.111 59.130 61.292 63.082 64.667 66.120 67.485 68.792 70.055 71.287 83.319

71 45.382 50.092 54.559 57.034 60.082 62.268 64.077 65.681 67.151 68.530 69.852 71.129 72.377 84.563

72 46.188 50.945 55.455 57.955 61.035 63.245 65.075 66.693 68.180 69.579 70.915 72.207 73.466 85.802

73 46.996 51.799 56.354 58.878 61.990 64.221 66.071 67.708 69.211 70.624 71.975 73.281 74.559 87.045

74 47.805 52.655 57.253 59.804 62.945 65.198 67.069 68.722 70.242 71.670 73.037 74.359 75.648 88.288

75 48.616 53.512 58.155 60.727 63.900 66.177 68.067 69.737 71.274 72.718 74.100 75.437 76.741 89.531

76 49.427 54.368 59.054 61.653 64.855 67.156 69.065 70.754 72.305 73.766 75.160 76.514 77.833 90.774

77 50.241 55.227 59.955 62.579 65.813 68.136 70.064 71.769 73.336 74.812 76.223 77.592 78.926 92.017

78 51.055 56.087 60.860 63.507 66.772 69.115 71.062 72.787 74.371 75.860 77.289 78.669 80.019 93.264

79 51.869 56.949 61.764 64.433 67.730 70.097 72.060 73.801 75.402 76.909 78.351 79.747 81.111 94.507

80 52.686 57.811 62.669 65.362 68.688 71.077 73.061 74.819 76.436 77.957 79.414 80.824 82.204 95.750

81 53.505 58.673 63.573 66.291 69.649 72.059 74.063 75.836 77.470 79.008 80.477 81.905 83.296 96.993

82 54.325 59.537 64.478 67.222 70.607 73.041 75.064 76.857 78.505 80.057 81.543 82.982 84.389 98.236

83 55.147 60.402 65.385 68.154 71.567 74.023 76.065 77.874 79.539 81.105 82.609 84.063 85.485 99.483

84 55.967 61.270 66.293 69.082 72.528 75.006 77.066 78.892 80.573 82.157 83.671 85.140 86.577 100.726

85 56.792 62.134 67.203 70.017 73.489 75.991 78.070 79.912 81.608 83.208 84.737 86.221 87.673 101.969

86 57.614 63.005 68.110 70.948 74.453 76.973 79.071 80.933 82.645 84.256 85.803 87.302 88.765 103.215

87 58.439 63.872 69.020 71.880 75.414 77.958 80.075 81.953 83.679 85.308 86.869 88.382 89.861 104.458

88 59.267 64.743 69.933 72.814 76.378 78.943 81.079 82.971 84.716 86.359 87.935 89.463 90.957 105.701

89 60.095 65.613 70.843 73.749 77.341 79.928 82.080 83.994 85.754 87.410 89.001 90.543 92.052 106.948

90 60.923 66.483 71.756 74.683 78.305 80.914 83.087 85.015 86.788 88.462 90.066 91.624 93.145 108.191

Erlang Tables

.

9-4

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


91 61.753 67.356 72.669 75.620 79.272 81.901 84.091 86.035 87.825 89.516 91.135 92.705 94.241 109.438

92 62.584 68.229 73.582 76.557 80.235 82.887 85.095 87.056 88.862 90.568 92.201 93.785 95.336 110.681

93 63.415 69.102 74.495 77.492 81.202 83.875 86.100 88.079 89.900 91.619 93.270 94.869 96.432 111.927

94 64.248 69.978 75.410 78.429 82.168 84.863 87.106 89.099 90.940 92.673 94.336 95.949 97.531 113.174

95 65.082 70.854 76.326 79.369 83.132 85.851 88.113 90.123 91.977 93.725 95.405 97.033 98.627 114.417

96 65.918 71.730 77.242 80.306 84.101 86.838 89.117 91.146 93.014 94.779 96.470 98.114 99.722 115.663

97 66.751 72.606 78.157 81.246 85.068 87.826 90.124 92.170 94.054 95.833 97.539 99.197 100.818 116.906

98 67.590 73.485 79.073 82.183 86.035 88.814 91.131 93.193 95.092 96.888 98.608 100.278 101.917 118.153

99 68.426 74.363 79.992 83.123 87.004 89.805 92.138 94.216 96.132 97.942 99.677 101.361 103.012 119.399

100 69.265 75.242 80.910 84.063 87.973 90.793 93.148 95.240 97.172 98.996 100.746 102.445 104.111 120.642

101 70.104 76.121 81.829 85.006 88.940 91.784 94.155 96.263 98.212 100.051 101.815 103.529 105.207 121.889

102 70.943 77.002 82.747 85.946 89.909 92.775 95.162 97.289 99.252 101.105 102.883 104.612 106.306 123.135

103 71.785 77.883 83.668 86.888 90.879 93.766 96.172 98.313 100.290 102.159 103.952 105.696 107.401 124.382

104 72.627 78.765 84.590 87.831 91.851 94.757 97.182 99.339 101.333 103.214 105.021 106.780 108.500 125.625

105 73.468 79.649 85.508 88.774 92.820 95.747 98.189 100.365 102.373 104.268 106.093 107.863 109.599 126.872

106 74.313 80.533 86.429 89.717 93.793 96.738 99.198 101.389 103.413 105.326 107.162 108.947 110.694 128.118

107 75.158 81.418 87.353 90.659 94.762 97.729 100.208 102.415 104.453 106.380 108.231 110.031 111.793 129.365

108 76.002 82.302 88.275 91.605 95.734 98.723 101.218 103.442 105.493 107.437 109.303 111.114 112.892 130.611

109 76.849 83.186 89.199 92.548 96.706 99.714 102.228 104.468 106.537 108.492 110.371 112.198 113.991 131.854

110 77.697 84.073 90.123 93.493 97.679 100.707 103.238 105.494 107.577 109.549 111.443 113.284 115.090 133.101

111 78.544 84.960 91.044 94.439 98.651 101.701 104.251 106.520 108.620 110.606 112.512 114.368 116.188 134.347

112 79.391 85.847 91.971 95.384 99.623 102.695 105.260 107.547 109.663 111.661 113.584 115.452 117.287 135.594

113 80.241 86.734 92.895 96.330 100.598 103.688 106.270 108.576 110.703 112.718 114.656 116.538 118.386 136.840

114 81.091 87.621 93.819 97.276 101.570 104.682 107.283 109.602 111.746 113.775 115.725 117.622 119.485 138.087

115 81.942 88.511 94.746 98.224 102.545 105.676 108.296 110.629 112.790 114.833 116.796 118.709 120.583 139.333

116 82.792 89.401 95.673 99.169 103.518 106.670 109.306 111.658 113.833 115.890 117.868 119.795 121.685 140.580

117 83.644 90.290 96.600 100.118 104.493 107.666 110.318 112.684 114.876 116.947 118.940 120.879 122.784 141.826

118 84.497 91.183 97.527 101.066 105.468 108.660 111.331 113.713 115.919 118.005 120.012 121.966 123.883 143.073

119 85.350 92.073 98.453 102.015 106.443 109.656 112.344 114.743 116.962 119.062 121.084 123.053 124.981 144.319

120 86.203 92.965 99.380 102.963 107.418 110.650 113.356 115.772 118.005 120.119 122.156 124.136 126.083 145.566

Erlang Tables

9-5

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


121 87.059 93.858 100.310 103.914 108.396 111.647 114.369 116.798 119.048 121.180 123.228 125.223 127.182 146.813

122 87.914 94.750 101.240 104.863 109.371 112.643 115.382 117.827 120.092 122.237 124.300 126.310 128.281 148.059

123 88.770 95.643 102.169 105.811 110.346 113.640 116.395 118.857 121.135 123.295 125.371 127.396 129.383 149.306

124 89.626 96.538 103.099 106.762 111.324 114.636 117.410 119.886 122.181 124.355 126.446 128.483 130.481 150.552

125 90.484 97.431 104.028 107.713 112.302 115.633 118.423 120.915 123.224 125.412 127.518 129.570 131.583 151.799

126 91.342 98.326 104.958 108.664 113.277 116.629 119.436 121.947 124.270 126.470 128.590 130.656 132.682 153.045

127 92.201 99.221 105.888 109.616 114.255 117.626 120.451 122.977 125.313 127.530 129.665 131.743 133.784 154.292

128 93.059 100.117 106.820 110.567 115.232 118.623 121.467 124.006 126.359 128.590 130.737 132.830 134.886 155.538

129 93.918 101.015 107.753 111.518 116.210 119.622 122.480 125.035 127.402 129.648 131.812 133.916 135.985 156.785

130 94.779 101.910 108.685 112.469 117.188 120.619 123.495 126.067 128.449 130.708 132.883 135.003 137.086 158.035

131 95.640 102.808 109.618 113.423 118.166 121.618 124.511 127.096 129.495 131.768 133.958 136.090 138.188 159.281

132 96.501 103.706 110.550 114.377 119.147 122.615 125.527 128.129 130.541 132.826 135.030 137.176 139.290 160.528

133 97.363 104.605 111.482 115.328 120.125 123.614 126.539 129.158 131.584 133.886 136.105 138.266 140.389 161.774

134 98.226 105.503 112.415 116.282 121.105 124.613 127.555 130.190 132.630 134.946 137.177 139.353 141.491 163.021

135 99.090 106.401 113.350 117.236 122.083 125.610 128.573 131.219 133.676 136.007 138.252 140.440 142.593 164.267

136 99.954 107.302 114.283 118.190 123.064 126.609 129.589 132.251 134.722 137.067 139.327 141.529 143.694 165.517

137 100.818 108.203 115.218 119.144 124.042 127.609 130.605 133.284 135.768 138.127 140.399 142.616 144.796 166.764

138 101.682 109.101 116.153 120.098 125.023 128.608 131.620 134.316 136.814 139.188 141.473 143.703 145.898 168.010

139 102.549 110.002 117.088 121.055 126.003 129.608 132.636 135.348 137.861 140.248 142.548 144.792 147.000 169.257

140 103.413 110.905 118.023 122.009 126.984 130.610 133.655 136.380 138.907 141.308 143.623 145.879 148.102 170.503

141 104.280 111.806 118.959 122.966 127.965 131.609 134.670 137.412 139.956 142.369 144.698 146.969 149.204 171.753

142 105.147 112.707 119.894 123.920 128.946 132.609 135.686 138.444 141.002 143.429 145.773 148.056 150.306 173.000

143 106.016 113.611 120.832 124.877 129.926 133.608 136.704 139.477 142.048 144.489 146.848 149.145 151.407 174.247

144 106.883 114.515 121.767 125.833 130.910 134.611 137.723 140.509 143.094 145.553 147.923 150.232 152.509 175.493

145 107.752 115.418 122.705 126.790 131.891 135.610 138.738 141.541 144.143 146.613 148.998 151.322 153.611 176.743

146 108.622 116.322 123.643 127.747 132.874 136.612 139.757 142.573 145.189 147.673 150.072 152.411 154.713 177.990

147 109.492 117.226 124.581 128.704 133.855 137.615 140.775 143.605 146.235 148.737 151.147 153.498 155.815 179.236

148 110.361 118.129 125.519 129.660 134.838 138.614 141.791 144.640 147.284 149.797 152.222 154.588 156.917 180.483

149 111.231 119.036 126.457 130.617 135.819 139.616 142.810 145.673 148.330 150.857 153.297 155.678 158.019 181.733

150 112.103 119.939 127.395 131.577 136.803 140.619 143.828 146.705 149.379 151.921 154.372 156.764 159.123 182.979

Erlang Tables

.

9-6

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


151 112.975 120.846 128.333 132.534 137.786 141.621 144.847 147.740 150.428 152.981 155.447 157.854 160.225 184.226

152 113.845 121.752 129.274 133.493 138.770 142.623 145.865 148.772 151.475 154.044 156.522 158.944 161.327 185.476

153 114.717 122.659 130.212 134.450 139.753 143.625 146.884 149.807 152.524 155.105 157.600 160.034 162.429 186.722

154 115.592 123.565 131.153 135.410 140.737 144.628 147.902 150.839 153.573 156.168 158.675 161.123 163.534 187.969

155 116.464 124.472 132.094 136.369 141.721 145.630 148.921 151.874 154.619 157.228 159.749 162.213 164.636 189.219

156 117.340 125.381 133.032 137.329 142.704 146.632 149.939 152.909 155.668 158.292 160.827 163.300 165.738 190.465

157 118.212 126.287 133.973 138.288 143.688 147.635 150.961 153.942 156.717 159.355 161.902 164.389 166.843 191.712

158 119.087 127.197 134.913 139.248 144.671 148.637 151.979 154.977 157.766 160.415 162.977 165.479 167.944 192.962

159 119.962 128.106 135.857 140.208 145.658 149.642 152.998 156.012 158.812 161.478 164.055 166.569 169.049 194.208

160 120.837 129.015 136.798 141.167 146.641 150.644 154.016 157.047 159.861 162.542 165.130 167.659 170.151 195.455

161 121.715 129.924 137.739 142.127 147.625 151.647 155.038 158.082 160.910 163.605 166.208 168.748 171.256 196.705

162 122.590 130.834 138.680 143.089 148.611 152.652 156.056 159.114 161.959 164.668 167.283 169.838 172.358 197.951

163 123.468 131.743 139.623 144.049 149.598 153.654 157.078 160.149 163.008 165.729 168.361 170.928 173.460 199.201

164 124.346 132.655 140.567 145.011 150.581 154.659 158.096 161.184 164.057 166.792 169.435 172.018 174.565 200.448

165 125.224 133.564 141.508 145.971 151.567 155.664 159.117 162.219 165.106 167.855 170.513 173.111 175.670 201.694

166 126.101 134.476 142.451 146.933 152.554 156.667 160.139 163.254 166.155 168.919 171.588 174.200 176.772 202.944

167 126.979 135.388 143.395 147.896 153.540 157.672 161.157 164.289 167.207 169.982 172.666 175.290 177.877 204.191

168 127.857 136.297 144.338 148.855 154.524 158.677 162.179 165.325 168.257 171.045 173.744 176.380 178.978 205.441

169 128.738 137.209 145.282 149.818 155.510 159.682 163.200 166.363 169.306 172.109 174.819 177.469 180.083 206.688

170 129.619 138.121 146.226 150.780 156.497 160.684 164.219 167.398 170.355 173.172 175.897 178.559 181.185 207.934

171 130.496 139.036 147.169 151.742 157.483 161.690 165.240 168.433 171.404 174.235 176.975 179.652 182.290 209.184

172 131.377 139.948 148.113 152.708 158.472 162.695 166.262 169.468 172.456 175.299 178.050 180.742 183.395 210.431

173 132.258 140.860 149.059 153.670 159.459 163.700 167.283 170.503 173.505 176.362 179.127 181.832 184.497 211.681

174 133.141 141.775 150.003 154.632 160.445 164.705 168.304 171.541 174.554 177.425 180.205 182.921 185.602 212.927

175 134.022 142.690 150.949 155.595 161.431 165.710 169.326 172.576 175.606 178.492 181.283 184.014 186.707 214.177

176 134.905 143.602 151.893 156.560 162.421 166.718 170.347 173.614 176.655 179.555 182.358 185.104 187.812 215.424

177 135.786 144.517 152.839 157.522 163.407 167.723 171.369 174.649 177.707 180.618 183.436 186.194 188.914 216.674

178 136.669 145.432 153.786 158.488 164.393 168.729 172.390 175.684 178.756 181.682 184.514 187.286 190.019 217.920

179 137.553 146.346 154.732 159.450 165.383 169.734 173.411 176.722 179.805 182.748 185.592 188.376 191.123 219.167

180 138.436 147.261 155.678 160.415 166.369 170.742 174.433 177.757 180.857 183.811 186.670 189.466 192.228 220.417

Erlang Tables

9-7

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


181 139.319 148.179 156.625 161.380 167.358 171.747 175.457 178.795 181.909 184.875 187.748 190.559 193.330 221.663

182 140.203 149.094 157.571 162.346 168.348 172.752 176.479 179.830 182.958 185.938 188.825 191.648 194.435 222.913

183 141.089 150.008 158.518 163.311 169.334 173.760 177.500 180.868 184.010 187.004 189.903 192.741 195.540 224.160

184 141.973 150.926 159.464 164.273 170.323 174.765 178.521 181.906 185.059 188.068 190.981 193.831 196.645 225.410

185 142.859 151.844 160.410 165.238 171.312 175.773 179.546 182.942 186.111 189.134 192.059 194.924 197.750 226.656

186 143.745 152.758 161.360 166.204 172.302 176.778 180.567 183.980 187.163 190.197 193.137 196.013 198.855 227.906

187 144.631 153.676 162.306 167.172 173.291 177.786 181.591 185.018 188.212 191.260 194.215 197.106 199.960 229.153

188 145.517 154.593 163.255 168.137 174.280 178.794 182.613 186.053 189.264 192.327 195.293 198.196 201.065 230.403

189 146.404 155.511 164.202 169.102 175.269 179.800 183.637 187.091 190.316 193.390 196.371 199.289 202.167 231.649

190 147.290 156.429 165.151 170.067 176.259 180.808 184.659 188.129 191.365 194.456 197.449 200.379 203.272 232.899

191 148.179 157.349 166.100 171.035 177.248 181.816 185.683 189.167 192.417 195.520 198.527 201.471 204.377 234.146

192 149.065 158.267 167.049 172.001 178.237 182.824 186.704 190.205 193.469 196.586 199.604 202.561 205.481 235.396

193 149.954 159.184 167.998 172.969 179.226 183.829 187.729 191.243 194.521 197.652 200.682 203.654 206.586 236.646

194 150.843 160.105 168.948 173.934 180.215 184.837 188.750 192.278 195.573 198.716 201.763 204.747 207.691 237.892

195 151.729 161.025 169.897 174.902 181.207 185.845 189.774 193.316 196.625 199.782 202.841 205.836 208.796 239.142

196 152.618 161.942 170.846 175.867 182.197 186.853 190.799 194.354 197.677 200.845 203.919 206.929 209.901 240.389

197 153.510 162.863 171.795 176.835 183.186 187.861 191.823 195.392 198.726 201.912 204.997 208.022 211.006 241.639

198 154.399 163.783 172.744 177.803 184.178 188.869 192.844 196.430 199.778 202.978 206.075 209.112 212.111 242.885

199 155.288 164.704 173.693 178.771 185.167 189.877 193.869 197.468 200.830 204.041 207.156 210.205 213.216 244.135

200 156.177 165.624 174.645 179.739 186.159 190.885 194.893 198.506 201.882 205.108 208.234 211.297 214.324 245.382

201 157.068 166.544 175.595 180.707 187.149 191.893 195.917 199.547 202.934 206.174 209.312 212.387 215.429 246.632

202 157.960 167.465 176.547 181.675 188.141 192.904 196.942 200.585 203.986 207.240 210.389 213.480 216.534 247.882

203 158.849 168.388 177.496 182.643 189.130 193.912 197.966 201.623 205.038 208.303 211.470 214.573 217.639 249.128

204 159.741 169.308 178.448 183.611 190.122 194.920 198.990 202.661 206.093 209.370 212.548 215.665 218.744 250.378

205 160.633 170.231 179.400 184.579 191.114 195.928 200.014 203.699 207.145 210.436 213.626 216.755 219.849 251.625

206 161.524 171.152 180.349 185.547 192.103 196.939 201.039 204.737 208.197 211.502 214.707 217.848 220.954 252.875

207 162.419 172.075 181.301 186.515 193.095 197.947 202.063 205.778 209.249 212.566 215.785 218.941 222.059 254.122

208 163.311 172.995 182.253 187.486 194.087 198.955 203.087 206.816 210.301 213.632 216.866 220.034 223.167 255.372

209 164.203 173.918 183.205 188.454 195.079 199.966 204.112 207.854 211.353 214.698 217.944 221.126 224.272 256.622

210 165.097 174.842 184.157 189.422 196.071 200.974 205.136 208.892 212.405 215.765 219.022 222.219 225.377 257.868

Erlang Tables

.

9-8

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


211 165.989 175.765 185.109 190.393 197.063 201.985 206.160 209.933 213.460 216.831 220.103 223.309 226.481 259.118

212 166.883 176.688 186.061 191.361 198.056 202.993 207.185 210.971 214.512 217.897 221.181 224.402 227.586 260.365

213 167.778 177.611 187.013 192.332 199.048 204.003 208.209 212.012 215.564 218.964 222.261 225.495 228.694 261.615

214 168.672 178.537 187.968 193.302 200.040 205.011 209.236 213.050 216.616 220.030 223.339 226.587 229.799 262.865

215 169.567 179.460 188.920 194.270 201.032 206.022 210.260 214.088 217.671 221.096 224.420 227.680 230.904 264.111

216 170.461 180.383 189.872 195.241 202.024 207.033 211.285 215.129 218.723 222.162 225.498 228.773 232.009 265.361

217 171.356 181.309 190.826 196.212 203.016 208.041 212.309 216.167 219.775 223.229 226.579 229.866 233.117 266.608

218 172.251 182.232 191.778 197.183 204.011 209.052 213.336 217.208 220.830 224.295 227.657 230.958 234.222 267.858

219 173.148 183.158 192.733 198.151 205.003 210.063 214.361 218.246 221.882 225.361 228.738 232.051 235.327 269.108

220 174.042 184.081 193.685 199.122 205.995 211.071 215.385 219.287 222.937 226.428 229.816 233.144 236.432 270.354

221 174.940 185.007 194.640 200.093 206.987 212.082 216.412 220.325 223.989 227.494 230.897 234.237 237.540 271.604

222 175.834 185.933 195.595 201.063 207.982 213.093 217.436 221.365 225.041 228.560 231.978 235.330 238.645 272.854

223 176.732 186.859 196.549 202.034 208.974 214.104 218.464 222.406 226.096 229.627 233.056 236.422 239.750 274.101

224 177.629 187.785 197.501 203.005 209.969 215.115 219.488 223.444 227.148 230.693 234.136 237.515 240.858 275.351

225 178.526 188.711 198.456 203.976 210.961 216.125 220.515 224.485 228.203 231.759 235.214 238.608 241.963 276.597

226 179.423 189.637 199.411 204.949 211.956 217.136 221.539 225.523 229.255 232.826 236.295 239.701 243.068 277.847

227 180.321 190.563 200.366 205.920 212.948 218.144 222.567 226.564 230.310 233.895 237.376 240.794 244.176 279.097

228 181.218 191.489 201.320 206.891 213.943 219.155 223.591 227.605 231.362 234.961 238.454 241.886 245.281 280.344

229 182.118 192.417 202.275 207.862 214.935 220.166 224.618 228.646 232.417 236.027 239.535 242.979 246.389 281.594

230 183.016 193.343 203.230 208.836 215.930 221.180 225.645 229.684 233.469 237.094 240.616 244.072 247.494 282.844

231 183.916 194.269 204.188 209.806 216.925 222.191 226.670 230.725 234.524 238.160 241.694 245.165 248.599 284.090

232 184.813 195.198 205.142 210.780 217.917 223.202 227.697 231.766 235.579 239.229 242.775 246.258 249.707 285.340

233 185.713 196.127 206.097 211.751 218.912 224.212 228.724 232.807 236.631 240.296 243.856 247.350 250.812 286.590

234 186.613 197.053 207.055 212.724 219.906 225.223 229.748 233.845 237.686 241.362 244.937 248.443 251.920 287.837

235 187.510 197.981 208.009 213.695 220.901 226.234 230.775 234.886 238.738 242.428 246.014 249.539 253.025 289.087

236 188.411 198.910 208.964 214.669 221.896 227.245 231.803 235.927 239.793 243.498 247.095 250.632 254.130 290.337

237 189.311 199.839 209.922 215.643 222.888 228.259 232.830 236.968 240.848 244.564 248.176 251.725 255.238 291.583

238 190.211 200.767 210.877 216.613 223.883 229.270 233.854 238.009 241.903 245.630 249.257 252.817 256.343 292.833

239 191.114 201.696 211.834 217.587 224.878 230.281 234.881 239.050 242.955 246.700 250.335 253.910 257.451 294.083

240 192.014 202.625 212.792 218.561 225.873 231.292 235.909 240.091 244.010 247.766 251.416 255.003 258.556 295.330

Erlang Tables

9-9

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


241 192.914 203.554 213.747 219.534 226.868 232.305 236.936 241.132 245.065 248.832 252.497 256.099 259.664 296.580

242 193.817 204.482 214.704 220.508 227.863 233.316 237.963 242.173 246.117 249.901 253.578 257.192 260.769 297.830

243 194.717 205.411 215.662 221.479 228.858 234.327 238.990 243.213 247.172 250.968 254.659 258.284 261.877 299.076

244 195.620 206.340 216.619 222.452 229.853 235.341 240.017 244.254 248.227 252.034 255.740 259.377 262.981 300.326

245 196.520 207.271 217.577 223.426 230.850 236.352 241.042 245.295 249.282 253.103 256.821 260.473 264.090 301.576

246 197.423 208.200 218.534 224.400 231.845 237.365 242.069 246.336 250.337 254.170 257.899 261.566 265.194 302.823

247 198.325 209.131 219.492 225.373 232.840 238.376 243.096 247.377 251.389 255.239 258.979 262.659 266.302 304.073

248 199.228 210.060 220.449 226.350 233.835 239.390 244.123 248.418 252.444 256.305 260.060 263.752 267.410 305.323

249 200.131 210.992 221.407 227.323 234.830 240.401 245.150 249.459 253.499 257.375 261.141 264.847 268.515 306.569

250 201.034 211.923 222.365 228.297 235.828 241.415 246.181 250.500 254.554 258.441 262.222 265.940 269.623 307.819

251 201.937 212.852 223.322 229.270 236.823 242.426 247.208 251.541 255.609 259.507 263.303 267.033 270.728 309.069

252 202.840 213.783 224.280 230.244 237.817 243.439 248.235 252.582 256.664 260.576 264.384 268.126 271.836 310.319

253 203.745 214.715 225.240 231.221 238.815 244.453 249.262 253.623 257.719 261.643 265.465 269.222 272.941 311.566

254 204.648 215.646 226.198 232.194 239.810 245.464 250.289 254.664 258.774 262.712 266.546 270.314 274.049 312.816

255 205.551 216.578 227.155 233.168 240.808 246.478 251.317 255.708 259.829 263.778 267.627 271.407 275.157 314.066

256 206.457 217.509 228.116 234.144 241.803 247.491 252.344 256.749 260.884 264.848 268.708 272.503 276.262 315.313

257 207.362 218.441 229.073 235.118 242.798 248.502 253.371 257.789 261.939 265.917 269.789 273.596 277.370 316.563

258 208.265 219.372 230.031 236.094 243.795 249.516 254.401 258.830 262.993 266.983 270.870 274.689 278.475 317.813

259 209.171 220.306 230.991 237.068 244.790 250.530 255.428 259.874 264.048 268.053 271.950 275.784 279.583 319.063

260 210.077 221.238 231.951 238.044 245.788 251.544 256.455 260.915 265.103 269.119 273.031 276.877 280.691 320.309

261 210.982 222.169 232.909 239.018 246.786 252.557 257.483 261.956 266.158 270.188 274.112 277.970 281.796 321.559

262 211.888 223.104 233.869 239.994 247.781 253.568 258.513 262.997 267.213 271.254 275.193 279.066 282.904 322.809

263 212.794 224.035 234.830 240.971 248.778 254.582 259.540 264.041 268.268 272.324 276.274 280.159 284.012 324.056

264 213.699 224.969 235.787 241.944 249.776 255.596 260.567 265.082 269.323 273.393 277.355 281.255 285.117 325.306

265 214.605 225.901 236.748 242.921 250.771 256.609 261.597 266.123 270.378 274.459 278.436 282.347 286.225 326.556

266 215.510 226.835 237.708 243.897 251.769 257.623 262.624 267.167 271.433 275.529 279.517 283.440 287.333 327.806

267 216.419 227.767 238.668 244.871 252.766 258.637 263.652 268.208 272.488 276.598 280.598 284.536 288.438 329.052

268 217.325 228.701 239.629 245.847 253.761 259.651 264.682 269.249 273.543 277.664 281.679 285.629 289.546 330.302

269 218.233 229.635 240.589 246.824 254.759 260.664 265.709 270.292 274.598 278.734 282.760 286.725 290.654 331.552

270 219.139 230.569 241.549 247.800 255.757 261.678 266.736 271.333 275.653 279.803 283.841 287.817 291.759 332.802

Erlang Tables

.

9-10

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


271 220.047 231.504 242.510 248.777 256.755 262.692 267.766 272.377 276.708 280.869 284.925 288.913 292.867 334.049

272 220.953 232.438 243.470 249.753 257.752 263.706 268.793 273.418 277.766 281.938 286.005 290.006 293.975 335.299

273 221.861 233.372 244.430 250.730 258.750 264.719 269.823 274.462 278.821 283.008 287.086 291.099 295.083 336.549

274 222.769 234.307 245.391 251.706 259.748 265.733 270.851 275.503 279.876 284.074 288.167 292.195 296.188 337.795

275 223.678 235.241 246.351 252.682 260.745 266.747 271.881 276.544 280.931 285.143 289.248 293.288 297.296 339.045

276 224.586 236.175 247.312 253.659 261.743 267.761 272.908 277.588 281.986 286.213 290.329 294.383 298.404 340.295

277 225.495 237.109 248.275 254.635 262.741 268.774 273.938 278.629 283.044 287.282 291.410 295.476 299.512 341.545

278 226.403 238.044 249.235 255.612 263.739 269.791 274.965 279.673 284.099 288.348 292.494 296.572 300.617 342.792

279 227.312 238.981 250.195 256.591 264.736 270.805 275.995 280.713 285.154 289.418 293.575 297.665 301.725 344.042

280 228.220 239.915 251.159 257.567 265.734 271.818 277.023 281.757 286.209 290.487 294.656 298.761 302.833 345.292

281 229.128 240.849 252.119 258.544 266.732 272.832 278.053 282.801 287.267 291.556 295.737 299.853 303.941 346.542

282 230.051 241.797 253.071 259.512 267.744 273.855 279.080 283.830 288.327 292.622 296.830 300.946 305.062 347.778

283 230.940 242.715 254.048 260.494 268.736 274.857 280.122 284.883 289.391 293.698 297.886 302.045 306.142 349.028

284 231.857 243.660 254.997 261.476 269.728 275.888 281.134 285.936 290.426 294.773 298.973 303.144 307.253 350.278

285 232.773 244.606 255.974 262.458 270.720 276.890 282.176 286.959 291.489 295.818 300.060 304.243 308.364 351.528

286 233.690 245.523 256.924 263.440 271.712 277.892 283.189 288.012 292.553 296.894 301.147 305.342 309.475 352.778

287 234.579 246.469 257.901 264.422 272.732 278.923 284.230 289.064 293.587 297.969 302.234 306.410 310.586 354.028

288 235.496 247.414 258.850 265.376 273.724 279.926 285.243 290.088 294.651 299.044 303.321 307.509 311.698 355.278

289 236.413 248.332 259.827 266.358 274.717 280.956 286.285 291.140 295.715 300.119 304.378 308.608 312.809 356.528

290 237.329 249.277 260.776 267.340 275.709 281.959 287.326 292.193 296.779 301.165 305.465 309.707 313.920 357.778

291 238.218 250.222 261.753 268.322 276.729 282.990 288.339 293.216 297.813 302.240 306.552 310.806 315.000 359.028

292 239.135 251.140 262.702 269.304 277.721 283.992 289.381 294.269 298.877 303.315 307.639 311.905 316.111 360.278

293 240.052 252.085 263.680 270.286 278.713 285.023 290.394 295.322 299.941 304.391 308.726 313.004 317.222 361.528

294 240.969 253.031 264.629 271.268 279.705 286.025 291.435 296.345 301.005 305.436 309.813 314.072 318.333 362.778

295 241.885 253.948 265.578 272.222 280.697 287.027 292.477 297.398 302.039 306.511 310.870 315.171 319.444 364.028

296 242.802 254.894 266.555 273.204 281.718 288.058 293.490 298.450 303.103 307.587 311.957 316.270 320.556 365.278

297 243.691 255.839 267.504 274.186 282.710 289.061 294.531 299.474 304.167 308.662 313.043 317.369 321.667 366.528

298 244.608 256.785 268.481 275.168 283.702 290.092 295.544 300.526 305.230 309.737 314.130 318.468 322.778 367.778

299 245.525 257.702 269.430 276.150 284.694 291.094 296.586 301.579 306.265 310.783 315.217 319.567 323.889 369.028

300 246.441 258.648 270.408 277.132 285.714 292.125 297.598 302.602 307.329 311.858 316.304 320.665 324.969 370.278

Erlang Tables

9-11

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


301 247.358 259.593 271.385 278.114 286.706 293.127 298.640 303.655 308.392 312.933 317.361 321.734 326.080 371.528

302 248.275 260.538 272.334 279.097 287.698 294.158 299.682 304.708 309.456 314.008 318.448 322.833 327.191 372.778

303 249.164 261.456 273.311 280.051 288.690 295.160 300.694 305.760 310.491 315.084 319.535 323.932 328.302 374.028

304 250.081 262.401 274.260 281.033 289.711 296.191 301.736 306.784 311.554 316.129 320.622 325.031 329.414 375.278

305 250.997 263.347 275.237 282.015 290.703 297.194 302.749 307.836 312.618 317.204 321.709 326.129 330.525 376.528

306 251.914 264.292 276.186 282.997 291.695 298.196 303.791 308.889 313.682 318.280 322.796 327.228 331.636 377.778

307 252.831 265.210 277.164 283.979 292.715 299.227 304.832 309.912 314.716 319.355 323.853 328.327 332.747 379.028

308 253.748 266.155 278.113 284.961 293.707 300.229 305.845 310.965 315.780 320.430 324.940 329.426 333.858 380.278

309 254.664 267.100 279.090 285.943 294.700 301.260 306.887 312.018 316.844 321.476 326.027 330.495 334.938 381.528

310 255.581 268.046 280.039 286.925 295.692 302.262 307.899 313.041 317.908 322.551 327.114 331.593 336.049 382.778

311 256.498 268.963 281.016 287.907 296.712 303.293 308.941 314.094 318.942 323.626 328.200 332.692 337.160 384.028

312 257.387 269.909 281.965 288.889 297.704 304.296 309.983 315.146 320.006 324.701 329.287 333.791 338.272 385.278

313 258.304 270.854 282.942 289.843 298.696 305.326 310.995 316.170 321.070 325.777 330.344 334.890 339.383 386.528

314 259.220 271.800 283.892 290.825 299.688 306.329 312.037 317.222 322.134 326.822 331.431 335.989 340.494 387.778

315 260.137 272.745 284.869 291.807 300.709 307.360 313.050 318.275 323.168 327.897 332.518 337.088 341.605 389.028

316 261.054 273.663 285.846 292.789 301.701 308.362 314.091 319.298 324.232 328.973 333.605 338.156 342.716 390.278

317 261.971 274.608 286.795 293.771 302.693 309.393 315.133 320.351 325.296 330.048 334.692 339.255 343.827 391.528

318 262.887 275.553 287.772 294.753 303.713 310.395 316.146 321.404 326.359 331.123 335.779 340.354 344.938 392.778

319 263.804 276.499 288.721 295.735 304.705 311.426 317.188 322.456 327.394 332.198 336.866 341.453 346.019 394.028

320 264.721 277.444 289.698 296.717 305.697 312.428 318.200 323.480 328.457 333.244 337.923 342.552 347.130 395.278

321 265.638 278.362 290.648 297.699 306.718 313.459 319.242 324.532 329.521 334.319 339.010 343.651 348.241 396.493

322 266.554 279.307 291.625 298.681 307.710 314.462 320.284 325.585 330.585 335.394 340.097 344.750 349.352 397.743

323 267.471 280.252 292.602 299.663 308.702 315.493 321.296 326.608 331.619 336.470 341.184 345.849 350.463 398.993

324 268.388 281.198 293.551 300.645 309.694 316.495 322.338 327.661 332.683 337.545 342.271 346.917 351.574 400.243

325 269.305 282.143 294.528 301.627 310.714 317.526 323.380 328.713 333.747 338.590 343.357 348.016 352.685 401.493

326 270.221 283.089 295.477 302.609 311.706 318.528 324.392 329.766 334.811 339.665 344.414 349.115 353.796 402.743

327 271.138 284.034 296.454 303.591 312.698 319.559 325.434 330.789 335.875 340.741 345.501 350.214 354.907 403.993

328 272.055 284.952 297.432 304.574 313.719 320.561 326.447 331.842 336.909 341.816 346.588 351.313 356.019 405.243

329 272.972 285.897 298.381 305.527 314.711 321.592 327.488 332.895 337.973 342.891 347.675 352.411 357.099 406.493

330 273.888 286.842 299.358 306.510 315.703 322.595 328.530 333.918 339.037 343.967 348.762 353.510 358.210 407.743

Erlang Tables

.

9-12

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


331 274.805 287.788 300.307 307.492 316.723 323.625 329.543 334.971 340.100 345.012 349.849 354.609 359.321 408.993

332 275.722 288.733 301.284 308.474 317.715 324.628 330.584 336.023 341.135 346.087 350.936 355.708 360.432 410.243

333 276.639 289.679 302.261 309.456 318.707 325.659 331.626 337.076 342.199 347.162 351.993 356.777 361.543 411.493

334 277.556 290.624 303.210 310.438 319.728 326.661 332.639 338.099 343.262 348.238 353.080 357.875 362.654 412.743

335 278.472 291.542 304.188 311.420 320.720 327.692 333.681 339.152 344.326 349.313 354.167 358.974 363.765 413.993

336 279.389 292.487 305.165 312.402 321.712 328.694 334.693 340.205 345.390 350.358 355.254 360.073 364.877 415.243

337 280.306 293.432 306.114 313.384 322.704 329.725 335.735 341.228 346.424 351.434 356.341 361.172 365.988 416.493

338 281.223 294.378 307.091 314.366 323.724 330.727 336.777 342.281 347.488 352.509 357.428 362.271 367.099 417.743

339 282.139 295.323 308.040 315.348 324.717 331.758 337.789 343.333 348.552 353.584 358.514 363.370 368.179 418.993

340 283.056 296.268 309.017 316.330 325.709 332.761 338.831 344.386 349.616 354.659 359.571 364.469 369.290 420.243

341 283.973 297.214 309.994 317.312 326.729 333.792 339.873 345.409 350.650 355.735 360.658 365.537 370.401 421.493

342 284.890 298.159 310.944 318.294 327.721 334.794 340.885 346.462 351.714 356.780 361.745 366.636 371.512 422.743

343 285.806 299.105 311.921 319.276 328.713 335.825 341.927 347.515 352.778 357.855 362.832 367.735 372.623 423.993

344 286.723 300.050 312.898 320.258 329.734 336.827 342.969 348.538 353.842 358.931 363.919 368.834 373.735 425.243

345 287.668 300.968 313.847 321.240 330.726 337.858 343.981 349.591 354.905 360.006 365.006 369.933 374.846 426.493

346 288.584 301.913 314.824 322.222 331.718 338.860 345.023 350.643 355.940 361.081 366.093 371.032 375.957 427.743

347 289.501 302.858 315.801 323.204 332.738 339.891 346.065 351.696 357.004 362.157 367.150 372.131 377.068 428.993

348 290.418 303.804 316.750 324.186 333.730 340.893 347.078 352.719 358.067 363.202 368.237 373.230 378.179 430.243

349 291.335 304.749 317.728 325.168 334.722 341.924 348.119 353.772 359.131 364.277 369.324 374.328 379.290 431.493

350 292.251 305.695 318.705 326.150 335.743 342.955 349.132 354.825 360.195 365.352 370.411 375.397 380.370 432.743

351 293.168 306.640 319.654 327.132 336.735 343.958 350.174 355.877 361.229 366.428 371.498 376.496 381.481 433.993

352 294.085 307.585 320.631 328.114 337.755 344.989 351.215 356.901 362.293 367.503 372.585 377.595 382.593 435.243

353 295.002 308.531 321.580 329.097 338.747 345.991 352.228 357.953 363.357 368.578 373.671 378.694 383.704 436.493

354 295.946 309.476 322.557 330.079 339.739 347.022 353.270 359.006 364.421 369.624 374.758 379.792 384.815 437.743

355 296.863 310.422 323.534 331.061 340.760 348.024 354.311 360.029 365.455 370.699 375.815 380.891 385.926 438.993

356 297.780 311.367 324.511 332.043 341.752 349.055 355.324 361.082 366.519 371.774 376.902 381.990 387.037 440.243

357 298.697 312.312 325.461 333.025 342.744 350.057 356.366 362.135 367.583 372.849 377.989 383.089 388.148 441.493

358 299.613 313.258 326.438 334.007 343.764 351.088 357.407 363.187 368.647 373.925 379.076 384.188 389.259 442.743

359 300.530 314.203 327.415 334.989 344.756 352.090 358.420 364.211 369.710 375.000 380.163 385.287 390.370 443.993

360 301.447 315.148 328.364 335.971 345.748 353.121 359.462 365.263 370.745 376.045 381.250 386.355 391.481 445.243

Erlang Tables

9-13

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


361 302.391 316.094 329.341 336.953 346.769 354.124 360.503 366.316 371.809 377.121 382.337 387.454 392.562 446.493

362 303.308 317.039 330.318 337.935 347.761 355.155 361.516 367.368 372.872 378.196 383.424 388.553 393.673 447.743

363 304.225 317.985 331.267 338.917 348.753 356.186 362.558 368.392 373.936 379.271 384.481 389.652 394.784 448.993

364 305.142 318.930 332.245 339.899 349.773 357.188 363.600 369.444 375.000 380.346 385.568 390.751 395.895 450.243

365 306.058 319.875 333.222 340.881 350.765 358.219 364.612 370.497 376.034 381.422 386.655 391.850 397.006 451.493

366 306.975 320.821 334.171 341.863 351.786 359.221 365.654 371.550 377.098 382.467 387.742 392.949 398.117 452.743

367 307.920 321.766 335.148 342.845 352.778 360.252 366.696 372.573 378.162 383.542 388.829 394.048 399.228 453.993

368 308.836 322.684 336.125 343.855 353.770 361.254 367.708 373.626 379.226 384.618 389.915 395.147 400.340 455.243

369 309.753 323.629 337.102 344.837 354.790 362.285 368.750 374.678 380.290 385.693 391.002 396.215 401.451 456.493

370 310.670 324.602 338.051 345.819 355.782 363.288 369.792 375.731 381.324 386.768 392.059 397.314 402.562 457.743

371 311.587 325.548 339.028 346.801 356.774 364.318 370.804 376.754 382.388 387.843 393.146 398.413 403.673 458.993

372 312.531 326.493 340.006 347.783 357.795 365.321 371.846 377.807 383.452 388.889 394.233 399.512 404.784 460.243

373 313.448 327.439 340.955 348.765 358.787 366.352 372.888 378.860 384.515 389.964 395.320 400.611 405.864 461.493

374 314.365 328.384 341.932 349.747 359.807 367.383 373.900 379.912 385.579 391.039 396.407 401.709 406.975 462.743

375 315.282 329.329 342.909 350.730 360.799 368.385 374.942 380.936 386.613 392.115 397.494 402.808 408.086 463.993

376 316.198 330.275 343.886 351.712 361.791 369.416 375.984 381.988 387.677 393.190 398.581 403.907 409.198 465.243

377 317.143 331.220 344.835 352.694 362.812 370.418 376.997 383.041 388.741 394.265 399.668 405.006 410.309 466.493

378 318.060 332.165 345.812 353.676 363.804 371.449 378.038 384.094 389.805 395.341 400.725 406.105 411.420 467.743

379 318.976 333.111 346.790 354.658 364.824 372.451 379.080 385.117 390.869 396.386 401.812 407.173 412.531 468.958

380 319.893 334.056 347.739 355.640 365.816 373.482 380.093 386.170 391.903 397.461 402.899 408.272 413.642 470.208

381 320.838 335.002 348.716 356.622 366.808 374.513 381.134 387.222 392.967 398.536 403.986 409.371 414.753 471.458

382 321.754 335.947 349.693 357.604 367.829 375.515 382.176 388.275 394.031 399.612 405.072 410.470 415.864 472.708

383 322.671 336.892 350.670 358.586 368.821 376.546 383.189 389.298 395.095 400.687 406.159 411.569 416.975 473.958

384 323.588 337.838 351.619 359.568 369.841 377.549 384.230 390.351 396.158 401.762 407.246 412.668 418.086 475.208

385 324.532 338.783 352.596 360.578 370.833 378.580 385.272 391.404 397.222 402.808 408.333 413.767 419.167 476.458

386 325.449 339.729 353.573 361.560 371.825 379.582 386.285 392.456 398.257 403.883 409.420 414.866 420.278 477.708

387 326.366 340.674 354.551 362.542 372.846 380.613 387.326 393.480 399.320 404.958 410.477 415.965 421.389 478.958

388 327.283 341.619 355.500 363.524 373.838 381.644 388.368 394.532 400.384 406.033 411.564 417.063 422.500 480.208

389 328.227 342.565 356.477 364.506 374.858 382.646 389.410 395.585 401.448 407.109 412.651 418.132 423.611 481.458

390 329.144 343.510 357.454 365.488 375.850 383.677 390.422 396.637 402.512 408.184 413.738 419.231 424.722 482.708

Erlang Tables

.

9-14

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


391 330.061 344.456 358.431 366.470 376.842 384.679 391.464 397.661 403.546 409.259 414.825 420.330 425.833 483.958

392 330.978 345.401 359.380 367.452 377.863 385.710 392.506 398.713 404.610 410.305 415.912 421.429 426.944 485.208

393 331.922 346.346 360.357 368.434 378.855 386.712 393.519 399.766 405.674 411.380 416.999 422.527 428.056 486.458

394 332.839 347.320 361.334 369.416 379.875 387.743 394.560 400.819 406.738 412.455 418.086 423.626 429.167 487.708

395 333.756 348.265 362.312 370.398 380.867 388.774 395.602 401.842 407.801 413.530 419.143 424.725 430.278 488.958

396 334.700 349.210 363.289 371.380 381.859 389.777 396.615 402.895 408.836 414.606 420.229 425.824 431.389 490.208

397 335.617 350.156 364.238 372.391 382.880 390.808 397.656 403.947 409.900 415.681 421.316 426.923 432.500 491.458

398 336.534 351.101 365.215 373.373 383.872 391.810 398.698 405.000 410.963 416.756 422.403 428.022 433.611 492.708

399 337.478 352.046 366.192 374.355 384.892 392.841 399.711 406.053 412.027 417.802 423.490 429.121 434.691 493.958

400 338.395 352.992 367.169 375.337 385.884 393.872 400.752 407.076 413.091 418.877 424.577 430.189 435.802 495.208

401 339.312 353.937 368.118 376.319 386.876 394.874 401.794 408.129 414.155 419.952 425.664 431.288 436.914 496.458

402 340.256 354.883 369.095 377.301 387.897 395.905 402.836 409.181 415.189 421.027 426.751 432.387 438.025 497.708

403 341.173 355.828 370.073 378.283 388.889 396.907 403.848 410.234 416.253 422.103 427.838 433.486 439.136 498.958

404 342.090 356.773 371.050 379.265 389.909 397.938 404.890 411.257 417.317 423.178 428.895 434.585 440.247 500.208

405 343.007 357.747 372.027 380.247 390.901 398.969 405.932 412.310 418.381 424.253 429.982 435.684 441.358 501.458

406 343.951 358.692 372.976 381.257 391.922 399.971 406.944 413.363 419.444 425.299 431.069 436.783 442.469 502.708

407 344.868 359.637 373.953 382.239 392.914 401.002 407.986 414.415 420.508 426.374 432.156 437.882 443.580 503.958

408 345.812 360.583 374.930 383.221 393.906 402.005 409.028 415.439 421.543 427.449 433.243 438.980 444.691 505.208

409 346.729 361.528 375.907 384.203 394.926 403.036 410.041 416.491 422.606 428.524 434.330 440.079 445.802 506.458

410 347.646 362.474 376.884 385.185 395.918 404.038 411.082 417.544 423.670 429.600 435.417 441.178 446.914 507.708

411 348.590 363.419 377.834 386.167 396.939 405.069 412.124 418.596 424.734 430.675 436.504 442.247 448.025 508.958

412 349.507 364.364 378.811 387.149 397.931 406.100 413.166 419.649 425.798 431.750 437.591 443.346 449.105 510.208

413 350.424 365.338 379.788 388.131 398.951 407.102 414.178 420.673 426.832 432.826 438.647 444.444 450.216 511.458

414 351.368 366.283 380.765 389.113 399.943 408.133 415.220 421.725 427.896 433.871 439.734 445.543 451.327 512.708

415 352.285 367.228 381.742 390.123 400.935 409.164 416.262 422.778 428.960 434.946 440.821 446.642 452.438 513.958

416 353.202 368.174 382.691 391.105 401.956 410.166 417.274 423.830 430.024 436.022 441.908 447.741 453.549 515.208

417 354.147 369.119 383.668 392.088 402.948 411.197 418.316 424.854 431.087 437.097 442.995 448.840 454.660 516.458

418 355.063 370.065 384.645 393.070 403.968 412.199 419.358 425.906 432.151 438.172 444.082 449.939 455.772 517.708

419 356.008 371.010 385.623 394.052 404.960 413.230 420.370 426.959 433.186 439.247 445.169 451.038 456.883 518.958

420 356.925 371.983 386.600 395.034 405.981 414.261 421.412 428.012 434.249 440.323 446.256 452.137 457.994 520.208

Erlang Tables

9-15

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


421 357.841 372.928 387.549 396.016 406.973 415.263 422.454 429.064 435.313 441.368 447.343 453.236 459.105 521.458

422 358.786 373.874 388.526 397.026 407.993 416.294 423.495 430.088 436.377 442.443 448.430 454.335 460.216 522.708

423 359.703 374.819 389.503 398.008 408.985 417.297 424.508 431.140 437.441 443.519 449.487 455.403 461.327 523.958

424 360.647 375.765 390.480 398.990 409.977 418.328 425.550 432.193 438.505 444.594 450.574 456.502 462.438 525.208

425 361.564 376.710 391.457 399.972 410.998 419.359 426.591 433.246 439.539 445.669 451.661 457.601 463.549 526.458

426 362.481 377.683 392.434 400.954 411.990 420.361 427.604 434.269 440.603 446.744 452.748 458.700 464.660 527.708

427 363.425 378.629 393.384 401.936 413.010 421.392 428.646 435.322 441.667 447.820 453.835 459.799 465.741 528.958

428 364.342 379.574 394.361 402.918 414.002 422.394 429.688 436.374 442.730 448.895 454.921 460.897 466.852 530.208

429 365.287 380.519 395.338 403.928 415.023 423.425 430.729 437.427 443.794 449.940 456.008 461.996 467.963 531.458

430 366.203 381.465 396.315 404.910 416.015 424.456 431.742 438.480 444.858 451.016 457.095 463.095 469.074 532.708

431 367.120 382.410 397.292 405.892 417.035 425.458 432.784 439.503 445.892 452.091 458.182 464.194 470.185 533.958

432 368.065 383.383 398.269 406.874 418.027 426.489 433.825 440.556 446.956 453.166 459.239 465.293 471.296 535.208

433 368.981 384.329 399.218 407.856 419.048 427.520 434.838 441.608 448.020 454.241 460.326 466.392 472.407 536.458

434 369.926 385.274 400.195 408.838 420.040 428.522 435.880 442.661 449.084 455.317 461.413 467.491 473.519 537.708

435 370.843 386.220 401.173 409.820 421.032 429.553 436.921 443.713 450.148 456.392 462.500 468.559 474.630 538.958

436 371.787 387.165 402.150 410.831 422.052 430.556 437.963 444.737 451.212 457.437 463.587 469.658 475.741 540.208

437 372.704 388.138 403.127 411.813 423.044 431.586 438.976 445.789 452.246 458.513 464.674 470.757 476.852 541.458

438 373.621 389.084 404.104 412.795 424.065 432.617 440.017 446.842 453.310 459.588 465.761 471.856 477.963 542.708

439 374.565 390.029 405.081 413.777 425.057 433.620 441.059 447.895 454.374 460.663 466.848 472.955 479.074 543.958

440 375.482 390.974 406.030 414.759 426.077 434.651 442.101 448.947 455.437 461.738 467.935 474.054 480.185 545.208

441 376.427 391.920 407.007 415.741 427.069 435.653 443.113 449.971 456.501 462.814 469.022 475.153 481.296 546.458

442 377.343 392.893 407.984 416.751 428.090 436.684 444.155 451.023 457.565 463.889 470.079 476.252 482.377 547.708

443 378.288 393.838 408.961 417.733 429.082 437.715 445.197 452.076 458.599 464.964 471.165 477.350 483.488 548.958

444 379.205 394.784 409.939 418.715 430.102 438.717 446.209 453.129 459.663 466.010 472.252 478.449 484.599 550.208

445 380.149 395.729 410.916 419.697 431.094 439.748 447.251 454.152 460.727 467.085 473.339 479.548 485.710 551.458

446 381.066 396.674 411.893 420.679 432.115 440.779 448.293 455.205 461.791 468.160 474.426 480.647 486.821 552.708

447 382.010 397.648 412.870 421.661 433.107 441.781 449.334 456.257 462.855 469.235 475.513 481.746 487.932 553.958

448 382.927 398.593 413.819 422.671 434.127 442.812 450.347 457.310 463.918 470.311 476.600 482.814 489.043 555.208

449 383.872 399.538 414.796 423.653 435.119 443.843 451.389 458.363 464.982 471.386 477.687 483.913 490.154 556.458

450 384.788 400.484 415.773 424.635 436.139 444.845 452.431 459.386 466.017 472.461 478.774 485.012 491.265 557.708

Erlang Tables

.

9-16

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


451 385.733 401.457 416.750 425.617 437.132 445.876 453.472 460.439 467.080 473.536 479.861 486.111 492.377 558.958

452 386.650 402.402 417.728 426.599 438.124 446.879 454.485 461.491 468.144 474.582 480.918 487.210 493.488 560.208

453 387.594 403.348 418.705 427.609 439.144 447.910 455.527 462.544 469.208 475.657 482.005 488.309 494.599 561.458

454 388.511 404.293 419.682 428.591 440.136 448.940 456.568 463.596 470.272 476.732 483.092 489.408 495.710 562.708

455 389.456 405.266 420.659 429.574 441.156 449.943 457.610 464.620 471.336 477.808 484.179 490.507 496.821 563.958

456 390.372 406.212 421.608 430.556 442.149 450.974 458.623 465.673 472.370 478.883 485.266 491.606 497.932 565.208

457 391.317 407.157 422.585 431.538 443.169 452.005 459.664 466.725 473.434 479.958 486.353 492.705 499.043 566.458

458 392.234 408.103 423.562 432.520 444.161 453.007 460.706 467.778 474.498 481.033 487.440 493.803 500.123 567.674

459 393.178 409.076 424.539 433.530 445.181 454.038 461.719 468.830 475.561 482.109 488.527 494.902 501.235 568.924

460 394.095 410.021 425.516 434.512 446.173 455.069 462.760 469.854 476.625 483.184 489.614 496.001 502.346 570.174

461 395.040 410.967 426.494 435.494 447.194 456.071 463.802 470.906 477.689 484.229 490.700 497.070 503.457 571.424

462 395.956 411.912 427.471 436.476 448.186 457.102 464.844 471.959 478.753 485.305 491.787 498.168 504.568 572.674

463 396.901 412.885 428.448 437.458 449.206 458.104 465.856 473.012 479.787 486.380 492.844 499.267 505.679 573.924

464 397.818 413.830 429.425 438.468 450.198 459.135 466.898 474.064 480.851 487.455 493.931 500.366 506.790 575.174

465 398.762 414.776 430.374 439.450 451.219 460.166 467.940 475.088 481.915 488.530 495.018 501.465 507.901 576.424

466 399.679 415.721 431.351 440.432 452.211 461.168 468.981 476.140 482.979 489.606 496.105 502.564 509.012 577.674

467 400.623 416.694 432.328 441.414 453.231 462.199 469.994 477.193 484.043 490.681 497.192 503.663 510.123 578.924

468 401.540 417.640 433.305 442.396 454.223 463.230 471.036 478.246 485.106 491.756 498.279 504.762 511.235 580.174

469 402.485 418.585 434.283 443.406 455.244 464.233 472.078 479.298 486.170 492.802 499.366 505.861 512.346 581.424

470 403.401 419.531 435.260 444.388 456.236 465.263 473.119 480.351 487.204 493.877 500.453 506.960 513.457 582.674

471 404.346 420.504 436.237 445.370 457.256 466.294 474.132 481.374 488.268 494.952 501.540 508.059 514.568 583.924

472 405.291 421.449 437.214 446.352 458.248 467.297 475.174 482.427 489.332 496.027 502.627 509.158 515.679 585.174

473 406.207 422.395 438.191 447.334 459.269 468.328 476.215 483.480 490.396 497.103 503.714 510.256 516.790 586.424

474 407.152 423.368 439.168 448.345 460.261 469.359 477.257 484.532 491.460 498.178 504.771 511.325 517.870 587.674

475 408.069 424.313 440.145 449.327 461.281 470.361 478.270 485.585 492.524 499.253 505.857 512.424 518.981 588.924

476 409.013 425.259 441.094 450.309 462.273 471.392 479.311 486.608 493.558 500.329 506.944 513.523 520.093 590.174

477 409.930 426.204 442.071 451.291 463.294 472.423 480.353 487.661 494.622 501.404 508.031 514.621 521.204 591.424

478 410.874 427.177 443.049 452.301 464.286 473.425 481.395 488.713 495.686 502.449 509.118 515.720 522.315 592.674

479 411.819 428.123 444.026 453.283 465.306 474.456 482.407 489.766 496.749 503.524 510.205 516.819 523.426 593.924

480 412.736 429.068 445.003 454.265 466.298 475.487 483.449 490.819 497.813 504.600 511.292 517.918 524.537 595.174

Erlang Tables

9-17

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


481 413.680 430.041 445.980 455.247 467.319 476.489 484.491 491.842 498.877 505.675 512.379 519.017 525.648 596.424

482 414.597 430.987 446.957 456.229 468.311 477.520 485.532 492.895 499.941 506.750 513.466 520.116 526.759 597.674

483 415.542 431.932 447.934 457.239 469.331 478.522 486.545 493.947 500.975 507.826 514.553 521.215 527.870 598.924

484 416.458 432.877 448.911 458.221 470.323 479.553 487.587 495.000 502.039 508.901 515.640 522.314 528.981 600.174

485 417.403 433.851 449.888 459.203 471.344 480.584 488.628 496.053 503.103 509.976 516.697 523.413 530.093 601.424

486 418.347 434.796 450.865 460.185 472.336 481.586 489.670 497.105 504.167 511.051 517.784 524.512 531.204 602.674

487 419.264 435.741 451.843 461.195 473.356 482.617 490.683 498.129 505.230 512.097 518.871 525.611 532.315 603.924

488 420.209 436.714 452.820 462.177 474.348 483.648 491.725 499.181 506.294 513.172 519.958 526.679 533.426 605.174

489 421.125 437.660 453.797 463.159 475.368 484.651 492.766 500.234 507.358 514.247 521.045 527.778 534.537 606.424

490 422.070 438.605 454.774 464.141 476.361 485.682 493.808 501.287 508.392 515.323 522.132 528.877 535.648 607.674

491 423.015 439.578 455.723 465.152 477.381 486.712 494.821 502.339 509.456 516.398 523.219 529.976 536.759 608.924

492 423.931 440.524 456.700 466.134 478.373 487.715 495.862 503.363 510.520 517.473 524.306 531.074 537.840 610.174

493 424.876 441.469 457.677 467.116 479.393 488.746 496.904 504.415 511.584 518.548 525.393 532.173 538.951 611.424

494 425.793 442.442 458.654 468.098 480.385 489.777 497.946 505.468 512.648 519.624 526.479 533.272 540.062 612.674

495 426.737 443.388 459.631 469.080 481.406 490.779 498.958 506.520 513.712 520.699 527.566 534.371 541.173 613.924

496 427.682 444.333 460.609 470.090 482.398 491.810 500.000 507.573 514.775 521.744 528.653 535.470 542.284 615.174

497 428.598 445.306 461.586 471.072 483.418 492.841 501.042 508.626 515.839 522.820 529.710 536.569 543.395 616.424

498 429.543 446.252 462.563 472.054 484.439 493.843 502.083 509.649 516.874 523.895 530.797 537.668 544.506 617.674

499 430.487 447.197 463.540 473.036 485.431 494.874 503.096 510.702 517.937 524.970 531.884 538.767 545.617 618.924

500 431.404 448.170 464.517 474.046 486.451 495.905 504.138 511.754 519.001 526.045 532.971 539.866 546.728 620.174

501 432.349 449.116 465.494 475.028 487.443 496.907 505.179 512.807 520.065 527.121 534.058 540.965 547.840 621.424

502 433.266 450.061 466.471 476.010 488.464 497.938 506.221 513.860 521.129 528.196 535.145 542.063 548.951 622.674

503 434.210 451.034 467.448 476.992 489.456 498.969 507.234 514.883 522.193 529.271 536.232 543.132 550.062 623.924

504 435.155 451.980 468.425 478.002 490.476 499.971 508.275 515.936 523.257 530.346 537.319 544.231 551.173 625.174

505 436.071 452.925 469.403 478.984 491.468 501.002 509.317 516.988 524.291 531.422 538.406 545.330 552.284 626.424

506 437.016 453.898 470.380 479.966 492.489 502.033 510.359 518.041 525.355 532.467 539.493 546.429 553.395 627.674

507 437.960 454.844 471.357 480.948 493.481 503.036 511.400 519.094 526.418 533.542 540.580 547.527 554.506 628.924

508 438.877 455.789 472.334 481.958 494.501 504.066 512.413 520.146 527.482 534.618 541.667 548.626 555.617 630.174

509 439.822 456.762 473.311 482.941 495.493 505.097 513.455 521.170 528.546 535.693 542.723 549.725 556.728 631.424

510 440.766 457.708 474.288 483.923 496.514 506.128 514.497 522.222 529.610 536.768 543.810 550.824 557.840 632.674

Erlang Tables

.

9-18

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


511 441.683 458.681 475.265 484.905 497.506 507.131 515.538 523.275 530.674 537.843 544.897 551.923 558.920 633.924

512 442.628 459.626 476.242 485.915 498.526 508.162 516.551 524.327 531.708 538.919 545.984 553.022 560.031 635.174

513 443.572 460.572 477.219 486.897 499.518 509.192 517.593 525.380 532.772 539.994 547.071 554.121 561.142 636.424

514 444.489 461.545 478.197 487.879 500.539 510.195 518.634 526.433 533.836 541.069 548.158 555.220 562.253 637.674

515 445.433 462.490 479.174 488.861 501.559 511.226 519.676 527.456 534.900 542.115 549.245 556.319 563.364 638.924

516 446.378 463.436 480.123 489.871 502.551 512.257 520.689 528.509 535.963 543.190 550.332 557.418 564.475 640.174

517 447.295 464.409 481.100 490.853 503.571 513.259 521.730 529.561 537.027 544.265 551.419 558.516 565.586 641.424

518 448.239 465.354 482.077 491.835 504.563 514.290 522.772 530.614 538.091 545.341 552.506 559.615 566.698 642.674

519 449.184 466.300 483.054 492.845 505.584 515.321 523.814 531.667 539.155 546.416 553.593 560.684 567.809 643.924

520 450.101 467.273 484.031 493.827 506.576 516.323 524.826 532.690 540.189 547.491 554.680 561.783 568.920 645.174

521 451.045 468.218 485.008 494.809 507.596 517.354 525.868 533.743 541.253 548.566 555.737 562.882 570.031 646.424

522 451.990 469.191 485.985 495.791 508.588 518.385 526.910 534.795 542.317 549.642 556.824 563.980 571.142 647.674

523 452.906 470.137 486.963 496.801 509.609 519.387 527.951 535.848 543.381 550.717 557.911 565.079 572.253 648.924

524 453.851 471.082 487.940 497.783 510.601 520.418 528.993 536.901 544.444 551.792 558.998 566.178 573.364 650.174

525 454.795 472.055 488.917 498.765 511.621 521.449 530.006 537.953 545.508 552.838 560.085 567.277 574.475 651.424

526 455.740 473.001 489.894 499.747 512.613 522.451 531.047 538.977 546.572 553.913 561.171 568.376 575.586 652.674

527 456.657 473.974 490.871 500.758 513.634 523.482 532.089 540.029 547.636 554.988 562.258 569.475 576.698 653.924

528 457.601 474.919 491.848 501.740 514.654 524.513 533.131 541.082 548.670 556.063 563.345 570.574 577.809 655.174

529 458.546 475.865 492.825 502.722 515.646 525.544 534.144 542.135 549.734 557.139 564.432 571.673 578.920 656.424

530 459.463 476.838 493.802 503.732 516.667 526.546 535.185 543.187 550.798 558.214 565.519 572.772 580.031 657.674

531 460.407 477.783 494.779 504.714 517.659 527.577 536.227 544.240 551.862 559.289 566.606 573.871 581.111 658.924

532 461.352 478.757 495.757 505.696 518.679 528.608 537.269 545.263 552.926 560.364 567.693 574.969 582.222 660.174

533 462.268 479.702 496.734 506.678 519.671 529.611 538.310 546.316 553.989 561.440 568.780 576.068 583.333 661.424

534 463.213 480.647 497.711 507.688 520.692 530.641 539.323 547.368 555.053 562.515 569.837 577.167 584.444 662.674

535 464.158 481.621 498.688 508.670 521.684 531.672 540.365 548.421 556.117 563.590 570.924 578.236 585.556 663.924

536 465.102 482.566 499.665 509.652 522.704 532.675 541.406 549.474 557.151 564.636 572.011 579.335 586.667 665.174

537 466.019 483.539 500.642 510.634 523.724 533.706 542.448 550.526 558.215 565.711 573.098 580.433 587.778 666.424

538 466.963 484.484 501.619 511.644 524.717 534.737 543.461 551.550 559.279 566.786 574.185 581.532 588.889 667.674

539 467.908 485.430 502.596 512.626 525.737 535.739 544.502 552.602 560.343 567.861 575.272 582.631 590.000 668.924

540 468.852 486.403 503.573 513.608 526.729 536.770 545.544 553.655 561.407 568.937 576.359 583.730 591.111 670.174

Erlang Tables

9-19

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


541 469.769 487.348 504.551 514.618 527.749 537.801 546.586 554.708 562.470 570.012 577.446 584.829 592.222 671.424

542 470.714 488.322 505.528 515.600 528.741 538.832 547.627 555.760 563.534 571.087 578.533 585.928 593.333 672.674

543 471.658 489.267 506.505 516.582 529.762 539.834 548.640 556.813 564.598 572.162 579.620 587.027 594.444 673.924

544 472.603 490.212 507.482 517.593 530.754 540.865 549.682 557.836 565.632 573.238 580.707 588.126 595.556 675.174

545 473.520 491.186 508.459 518.575 531.774 541.896 550.723 558.889 566.696 574.313 581.793 589.225 596.667 676.424

546 474.464 492.131 509.436 519.557 532.795 542.898 551.765 559.942 567.760 575.358 582.880 590.324 597.778 677.674

547 475.409 493.104 510.413 520.539 533.787 543.929 552.778 560.994 568.824 576.434 583.967 591.422 598.889 678.924

548 476.325 494.050 511.418 521.549 534.807 544.960 553.819 562.047 569.888 577.509 585.024 592.521 600.000 680.174

549 477.270 495.023 512.395 522.531 535.799 545.962 554.861 563.099 570.952 578.584 586.111 593.620 601.111 681.424

550 478.214 495.968 513.372 523.513 536.820 546.993 555.903 564.152 572.015 579.659 587.198 594.719 602.222 682.674

551 479.159 496.914 514.350 524.523 537.812 548.024 556.944 565.175 573.079 580.735 588.285 595.818 603.333 683.924

552 480.104 497.887 515.327 525.505 538.832 549.026 557.957 566.228 574.113 581.810 589.372 596.886 604.414 685.174

553 481.020 498.832 516.304 526.487 539.824 550.057 558.999 567.281 575.177 582.885 590.459 597.985 605.525 686.424

554 481.965 499.805 517.281 527.469 540.845 551.088 560.041 568.333 576.241 583.961 591.546 599.084 606.636 687.674

555 482.909 500.751 518.258 528.479 541.865 552.119 561.082 569.386 577.305 585.036 592.633 600.183 607.747 688.924

556 483.854 501.724 519.235 529.461 542.857 553.121 562.124 570.439 578.369 586.111 593.720 601.282 608.858 690.174

557 484.771 502.669 520.212 530.443 543.878 554.152 563.137 571.462 579.433 587.157 594.807 602.381 609.969 691.424

558 485.715 503.643 521.189 531.453 544.870 555.183 564.178 572.515 580.496 588.232 595.894 603.480 611.080 692.674

559 486.660 504.588 522.166 532.435 545.890 556.186 565.220 573.567 581.560 589.307 596.981 604.579 612.191 693.924

560 487.604 505.533 523.143 533.418 546.882 557.216 566.262 574.620 582.595 590.382 598.068 605.678 613.302 695.174

561 488.521 506.507 524.121 534.428 547.902 558.247 567.274 575.673 583.658 591.458 599.124 606.777 614.414 696.424

562 489.466 507.452 525.098 535.410 548.923 559.278 568.316 576.725 584.722 592.533 600.211 607.875 615.525 697.674

563 490.410 508.425 526.075 536.392 549.915 560.281 569.358 577.749 585.786 593.608 601.298 608.974 616.636 698.924

564 491.355 509.370 527.052 537.402 550.935 561.312 570.399 578.801 586.850 594.683 602.385 610.073 617.747 700.174

565 492.299 510.344 528.029 538.384 551.927 562.342 571.441 579.854 587.914 595.759 603.472 611.172 618.858 701.424

566 493.216 511.289 529.006 539.366 552.948 563.345 572.454 580.906 588.978 596.834 604.559 612.271 619.969 702.674

567 494.161 512.262 529.983 540.376 553.940 564.376 573.495 581.959 590.041 597.909 605.646 613.370 621.080 703.924

568 495.105 513.208 530.960 541.358 554.960 565.407 574.537 583.012 591.105 598.955 606.733 614.469 622.191 705.174

569 496.050 514.181 531.937 542.340 555.981 566.438 575.579 584.064 592.139 600.030 607.820 615.568 623.302 706.424

570 496.994 515.126 532.915 543.322 556.973 567.440 576.620 585.088 593.203 601.105 608.907 616.636 624.414 707.674

Erlang Tables

.

9-20

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


571 497.911 516.099 533.892 544.332 557.993 568.471 577.633 586.140 594.267 602.180 609.994 617.735 625.525 708.924

572 498.855 517.045 534.869 545.314 558.985 569.502 578.675 587.193 595.331 603.256 611.081 618.834 626.636 710.174

573 499.800 517.990 535.846 546.296 560.006 570.504 579.716 588.246 596.395 604.331 612.168 619.933 627.747 711.424

574 500.745 518.963 536.823 547.306 561.026 571.535 580.758 589.298 597.459 605.406 613.255 621.032 628.827 712.639

575 501.689 519.909 537.828 548.288 562.018 572.566 581.800 590.351 598.522 606.481 614.342 622.131 629.938 713.889

576 502.606 520.882 538.805 549.270 563.039 573.568 582.813 591.374 599.586 607.557 615.399 623.230 631.049 715.139

577 503.550 521.827 539.782 550.281 564.031 574.599 583.854 592.427 600.650 608.632 616.486 624.328 632.160 716.389

578 504.495 522.801 540.759 551.263 565.051 575.630 584.896 593.480 601.684 609.707 617.572 625.427 633.272 717.639

579 505.439 523.746 541.736 552.245 566.043 576.661 585.938 594.532 602.748 610.753 618.659 626.526 634.383 718.889

580 506.384 524.719 542.714 553.255 567.063 577.663 586.979 595.585 603.812 611.828 619.746 627.625 635.494 720.139

581 507.301 525.665 543.691 554.237 568.084 578.694 587.992 596.637 604.876 612.903 620.833 628.724 636.605 721.389

582 508.245 526.638 544.668 555.219 569.076 579.725 589.034 597.690 605.940 613.978 621.920 629.823 637.716 722.639

583 509.190 527.583 545.645 556.229 570.096 580.756 590.075 598.713 607.004 615.054 623.007 630.922 638.827 723.889

584 510.134 528.556 546.622 557.211 571.088 581.758 591.117 599.766 608.067 616.129 624.094 632.021 639.938 725.139

585 511.079 529.502 547.599 558.193 572.109 582.789 592.159 600.819 609.131 617.204 625.181 633.120 641.049 726.389

586 512.023 530.475 548.576 559.203 573.129 583.820 593.171 601.871 610.165 618.280 626.268 634.219 642.160 727.639

587 512.940 531.420 549.553 560.185 574.121 584.822 594.213 602.924 611.229 619.355 627.355 635.317 643.272 728.889

588 513.885 532.394 550.530 561.167 575.142 585.853 595.255 603.977 612.293 620.430 628.442 636.386 644.383 730.139

589 514.829 533.339 551.508 562.177 576.134 586.884 596.296 605.029 613.357 621.505 629.529 637.485 645.494 731.389

590 515.774 534.312 552.485 563.159 577.154 587.915 597.338 606.053 614.421 622.581 630.616 638.584 646.605 732.639

591 516.718 535.257 553.490 564.141 578.146 588.918 598.351 607.105 615.485 623.626 631.673 639.683 647.716 733.889

592 517.663 536.231 554.467 565.152 579.167 589.948 599.392 608.158 616.548 624.701 632.760 640.781 648.827 735.139

593 518.607 537.176 555.444 566.134 580.187 590.979 600.434 609.211 617.612 625.777 633.847 641.880 649.938 736.389

594 519.524 538.149 556.421 567.116 581.179 591.982 601.476 610.263 618.676 626.852 634.934 642.979 651.049 737.639

595 520.469 539.095 557.398 568.126 582.200 593.013 602.517 611.316 619.710 627.927 636.021 644.078 652.160 738.889

596 521.413 540.068 558.375 569.108 583.192 594.044 603.530 612.368 620.774 629.002 637.107 645.177 653.272 740.139

597 522.358 541.013 559.352 570.090 584.212 595.074 604.572 613.392 621.838 630.078 638.194 646.276 654.383 741.389

598 523.302 541.986 560.329 571.100 585.232 596.077 605.613 614.444 622.902 631.153 639.281 647.375 655.463 742.639

599 524.247 542.932 561.307 572.082 586.224 597.108 606.655 615.497 623.966 632.228 640.368 648.474 656.574 743.889

600 525.191 543.905 562.284 573.064 587.245 598.139 607.697 616.550 625.030 633.303 641.455 649.573 657.685 745.139

Erlang Tables

9-21

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


601 526.108 544.850 563.261 574.074 588.237 599.170 608.709 617.602 626.093 634.379 642.542 650.672 658.796 746.389

602 527.053 545.824 564.238 575.056 589.257 600.172 609.751 618.655 627.157 635.454 643.629 651.770 659.907 747.639

603 527.997 546.769 565.243 576.038 590.278 601.203 610.793 619.708 628.221 636.499 644.716 652.869 661.019 748.889

604 528.942 547.742 566.220 577.048 591.270 602.234 611.834 620.731 629.285 637.575 645.803 653.968 662.130 750.139

605 529.886 548.688 567.197 578.030 592.290 603.236 612.876 621.784 630.319 638.650 646.890 655.067 663.241 751.389

606 530.831 549.661 568.174 579.040 593.282 604.267 613.889 622.836 631.383 639.725 647.947 656.166 664.352 752.639

607 531.775 550.606 569.151 580.022 594.303 605.298 614.931 623.889 632.447 640.800 649.034 657.265 665.463 753.889

608 532.692 551.579 570.128 581.004 595.323 606.329 615.972 624.942 633.511 641.876 650.121 658.333 666.574 755.139

609 533.637 552.553 571.106 582.015 596.315 607.331 617.014 625.994 634.574 642.951 651.208 659.432 667.685 756.389

610 534.581 553.498 572.083 582.997 597.336 608.362 618.056 627.047 635.638 644.026 652.295 660.531 668.796 757.639

611 535.526 554.471 573.060 583.979 598.328 609.393 619.068 628.070 636.702 645.102 653.382 661.630 669.907 758.889

612 536.470 555.417 574.037 584.989 599.348 610.424 620.110 629.123 637.766 646.177 654.469 662.729 671.019 760.139

613 537.415 556.390 575.014 585.971 600.368 611.426 621.152 630.175 638.830 647.252 655.556 663.828 672.130 761.389

614 538.359 557.335 576.019 586.953 601.361 612.457 622.193 631.228 639.864 648.327 656.643 664.927 673.241 762.639

615 539.304 558.308 576.996 587.963 602.381 613.488 623.235 632.281 640.928 649.373 657.729 666.026 674.352 763.889

616 540.248 559.254 577.973 588.945 603.373 614.490 624.277 633.333 641.992 650.448 658.816 667.125 675.463 765.139

617 541.165 560.227 578.950 589.927 604.393 615.521 625.289 634.386 643.056 651.523 659.903 668.223 676.574 766.389

618 542.110 561.172 579.927 590.937 605.414 616.552 626.331 635.409 644.119 652.599 660.990 669.322 677.685 767.639

619 543.054 562.145 580.905 591.919 606.406 617.583 627.373 636.462 645.183 653.674 662.077 670.421 678.796 768.889

620 543.999 563.091 581.882 592.929 607.426 618.585 628.414 637.515 646.247 654.749 663.164 671.520 679.907 770.139

621 544.943 564.064 582.859 593.911 608.418 619.616 629.456 638.567 647.311 655.824 664.251 672.619 681.019 771.389

622 545.888 565.037 583.836 594.893 609.439 620.647 630.469 639.620 648.375 656.900 665.308 673.718 682.130 772.639

623 546.832 565.983 584.813 595.903 610.459 621.678 631.510 640.673 649.439 657.975 666.395 674.817 683.210 773.889

624 547.777 566.956 585.818 596.886 611.451 622.680 632.552 641.725 650.473 659.050 667.482 675.916 684.321 775.139

625 548.722 567.901 586.795 597.868 612.472 623.711 633.594 642.749 651.537 660.125 668.569 677.015 685.432 776.389

626 549.666 568.874 587.772 598.878 613.492 624.742 634.635 643.801 652.600 661.201 669.656 678.114 686.543 777.639

627 550.611 569.820 588.749 599.860 614.484 625.773 635.648 644.854 653.664 662.276 670.743 679.212 687.654 778.889

628 551.527 570.793 589.726 600.842 615.505 626.775 636.690 645.906 654.728 663.321 671.830 680.281 688.765 780.139

629 552.472 571.738 590.704 601.852 616.497 627.806 637.731 646.959 655.792 664.397 672.917 681.380 689.877 781.389

630 553.416 572.712 591.681 602.834 617.517 628.837 638.773 648.012 656.856 665.472 674.004 682.479 690.988 782.639

Erlang Tables

.

9-22

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


631 554.361 573.657 592.658 603.844 618.537 629.868 639.815 649.064 657.920 666.547 675.091 683.578 692.099 783.889

632 555.306 574.630 593.635 604.826 619.529 630.871 640.856 650.088 658.983 667.622 676.178 684.676 693.210 785.139

633 556.250 575.603 594.640 605.808 620.550 631.901 641.869 651.140 660.047 668.698 677.264 685.775 694.321 786.389

634 557.195 576.549 595.617 606.818 621.542 632.932 642.911 652.193 661.082 669.773 678.351 686.874 695.432 787.639

635 558.139 577.522 596.594 607.800 622.562 633.935 643.953 653.246 662.145 670.848 679.438 687.973 696.543 788.889

636 559.084 578.467 597.571 608.782 623.583 634.966 644.994 654.298 663.209 671.924 680.525 689.072 697.654 790.139

637 560.028 579.441 598.548 609.792 624.575 635.997 646.036 655.351 664.273 672.999 681.612 690.171 698.765 791.389

638 560.973 580.386 599.525 610.774 625.595 637.027 647.049 656.404 665.337 674.074 682.669 691.270 699.877 792.639

639 561.917 581.359 600.503 611.785 626.616 638.030 648.090 657.456 666.401 675.149 683.756 692.369 700.988 793.889

640 562.862 582.332 601.480 612.767 627.608 639.061 649.132 658.480 667.465 676.225 684.843 693.468 702.099 795.139

641 563.806 583.278 602.485 613.749 628.628 640.092 650.174 659.532 668.528 677.270 685.930 694.567 703.210 796.389

642 564.723 584.251 603.462 614.759 629.620 641.123 651.215 660.585 669.592 678.345 687.017 695.665 704.321 797.639

643 565.668 585.196 604.439 615.741 630.641 642.125 652.257 661.637 670.656 679.421 688.104 696.764 705.432 798.889

644 566.612 586.170 605.416 616.723 631.661 643.156 653.270 662.690 671.690 680.496 689.191 697.863 706.543 800.139

645 567.557 587.115 606.393 617.733 632.653 644.187 654.311 663.743 672.754 681.571 690.278 698.962 707.654 801.389

646 568.501 588.088 607.370 618.715 633.673 645.218 655.353 664.795 673.818 682.646 691.365 700.061 708.765 802.639

647 569.446 589.061 608.347 619.725 634.694 646.220 656.395 665.848 674.882 683.722 692.452 701.160 709.877 803.889

648 570.390 590.007 609.324 620.707 635.686 647.251 657.436 666.871 675.946 684.797 693.539 702.259 710.988 805.139

649 571.335 590.980 610.329 621.689 636.706 648.282 658.449 667.924 677.009 685.872 694.626 703.358 712.099 806.389

650 572.279 591.925 611.307 622.699 637.698 649.313 659.491 668.977 678.073 686.947 695.713 704.426 713.179 807.639

651 573.224 592.898 612.284 623.681 638.719 650.315 660.532 670.029 679.137 688.023 696.800 705.525 714.290 808.889

652 574.169 593.872 613.261 624.691 639.739 651.346 661.574 671.082 680.201 689.098 697.886 706.624 715.401 810.139

653 575.113 594.817 614.238 625.673 640.731 652.377 662.616 672.135 681.265 690.173 698.973 707.723 716.512 811.389

654 576.058 595.790 615.215 626.655 641.752 653.408 663.657 673.187 682.299 691.219 700.060 708.822 717.623 812.639

655 577.002 596.736 616.192 627.666 642.772 654.410 664.670 674.211 683.363 692.294 701.147 709.921 718.735 813.889

656 577.947 597.709 617.197 628.648 643.764 655.441 665.712 675.263 684.427 693.369 702.204 711.020 719.846 815.139

657 578.891 598.682 618.174 629.630 644.785 656.472 666.753 676.316 685.491 694.444 703.291 712.118 720.957 816.389

658 579.836 599.627 619.151 630.640 645.777 657.503 667.795 677.368 686.554 695.520 704.378 713.217 722.068 817.639

659 580.780 600.601 620.128 631.622 646.797 658.505 668.837 678.421 687.618 696.595 705.465 714.316 723.179 818.889

660 581.725 601.546 621.106 632.632 647.817 659.536 669.850 679.474 688.682 697.670 706.552 715.415 724.290 820.139

Erlang Tables

9-23

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


661 582.669 602.519 622.083 633.614 648.810 660.567 670.891 680.526 689.746 698.746 707.639 716.514 725.401 821.389

662 583.614 603.492 623.060 634.596 649.830 661.598 671.933 681.579 690.810 699.821 708.726 717.613 726.512 822.639

663 584.558 604.438 624.065 635.606 650.850 662.600 672.975 682.602 691.874 700.896 709.813 718.712 727.623 823.889

664 585.503 605.411 625.042 636.588 651.842 663.631 674.016 683.655 692.908 701.971 710.900 719.811 728.735 825.139

665 586.448 606.356 626.019 637.598 652.863 664.662 675.058 684.708 693.972 703.047 711.987 720.910 729.846 826.389

666 587.392 607.330 626.996 638.580 653.883 665.693 676.071 685.760 695.035 704.122 713.074 722.009 730.957 827.639

667 588.337 608.303 627.973 639.562 654.875 666.695 677.112 686.813 696.099 705.197 714.161 723.107 732.068 828.889

668 589.281 609.248 628.950 640.572 655.896 667.726 678.154 687.865 697.163 706.243 715.248 724.206 733.179 830.139

669 590.226 610.221 629.927 641.554 656.888 668.757 679.196 688.918 698.227 707.318 716.335 725.305 734.290 831.389

670 591.170 611.167 630.932 642.565 657.908 669.788 680.237 689.971 699.291 708.393 717.421 726.404 735.401 832.639

671 592.115 612.140 631.910 643.547 658.929 670.790 681.279 690.994 700.355 709.468 718.508 727.503 736.512 833.889

672 593.059 613.113 632.887 644.529 659.921 671.821 682.292 692.047 701.418 710.544 719.595 728.571 737.623 835.139

673 594.004 614.059 633.864 645.539 660.941 672.852 683.333 693.099 702.482 711.619 720.682 729.670 738.735 836.389

674 594.948 615.032 634.841 646.521 661.961 673.883 684.375 694.152 703.546 712.694 721.739 730.769 739.846 837.639

675 595.893 615.977 635.818 647.531 662.954 674.885 685.417 695.205 704.580 713.769 722.826 731.868 740.957 838.889

676 596.837 616.950 636.823 648.513 663.974 675.916 686.458 696.257 705.644 714.845 723.913 732.967 742.068 840.139

677 597.782 617.923 637.800 649.495 664.994 676.947 687.500 697.310 706.708 715.920 725.000 734.066 743.179 841.389

678 598.727 618.869 638.777 650.505 665.986 677.978 688.513 698.363 707.772 716.995 726.087 735.165 744.259 842.639

679 599.671 619.842 639.754 651.487 667.007 679.009 689.554 699.386 708.836 718.070 727.174 736.264 745.370 843.889

680 600.616 620.815 640.731 652.497 667.999 680.011 690.596 700.439 709.900 719.146 728.261 737.363 746.481 845.139

681 601.560 621.761 641.709 653.479 669.019 681.042 691.638 701.491 710.963 720.221 729.348 738.462 747.593 846.389

682 602.505 622.734 642.686 654.461 670.040 682.073 692.679 702.544 712.027 721.266 730.435 739.560 748.704 847.639

683 603.449 623.679 643.691 655.471 671.032 683.104 693.721 703.596 713.091 722.342 731.522 740.659 749.815 848.889

684 604.394 624.652 644.668 656.453 672.052 684.107 694.734 704.649 714.155 723.417 732.609 741.758 750.926 850.139

685 605.338 625.626 645.645 657.464 673.073 685.137 695.775 705.702 715.219 724.492 733.696 742.857 752.037 851.389

686 606.283 626.571 646.622 658.446 674.065 686.168 696.817 706.754 716.253 725.568 734.783 743.956 753.148 852.639

687 607.227 627.544 647.599 659.456 675.085 687.199 697.859 707.778 717.317 726.643 735.870 745.055 754.259 853.889

688 608.172 628.517 648.576 660.438 676.105 688.202 698.900 708.830 718.381 727.718 736.957 746.154 755.370 855.139

689 609.116 629.463 649.581 661.420 677.098 689.233 699.942 709.883 719.444 728.793 738.043 747.253 756.481 856.389

690 610.061 630.436 650.558 662.430 678.118 690.263 700.955 710.936 720.508 729.869 739.130 748.352 757.593 857.639

Erlang Tables

.

9-24

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


691 611.006 631.409 651.535 663.412 679.138 691.294 701.997 711.988 721.572 730.944 740.217 749.451 758.704 858.889

692 611.950 632.355 652.513 664.422 680.130 692.297 703.038 713.041 722.636 732.019 741.274 750.549 759.815 860.139

693 612.895 633.328 653.490 665.404 681.151 693.328 704.080 714.094 723.700 733.094 742.361 751.648 760.926 861.389

694 613.839 634.273 654.467 666.386 682.143 694.359 705.122 715.146 724.764 734.170 743.448 752.747 762.037 862.639

695 614.784 635.246 655.472 667.396 683.163 695.389 706.163 716.170 725.827 735.245 744.535 753.846 763.148 863.889

696 615.728 636.220 656.449 668.378 684.184 696.392 707.176 717.222 726.891 736.290 745.622 754.915 764.259 865.139

697 616.673 637.165 657.426 669.388 685.176 697.423 708.218 718.275 727.926 737.366 746.709 756.013 765.370 866.389

698 617.617 638.138 658.403 670.370 686.196 698.454 709.259 719.327 728.989 738.441 747.796 757.112 766.481 867.639

699 618.562 639.111 659.380 671.380 687.217 699.485 710.301 720.380 730.053 739.516 748.883 758.211 767.593 868.889

700 619.506 640.057 660.385 672.363 688.209 700.515 711.343 721.433 731.117 740.591 749.970 759.310 768.704 870.139

701 620.451 641.030 661.362 673.345 689.229 701.518 712.384 722.485 732.181 741.667 751.057 760.409 769.815 871.389

702 621.395 642.003 662.339 674.355 690.249 702.549 713.397 723.538 733.245 742.742 752.144 761.508 770.926 872.639

703 622.340 642.949 663.317 675.337 691.241 703.580 714.439 724.591 734.309 743.817 753.231 762.607 772.037 873.889

704 623.285 643.922 664.294 676.347 692.262 704.611 715.480 725.614 735.372 744.892 754.318 763.706 773.148 875.139

705 624.229 644.895 665.271 677.329 693.282 705.613 716.522 726.667 736.436 745.968 755.405 764.805 774.259 876.389

706 625.174 645.840 666.276 678.339 694.274 706.644 717.564 727.719 737.500 747.043 756.492 765.904 775.370 877.639

707 626.118 646.813 667.253 679.321 695.295 707.675 718.605 728.772 738.564 748.118 757.579 767.002 776.481 878.889

708 627.063 647.787 668.230 680.303 696.315 708.706 719.618 729.825 739.598 749.194 758.665 768.101 777.593 880.139

709 628.007 648.732 669.207 681.313 697.307 709.708 720.660 730.877 740.662 750.269 759.752 769.200 778.673 881.389

710 628.952 649.705 670.184 682.295 698.328 710.739 721.701 731.930 741.726 751.344 760.839 770.299 779.784 882.639

711 629.924 650.678 671.189 683.305 699.348 711.770 722.743 732.982 742.790 752.389 761.926 771.398 780.895 883.889

712 630.869 651.624 672.166 684.287 700.340 712.801 723.785 734.006 743.853 753.465 762.983 772.497 782.006 885.139

713 631.813 652.597 673.143 685.297 701.361 713.832 724.826 735.058 744.917 754.540 764.070 773.596 783.117 886.389

714 632.758 653.570 674.121 686.279 702.381 714.834 725.839 736.111 745.981 755.615 765.157 774.695 784.228 887.639

715 633.702 654.516 675.098 687.262 703.373 715.865 726.881 737.164 747.045 756.691 766.244 775.794 785.340 888.889

716 634.647 655.489 676.103 688.272 704.393 716.896 727.922 738.216 748.109 757.766 767.331 776.893 786.451 890.139

717 635.591 656.462 677.080 689.254 705.414 717.927 728.964 739.269 749.173 758.841 768.418 777.991 787.562 891.389

718 636.536 657.407 678.057 690.264 706.406 718.929 730.006 740.322 750.236 759.916 769.505 779.090 788.673 892.639

719 637.480 658.381 679.034 691.246 707.426 719.960 731.047 741.374 751.300 760.992 770.592 780.189 789.784 893.889

720 638.425 659.354 680.011 692.256 708.418 720.991 732.089 742.427 752.335 762.067 771.679 781.288 790.895 895.139

Erlang Tables

9-25

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


721 639.369 660.299 680.988 693.238 709.439 722.022 733.102 743.450 753.398 763.142 772.766 782.357 792.006 896.389

722 640.314 661.272 681.993 694.220 710.459 723.053 734.144 744.503 754.462 764.217 773.853 783.455 793.117 897.639

723 641.259 662.246 682.970 695.230 711.451 724.055 735.185 745.556 755.526 765.293 774.940 784.554 794.228 898.889

724 642.203 663.191 683.948 696.212 712.472 725.086 736.227 746.608 756.590 766.368 776.027 785.653 795.340 900.139

725 643.175 664.164 684.925 697.222 713.492 726.117 737.269 747.661 757.654 767.443 777.114 786.752 796.451 901.389

726 644.120 665.137 685.902 698.204 714.484 727.148 738.310 748.713 758.717 768.519 778.200 787.851 797.562 902.639

727 645.065 666.083 686.907 699.214 715.505 728.150 739.323 749.766 759.781 769.564 779.287 788.950 798.673 903.889

728 646.009 667.056 687.884 700.196 716.525 729.181 740.365 750.819 760.845 770.639 780.374 790.049 799.784 905.139

729 646.954 668.029 688.861 701.178 717.517 730.212 741.406 751.871 761.909 771.714 781.461 791.148 800.895 906.389

730 647.898 668.975 689.838 702.189 718.537 731.243 742.448 752.895 762.973 772.790 782.548 792.247 802.006 907.639

731 648.843 669.948 690.815 703.171 719.558 732.274 743.490 753.947 764.037 773.865 783.635 793.346 803.117 908.889

732 649.787 670.921 691.820 704.181 720.550 733.276 744.531 755.000 765.071 774.940 784.692 794.444 804.228 910.139

733 650.732 671.866 692.797 705.163 721.570 734.307 745.544 756.053 766.135 776.016 785.779 795.543 805.340 911.389

734 651.676 672.840 693.774 706.173 722.591 735.338 746.586 757.105 767.199 777.091 786.866 796.642 806.451 912.639

735 652.621 673.813 694.752 707.155 723.583 736.369 747.627 758.158 768.262 778.166 787.953 797.741 807.562 913.889

736 653.565 674.758 695.757 708.165 724.603 737.371 748.669 759.211 769.326 779.241 789.040 798.840 808.673 915.139

737 654.538 675.731 696.734 709.147 725.624 738.402 749.711 760.263 770.390 780.317 790.127 799.939 809.784 916.389

738 655.482 676.704 697.711 710.129 726.616 739.433 750.752 761.316 771.454 781.392 791.214 801.038 810.895 917.639

739 656.427 677.678 698.688 711.139 727.636 740.464 751.794 762.339 772.518 782.467 792.301 802.137 812.006 918.889

740 657.371 678.623 699.665 712.121 728.656 741.495 752.807 763.392 773.582 783.542 793.388 803.236 813.117 920.139

741 658.316 679.596 700.670 713.131 729.649 742.497 753.848 764.444 774.645 784.618 794.475 804.335 814.228 921.389

742 659.260 680.569 701.647 714.113 730.669 743.528 754.890 765.497 775.709 785.693 795.562 805.433 815.309 922.639

743 660.205 681.515 702.624 715.123 731.689 744.559 755.932 766.550 776.773 786.738 796.649 806.532 816.420 923.889

744 661.149 682.488 703.601 716.105 732.681 745.590 756.973 767.602 777.807 787.814 797.736 807.631 817.531 925.139

745 662.094 683.461 704.578 717.116 733.702 746.592 758.015 768.655 778.871 788.889 798.822 808.730 818.642 926.389

746 663.039 684.407 705.583 718.098 734.722 747.623 759.028 769.708 779.935 789.964 799.909 809.829 819.753 927.639

747 664.011 685.380 706.561 719.108 735.714 748.654 760.069 770.760 780.999 791.039 800.996 810.928 820.864 928.889

748 664.955 686.353 707.538 720.090 736.735 749.685 761.111 771.784 782.063 792.115 802.083 811.996 821.975 930.139

749 665.900 687.326 708.515 721.072 737.755 750.716 762.153 772.836 783.126 793.190 803.170 813.095 823.086 931.389

750 666.844 688.272 709.492 722.082 738.747 751.718 763.194 773.889 784.190 794.265 804.257 814.194 824.198 932.639

Erlang Tables

.

9-26

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


751 667.789 689.245 710.497 723.064 739.768 752.749 764.236 774.942 785.254 795.341 805.344 815.293 825.309 933.889

752 668.734 690.218 711.474 724.074 740.788 753.780 765.278 775.994 786.318 796.416 806.431 816.392 826.420 935.139

753 669.678 691.163 712.451 725.056 741.808 754.811 766.291 777.047 787.382 797.491 807.488 817.491 827.531 936.389

754 670.623 692.137 713.428 726.066 742.800 755.813 767.332 778.099 788.446 798.566 808.575 818.590 828.642 937.639

755 671.595 693.110 714.433 727.048 743.821 756.844 768.374 779.152 789.509 799.642 809.662 819.689 829.753 938.889

756 672.539 694.055 715.410 728.058 744.841 757.875 769.416 780.205 790.544 800.717 810.749 820.788 830.864 940.104

757 673.484 695.028 716.387 729.040 745.833 758.906 770.457 781.228 791.608 801.792 811.836 821.886 831.975 941.354

758 674.429 696.002 717.365 730.051 746.854 759.937 771.499 782.281 792.671 802.867 812.923 822.985 833.086 942.604

759 675.373 696.975 718.342 731.033 747.874 760.939 772.541 783.333 793.735 803.913 814.010 824.084 834.198 943.854

760 676.318 697.920 719.347 732.015 748.866 761.970 773.553 784.386 794.799 804.988 815.097 825.183 835.309 945.104

761 677.262 698.893 720.324 733.025 749.887 763.001 774.595 785.439 795.863 806.063 816.184 826.282 836.420 946.354

762 678.207 699.867 721.301 734.007 750.907 764.032 775.637 786.491 796.927 807.139 817.271 827.381 837.531 947.604

763 679.179 700.840 722.278 735.017 751.899 765.063 776.678 787.544 797.991 808.214 818.357 828.480 838.642 948.854

764 680.124 701.785 723.283 735.999 752.920 766.065 777.720 788.596 799.054 809.289 819.444 829.579 839.753 950.104

765 681.068 702.758 724.260 737.009 753.940 767.096 778.762 789.649 800.118 810.364 820.531 830.678 840.864 951.354

766 682.013 703.732 725.237 737.991 754.932 768.127 779.774 790.673 801.182 811.440 821.618 831.777 841.975 952.604

767 682.957 704.677 726.214 739.001 755.952 769.158 780.816 791.725 802.246 812.515 822.705 832.875 843.086 953.854

768 683.902 705.650 727.219 739.983 756.973 770.160 781.858 792.778 803.310 813.590 823.792 833.974 844.198 955.104

769 684.846 706.623 728.197 740.993 757.965 771.191 782.899 793.830 804.344 814.665 824.879 835.073 845.309 956.354

770 685.819 707.596 729.174 741.975 758.985 772.222 783.941 794.883 805.408 815.741 825.966 836.172 846.420 957.604

771 686.763 708.542 730.151 742.985 760.006 773.253 784.983 795.936 806.472 816.816 827.053 837.271 847.531 958.854

772 687.708 709.515 731.128 743.967 760.998 774.284 786.024 796.988 807.535 817.891 828.140 838.370 848.642 960.104

773 688.652 710.488 732.133 744.949 762.018 775.286 787.037 798.041 808.599 818.967 829.227 839.469 849.753 961.354

774 689.597 711.434 733.110 745.960 763.039 776.317 788.079 799.094 809.663 820.042 830.314 840.568 850.864 962.604

775 690.541 712.407 734.087 746.942 764.031 777.348 789.120 800.146 810.727 821.117 831.371 841.667 851.975 963.854

776 691.486 713.380 735.064 747.952 765.051 778.379 790.162 801.170 811.791 822.162 832.458 842.735 853.086 965.104

777 692.458 714.353 736.069 748.934 766.071 779.410 791.204 802.222 812.855 823.238 833.545 843.834 854.198 966.354

778 693.403 715.299 737.046 749.944 767.092 780.412 792.245 803.275 813.918 824.313 834.632 844.933 855.278 967.604

779 694.347 716.272 738.023 750.926 768.084 781.443 793.287 804.327 814.982 825.388 835.719 846.032 856.389 968.854

780 695.292 717.245 739.001 751.936 769.104 782.474 794.300 805.380 816.046 826.464 836.806 847.131 857.500 970.104

Erlang Tables

9-27

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


781 696.236 718.218 740.006 752.918 770.125 783.505 795.341 806.433 817.110 827.539 837.893 848.230 858.611 971.354

782 697.181 719.164 740.983 753.928 771.117 784.536 796.383 807.485 818.144 828.614 838.979 849.328 859.722 972.604

783 698.125 720.137 741.960 754.910 772.137 785.538 797.425 808.538 819.208 829.689 840.066 850.427 860.833 973.854

784 699.098 721.110 742.937 755.920 773.158 786.569 798.466 809.591 820.272 830.765 841.153 851.526 861.944 975.104

785 700.042 722.083 743.942 756.902 774.150 787.600 799.508 810.614 821.336 831.840 842.240 852.625 863.056 976.354

786 700.987 723.029 744.919 757.912 775.170 788.631 800.550 811.667 822.400 832.915 843.327 853.724 864.167 977.604

787 701.931 724.002 745.896 758.895 776.190 789.662 801.563 812.719 823.463 833.990 844.414 854.823 865.278 978.854

788 702.876 724.975 746.873 759.877 777.183 790.664 802.604 813.772 824.527 835.066 845.501 855.922 866.389 980.104

789 703.820 725.948 747.878 760.887 778.203 791.695 803.646 814.825 825.591 836.141 846.588 857.021 867.500 981.354

790 704.793 726.894 748.855 761.869 779.223 792.726 804.688 815.877 826.655 837.216 847.675 858.120 868.611 982.604

791 705.737 727.867 749.832 762.879 780.215 793.757 805.729 816.930 827.719 838.292 848.762 859.219 869.722 983.854

792 706.682 728.840 750.810 763.861 781.236 794.788 806.771 817.982 828.783 839.367 849.849 860.317 870.833 985.104

793 707.626 729.813 751.815 764.871 782.256 795.790 807.813 819.035 829.846 840.442 850.936 861.416 871.944 986.354

794 708.571 730.759 752.792 765.853 783.277 796.821 808.825 820.088 830.910 841.487 852.023 862.515 873.056 987.604

795 709.515 731.732 753.769 766.863 784.269 797.852 809.867 821.111 831.944 842.563 853.110 863.614 874.167 988.854

796 710.488 732.705 754.746 767.845 785.289 798.883 810.909 822.164 833.008 843.638 854.197 864.713 875.278 990.104

797 711.432 733.678 755.751 768.855 786.310 799.885 811.950 823.216 834.072 844.713 855.284 865.812 876.389 991.354

798 712.377 734.624 756.728 769.837 787.302 800.916 812.992 824.269 835.136 845.789 856.341 866.911 877.500 992.604

799 713.321 735.597 757.705 770.847 788.322 801.947 814.034 825.322 836.200 846.864 857.428 868.010 878.611 993.854

800 714.266 736.570 758.682 771.829 789.342 802.978 815.075 826.374 837.264 847.939 858.514 869.109 879.722 995.104

801 715.238 737.543 759.687 772.840 790.334 804.009 816.088 827.427 838.327 849.014 859.601 870.208 880.833 996.354

802 716.183 738.488 760.664 773.822 791.355 805.011 817.130 828.480 839.391 850.090 860.688 871.306 881.944 997.604

803 717.127 739.462 761.642 774.832 792.375 806.042 818.171 829.532 840.455 851.165 861.775 872.405 883.056 998.854

804 718.072 740.435 762.619 775.814 793.367 807.073 819.213 830.585 841.519 852.240 862.862 873.504 884.167 1000.104

805 719.016 741.408 763.624 776.824 794.388 808.104 820.255 831.608 842.583 853.315 863.949 874.603 885.278 1001.354

806 719.989 742.353 764.601 777.806 795.408 809.135 821.296 832.661 843.647 854.391 865.036 875.672 886.389 1002.604

807 720.933 743.327 765.578 778.816 796.429 810.137 822.338 833.713 844.710 855.466 866.123 876.770 887.500 1003.854

808 721.878 744.300 766.555 779.798 797.421 811.168 823.351 834.766 845.774 856.541 867.210 877.869 888.611 1005.104

809 722.822 745.273 767.560 780.808 798.441 812.199 824.392 835.819 846.809 857.616 868.297 878.968 889.722 1006.354

810 723.767 746.218 768.537 781.790 799.461 813.230 825.434 836.871 847.872 858.692 869.384 880.067 890.833 1007.604

Erlang Tables

.

9-28

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


811 724.711 747.192 769.514 782.800 800.454 814.261 826.476 837.924 848.936 859.767 870.471 881.166 891.944 1008.854

812 725.684 748.165 770.491 783.782 801.474 815.263 827.517 838.977 850.000 860.812 871.558 882.265 893.056 1010.104

813 726.628 749.138 771.496 784.792 802.494 816.294 828.559 840.029 851.064 861.888 872.645 883.364 894.167 1011.354

814 727.573 750.111 772.473 785.774 803.486 817.325 829.601 841.082 852.128 862.963 873.732 884.463 895.278 1012.604

815 728.517 751.057 773.451 786.785 804.507 818.356 830.642 842.105 853.191 864.038 874.819 885.562 896.389 1013.854

816 729.462 752.030 774.428 787.767 805.527 819.387 831.655 843.158 854.255 865.114 875.906 886.661 897.469 1015.104

817 730.434 753.003 775.433 788.749 806.519 820.389 832.697 844.211 855.319 866.189 876.993 887.759 898.580 1016.354

818 731.379 753.976 776.410 789.759 807.540 821.420 833.738 845.263 856.383 867.264 878.080 888.858 899.691 1017.604

819 732.323 754.922 777.387 790.741 808.560 822.451 834.780 846.316 857.447 868.339 879.167 889.957 900.802 1018.854

820 733.268 755.895 778.392 791.751 809.580 823.482 835.822 847.368 858.511 869.415 880.254 891.056 901.914 1020.104

821 734.212 756.868 779.369 792.733 810.573 824.513 836.863 848.421 859.574 870.490 881.341 892.155 903.025 1021.354

822 735.185 757.841 780.346 793.743 811.593 825.544 837.905 849.474 860.609 871.565 882.397 893.254 904.136 1022.604

823 736.129 758.787 781.323 794.725 812.613 826.546 838.918 850.526 861.673 872.640 883.484 894.353 905.247 1023.854

824 737.074 759.760 782.328 795.735 813.605 827.577 839.959 851.579 862.736 873.716 884.571 895.452 906.358 1025.104

825 738.018 760.733 783.305 796.717 814.626 828.608 841.001 852.632 863.800 874.791 885.658 896.551 907.469 1026.354

826 738.991 761.706 784.283 797.727 815.646 829.639 842.043 853.655 864.864 875.866 886.745 897.650 908.580 1027.604

827 739.935 762.679 785.260 798.709 816.638 830.670 843.084 854.708 865.928 876.941 887.832 898.748 909.691 1028.854

828 740.880 763.625 786.265 799.719 817.659 831.672 844.126 855.760 866.992 878.017 888.919 899.847 910.802 1030.104

829 741.824 764.598 787.242 800.701 818.679 832.703 845.168 856.813 868.056 879.092 890.006 900.946 911.914 1031.354

830 742.769 765.571 788.219 801.712 819.700 833.734 846.181 857.865 869.119 880.137 891.093 902.045 913.025 1032.604

831 743.741 766.544 789.224 802.694 820.692 834.765 847.222 858.918 870.183 881.213 892.180 903.144 914.136 1033.854

832 744.686 767.518 790.201 803.704 821.712 835.796 848.264 859.971 871.247 882.288 893.267 904.243 915.247 1035.104

833 745.630 768.463 791.178 804.686 822.732 836.798 849.306 861.023 872.311 883.363 894.354 905.342 916.358 1036.354

834 746.575 769.436 792.155 805.696 823.724 837.829 850.347 862.076 873.375 884.438 895.441 906.441 917.469 1037.604

835 747.547 770.409 793.160 806.678 824.745 838.860 851.389 863.129 874.439 885.514 896.528 907.540 918.580 1038.854

836 748.492 771.382 794.137 807.688 825.765 839.891 852.431 864.152 875.502 886.589 897.615 908.639 919.691 1040.104

837 749.436 772.328 795.114 808.670 826.786 840.922 853.472 865.205 876.537 887.664 898.702 909.707 920.802 1041.354

838 750.381 773.301 796.092 809.680 827.778 841.924 854.485 866.257 877.600 888.740 899.789 910.806 921.914 1042.604

839 751.325 774.274 797.097 810.662 828.798 842.955 855.527 867.310 878.664 889.815 900.876 911.905 923.025 1043.854

840 752.297 775.247 798.074 811.672 829.819 843.986 856.568 868.363 879.728 890.890 901.963 913.004 924.136 1045.104

Erlang Tables

9-29

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


841 753.242 776.221 799.051 812.654 830.811 845.017 857.610 869.415 880.792 891.965 903.050 914.103 925.247 1046.354

842 754.187 777.166 800.056 813.664 831.831 846.048 858.652 870.468 881.856 893.041 904.136 915.201 926.358 1047.604

843 755.131 778.139 801.033 814.646 832.851 847.050 859.693 871.520 882.920 894.116 905.223 916.300 927.469 1048.854

844 756.103 779.112 802.010 815.657 833.844 848.081 860.735 872.573 883.983 895.191 906.310 917.399 928.580 1050.104

845 757.048 780.086 802.987 816.639 834.864 849.112 861.777 873.626 885.047 896.266 907.397 918.498 929.691 1051.354

846 757.992 781.059 803.992 817.649 835.884 850.143 862.789 874.678 886.111 897.342 908.484 919.597 930.802 1052.604

847 758.937 782.004 804.969 818.631 836.905 851.174 863.831 875.702 887.175 898.417 909.541 920.696 931.914 1053.854

848 759.909 782.977 805.946 819.641 837.897 852.176 864.873 876.754 888.239 899.492 910.628 921.795 933.025 1055.104

849 760.854 783.951 806.951 820.623 838.917 853.207 865.914 877.807 889.303 900.568 911.715 922.894 934.136 1056.354

850 761.798 784.924 807.929 821.633 839.938 854.238 866.956 878.860 890.366 901.613 912.802 923.993 935.247 1057.604

851 762.743 785.897 808.906 822.615 840.930 855.269 867.998 879.912 891.401 902.688 913.889 925.092 936.358 1058.854

852 763.715 786.842 809.883 823.625 841.950 856.300 869.039 880.965 892.465 903.763 914.976 926.190 937.469 1060.104

853 764.660 787.816 810.888 824.607 842.971 857.331 870.052 882.018 893.528 904.839 916.063 927.289 938.580 1061.354

854 765.604 788.789 811.865 825.617 843.991 858.333 871.094 883.070 894.592 905.914 917.150 928.388 939.691 1062.604

855 766.549 789.762 812.842 826.599 844.983 859.364 872.135 884.123 895.656 906.989 918.237 929.487 940.802 1063.854

856 767.521 790.735 813.847 827.609 846.003 860.395 873.177 885.175 896.720 908.065 919.324 930.586 941.914 1065.104

857 768.466 791.681 814.824 828.591 847.024 861.426 874.219 886.199 897.784 909.140 920.411 931.685 943.025 1066.354

858 769.410 792.654 815.801 829.602 848.016 862.457 875.260 887.251 898.848 910.215 921.498 932.784 944.105 1067.604

859 770.355 793.627 816.778 830.584 849.036 863.459 876.302 888.304 899.911 911.290 922.585 933.883 945.216 1068.854

860 771.327 794.600 817.783 831.594 850.057 864.490 877.344 889.357 900.975 912.366 923.671 934.982 946.327 1070.104

861 772.272 795.573 818.760 832.604 851.077 865.521 878.356 890.409 902.039 913.441 924.758 936.081 947.438 1071.354

862 773.216 796.547 819.738 833.586 852.069 866.552 879.398 891.462 903.103 914.516 925.845 937.179 948.549 1072.604

863 774.161 797.492 820.743 834.596 853.090 867.583 880.440 892.515 904.167 915.591 926.932 938.278 949.660 1073.854

864 775.133 798.465 821.720 835.578 854.110 868.585 881.481 893.567 905.230 916.667 928.019 939.377 950.772 1075.104

865 776.078 799.438 822.697 836.588 855.102 869.616 882.523 894.620 906.294 917.742 929.106 940.476 951.883 1076.354

866 777.022 800.412 823.702 837.570 856.122 870.647 883.565 895.673 907.329 918.817 930.193 941.575 952.994 1077.604

867 777.967 801.385 824.679 838.580 857.143 871.678 884.606 896.725 908.392 919.892 931.280 942.674 954.105 1078.854

868 778.939 802.330 825.656 839.562 858.163 872.709 885.648 897.749 909.456 920.968 932.367 943.773 955.216 1080.104

869 779.884 803.303 826.633 840.572 859.155 873.740 886.661 898.801 910.520 922.043 933.454 944.872 956.327 1081.354

870 780.828 804.276 827.638 841.554 860.176 874.742 887.703 899.854 911.584 923.088 934.541 945.971 957.438 1082.604

Erlang Tables

.

9-30

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


871 781.773 805.250 828.615 842.565 861.196 875.773 888.744 900.906 912.648 924.164 935.628 947.039 958.549 1083.854

872 782.745 806.223 829.592 843.547 862.188 876.804 889.786 901.959 913.712 925.239 936.715 948.138 959.660 1085.104

873 783.689 807.196 830.597 844.557 863.209 877.835 890.828 903.012 914.775 926.314 937.772 949.237 960.772 1086.354

874 784.634 808.141 831.575 845.539 864.229 878.866 891.869 904.064 915.839 927.389 938.859 950.336 961.883 1087.604

875 785.579 809.115 832.552 846.549 865.249 879.868 892.911 905.117 916.903 928.465 939.946 951.435 962.994 1088.854

876 786.551 810.088 833.529 847.531 866.241 880.899 893.953 906.170 917.967 929.540 941.033 952.534 964.105 1090.104

877 787.495 811.061 834.534 848.541 867.262 881.930 894.965 907.222 919.031 930.615 942.120 953.632 965.216 1091.354

878 788.440 812.034 835.511 849.523 868.282 882.961 896.007 908.275 920.095 931.691 943.207 954.731 966.327 1092.604

879 789.412 812.980 836.488 850.533 869.274 883.992 897.049 909.327 921.158 932.766 944.293 955.830 967.438 1093.854

880 790.357 813.953 837.493 851.515 870.295 885.023 898.090 910.351 922.222 933.841 945.380 956.929 968.549 1095.104

881 791.301 814.926 838.470 852.525 871.315 886.025 899.132 911.404 923.257 934.916 946.467 958.028 969.660 1096.354

882 792.246 815.899 839.447 853.507 872.336 887.056 900.174 912.456 924.320 935.992 947.554 959.127 970.772 1097.604

883 793.218 816.872 840.452 854.517 873.328 888.087 901.215 913.509 925.384 937.067 948.641 960.226 971.883 1098.854

884 794.163 817.846 841.429 855.499 874.348 889.118 902.257 914.561 926.448 938.142 949.728 961.325 972.994 1100.104

885 795.107 818.791 842.406 856.510 875.368 890.149 903.270 915.614 927.512 939.217 950.815 962.424 974.105 1101.354

886 796.080 819.764 843.412 857.492 876.389 891.151 904.311 916.667 928.576 940.293 951.902 963.523 975.216 1102.604

887 797.024 820.737 844.389 858.502 877.381 892.182 905.353 917.719 929.639 941.368 952.989 964.621 976.327 1103.854

888 797.969 821.711 845.366 859.484 878.401 893.213 906.395 918.772 930.703 942.443 954.076 965.720 977.438 1105.104

889 798.913 822.684 846.343 860.494 879.422 894.244 907.436 919.825 931.767 943.519 955.163 966.819 978.549 1106.354

890 799.886 823.657 847.348 861.504 880.414 895.275 908.478 920.877 932.831 944.564 956.250 967.918 979.660 1107.604

891 800.830 824.602 848.325 862.486 881.434 896.306 909.520 921.901 933.895 945.639 957.337 969.017 980.772 1108.854

892 801.775 825.576 849.302 863.496 882.455 897.308 910.561 922.953 934.959 946.714 958.424 970.116 981.883 1110.104

893 802.747 826.549 850.307 864.478 883.475 898.339 911.574 924.006 936.022 947.790 959.511 971.215 982.994 1111.354

894 803.691 827.522 851.284 865.488 884.467 899.370 912.616 925.058 937.086 948.865 960.598 972.314 984.105 1112.604

895 804.636 828.495 852.261 866.470 885.488 900.401 913.657 926.111 938.150 949.940 961.685 973.413 985.216 1113.854

896 805.581 829.468 853.266 867.480 886.508 901.432 914.699 927.164 939.214 951.016 962.772 974.512 986.327 1115.104

897 806.553 830.414 854.243 868.462 887.500 902.434 915.741 928.216 940.248 952.091 963.859 975.611 987.438 1116.354

898 807.497 831.387 855.221 869.473 888.520 903.465 916.782 929.269 941.312 953.166 964.946 976.709 988.549 1117.604

899 808.442 832.360 856.226 870.455 889.541 904.496 917.824 930.322 942.376 954.241 966.033 977.808 989.660 1118.854

900 809.414 833.333 857.203 871.465 890.561 905.527 918.866 931.374 943.440 955.317 967.089 978.907 990.772 1120.104

Erlang Tables

9-31

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


901 810.359 834.307 858.180 872.447 891.553 906.558 919.878 932.427 944.504 956.392 968.176 980.006 991.883 1121.354

902 811.303 835.280 859.185 873.457 892.574 907.589 920.920 933.450 945.567 957.467 969.263 981.105 992.963 1122.604

903 812.276 836.253 860.162 874.439 893.594 908.591 921.962 934.503 946.631 958.542 970.350 982.204 994.074 1123.854

904 813.220 837.198 861.139 875.449 894.615 909.622 923.003 935.556 947.695 959.618 971.437 983.303 995.185 1125.104

905 814.165 838.172 862.116 876.431 895.607 910.653 924.045 936.608 948.759 960.693 972.524 984.402 996.296 1126.354

906 815.109 839.145 863.121 877.441 896.627 911.684 925.087 937.661 949.823 961.768 973.611 985.501 997.407 1127.604

907 816.082 840.118 864.098 878.451 897.647 912.715 926.128 938.713 950.887 962.843 974.698 986.569 998.519 1128.854

908 817.026 841.091 865.075 879.433 898.639 913.746 927.170 939.766 951.950 963.919 975.785 987.668 999.630 1130.104

909 817.971 842.064 866.080 880.443 899.660 914.748 928.183 940.819 953.014 964.994 976.872 988.767 1000.741 1131.354

910 818.943 843.010 867.058 881.425 900.680 915.779 929.225 941.871 954.078 966.069 977.959 989.866 1001.852 1132.604

911 819.888 843.983 868.035 882.435 901.701 916.810 930.266 942.924 955.142 967.145 979.046 990.965 1002.963 1133.854

912 820.832 844.956 869.040 883.418 902.693 917.841 931.308 943.977 956.206 968.190 980.133 992.063 1004.074 1135.104

913 821.804 845.929 870.017 884.428 903.713 918.872 932.350 945.029 957.240 969.265 981.220 993.162 1005.185 1136.354

914 822.749 846.902 870.994 885.410 904.734 919.874 933.391 946.053 958.304 970.341 982.307 994.261 1006.296 1137.604

915 823.693 847.876 871.999 886.420 905.754 920.905 934.433 947.105 959.368 971.416 983.394 995.360 1007.407 1138.854

916 824.666 848.849 872.976 887.402 906.746 921.936 935.475 948.158 960.431 972.491 984.481 996.459 1008.519 1140.104

917 825.610 849.794 873.953 888.412 907.766 922.967 936.516 949.211 961.495 973.566 985.568 997.558 1009.630 1141.354

918 826.555 850.767 874.958 889.394 908.787 923.998 937.529 950.263 962.559 974.642 986.655 998.657 1010.741 1142.604

919 827.527 851.741 875.935 890.404 909.779 925.029 938.571 951.316 963.623 975.717 987.742 999.756 1011.852 1143.854

920 828.472 852.714 876.912 891.386 910.799 926.031 939.612 952.368 964.687 976.792 988.829 1000.855 1012.963 1145.104

921 829.416 853.687 877.917 892.396 911.820 927.062 940.654 953.421 965.751 977.867 989.915 1001.954 1014.074 1146.354

922 830.361 854.660 878.894 893.406 912.840 928.093 941.696 954.474 966.814 978.943 991.002 1003.053 1015.185 1147.604

923 831.333 855.633 879.872 894.388 913.832 929.124 942.737 955.526 967.878 980.018 992.089 1004.151 1016.296 1148.854

924 832.278 856.607 880.877 895.398 914.853 930.155 943.779 956.579 968.942 981.093 993.176 1005.250 1017.407 1150.104

925 833.222 857.552 881.854 896.380 915.873 931.186 944.821 957.632 970.006 982.168 994.263 1006.349 1018.519 1151.354

926 834.195 858.525 882.831 897.391 916.893 932.188 945.833 958.655 971.070 983.244 995.350 1007.448 1019.630 1152.604

927 835.139 859.498 883.836 898.373 917.885 933.219 946.875 959.708 972.134 984.319 996.437 1008.547 1020.741 1153.854

928 836.084 860.472 884.813 899.383 918.906 934.250 947.917 960.760 973.197 985.394 997.524 1009.646 1021.852 1155.104

929 837.056 861.445 885.790 900.365 919.926 935.281 948.958 961.813 974.232 986.470 998.581 1010.745 1022.963 1156.354

930 838.000 862.418 886.795 901.375 920.947 936.312 950.000 962.865 975.296 987.545 999.668 1011.844 1024.074 1157.604

Erlang Tables

.

9-32

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


931 838.945 863.391 887.772 902.357 921.939 937.342 951.042 963.918 976.359 988.620 1000.755 1012.943 1025.185 1158.854

932 839.917 864.337 888.749 903.367 922.959 938.345 952.083 964.971 977.423 989.695 1001.842 1014.042 1026.296 1160.104

933 840.862 865.310 889.754 904.349 923.980 939.376 953.125 966.023 978.487 990.771 1002.929 1015.140 1027.407 1161.354

934 841.806 866.283 890.731 905.359 924.972 940.407 954.167 967.076 979.551 991.816 1004.016 1016.239 1028.519 1162.604

935 842.779 867.256 891.709 906.369 925.992 941.438 955.179 968.129 980.615 992.891 1005.103 1017.338 1029.630 1163.854

936 843.723 868.229 892.714 907.351 927.012 942.468 956.221 969.181 981.678 993.967 1006.190 1018.437 1030.741 1165.104

937 844.668 869.203 893.691 908.361 928.033 943.499 957.263 970.234 982.742 995.042 1007.277 1019.536 1031.852 1166.354

938 845.640 870.176 894.668 909.343 929.025 944.502 958.304 971.257 983.806 996.117 1008.364 1020.635 1032.963 1167.604

939 846.585 871.149 895.673 910.354 930.045 945.533 959.346 972.310 984.870 997.192 1009.450 1021.734 1034.074 1168.854

940 847.529 872.094 896.650 911.336 931.066 946.564 960.388 973.363 985.934 998.268 1010.537 1022.833 1035.185 1170.104

941 848.502 873.068 897.627 912.346 932.086 947.595 961.429 974.415 986.998 999.343 1011.624 1023.932 1036.296 1171.354

942 849.446 874.041 898.632 913.328 933.078 948.625 962.471 975.468 988.061 1000.418 1012.711 1025.031 1037.407 1172.604

943 850.391 875.014 899.609 914.338 934.099 949.656 963.484 976.520 989.125 1001.493 1013.798 1026.129 1038.519 1173.854

944 851.363 875.987 900.586 915.320 935.119 950.659 964.525 977.573 990.189 1002.569 1014.885 1027.228 1039.630 1175.104

945 852.307 876.960 901.591 916.330 936.139 951.690 965.567 978.626 991.253 1003.644 1015.972 1028.297 1040.741 1176.354

946 853.252 877.933 902.568 917.340 937.132 952.721 966.609 979.678 992.287 1004.719 1017.059 1029.396 1041.852 1177.604

947 854.224 878.907 903.546 918.322 938.152 953.751 967.650 980.731 993.351 1005.795 1018.146 1030.495 1042.963 1178.854

948 855.169 879.852 904.551 919.332 939.172 954.782 968.692 981.784 994.415 1006.870 1019.233 1031.593 1044.074 1180.104

949 856.141 880.825 905.528 920.314 940.193 955.785 969.734 982.836 995.479 1007.945 1020.320 1032.692 1045.185 1181.354

950 857.086 881.798 906.505 921.324 941.185 956.816 970.775 983.889 996.543 1009.020 1021.407 1033.791 1046.296 1182.604

951 858.030 882.772 907.510 922.306 942.205 957.847 971.817 984.912 997.606 1010.096 1022.494 1034.890 1047.377 1183.854

952 859.003 883.745 908.487 923.316 943.226 958.877 972.830 985.965 998.670 1011.171 1023.581 1035.989 1048.488 1185.104

953 859.947 884.718 909.464 924.299 944.246 959.908 973.872 987.018 999.734 1012.246 1024.668 1037.088 1049.599 1186.354

954 860.892 885.691 910.469 925.309 945.238 960.939 974.913 988.070 1000.798 1013.321 1025.755 1038.187 1050.710 1187.604

955 861.864 886.664 911.446 926.319 946.259 961.942 975.955 989.123 1001.862 1014.397 1026.842 1039.286 1051.821 1188.854

956 862.809 887.638 912.423 927.301 947.279 962.973 976.997 990.175 1002.926 1015.472 1027.929 1040.385 1052.932 1190.104

957 863.753 888.583 913.428 928.311 948.271 964.003 978.038 991.228 1003.989 1016.517 1029.016 1041.484 1054.043 1191.354

958 864.725 889.556 914.405 929.293 949.291 965.034 979.080 992.281 1005.053 1017.593 1030.103 1042.582 1055.154 1192.604

959 865.670 890.529 915.382 930.303 950.312 966.065 980.122 993.333 1006.117 1018.668 1031.159 1043.681 1056.265 1193.854

960 866.614 891.503 916.387 931.285 951.332 967.096 981.163 994.386 1007.181 1019.743 1032.246 1044.780 1057.377 1195.104

Erlang Tables

9-33

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


961 867.587 892.476 917.365 932.295 952.324 968.127 982.176 995.439 1008.245 1020.818 1033.333 1045.879 1058.488 1196.354

962 868.531 893.449 918.342 933.277 953.345 969.129 983.218 996.491 1009.309 1021.894 1034.420 1046.978 1059.599 1197.604

963 869.504 894.422 919.347 934.287 954.365 970.160 984.259 997.515 1010.343 1022.969 1035.507 1048.077 1060.710 1198.854

964 870.448 895.395 920.324 935.269 955.385 971.191 985.301 998.567 1011.407 1024.044 1036.594 1049.176 1061.821 1200.104

965 871.393 896.369 921.329 936.279 956.378 972.222 986.343 999.620 1012.470 1025.119 1037.681 1050.275 1062.932 1201.354

966 872.365 897.314 922.306 937.290 957.398 973.253 987.384 1000.673 1013.534 1026.195 1038.768 1051.374 1064.043 1202.604

967 873.310 898.287 923.283 938.272 958.418 974.284 988.426 1001.725 1014.598 1027.270 1039.855 1052.473 1065.154 1203.854

968 874.254 899.260 924.288 939.282 959.439 975.286 989.468 1002.778 1015.662 1028.345 1040.942 1053.571 1066.265 1205.104

969 875.226 900.234 925.265 940.264 960.431 976.317 990.509 1003.830 1016.726 1029.421 1042.029 1054.670 1067.377 1206.354

970 876.171 901.207 926.242 941.274 961.451 977.348 991.522 1004.883 1017.790 1030.496 1043.116 1055.769 1068.488 1207.604

971 877.115 902.180 927.247 942.256 962.472 978.379 992.564 1005.936 1018.853 1031.571 1044.203 1056.868 1069.599 1208.854

972 878.088 903.153 928.224 943.266 963.492 979.410 993.605 1006.988 1019.917 1032.646 1045.290 1057.967 1070.710 1210.104

973 879.032 904.126 929.202 944.276 964.484 980.441 994.647 1008.041 1020.981 1033.722 1046.377 1059.066 1071.821 1211.354

974 880.005 905.100 930.207 945.258 965.505 981.443 995.689 1009.094 1022.045 1034.797 1047.464 1060.165 1072.932 1212.604

975 880.949 906.045 931.184 946.268 966.525 982.474 996.730 1010.146 1023.109 1035.872 1048.551 1061.264 1074.043 1213.854

976 881.894 907.018 932.161 947.250 967.545 983.505 997.772 1011.170 1024.173 1036.947 1049.638 1062.363 1075.154 1215.104

977 882.866 907.991 933.166 948.260 968.537 984.536 998.814 1012.222 1025.236 1038.023 1050.725 1063.462 1076.265 1216.354

978 883.811 908.965 934.143 949.242 969.558 985.567 999.855 1013.275 1026.300 1039.098 1051.812 1064.560 1077.377 1217.604

979 884.755 909.938 935.120 950.253 970.578 986.598 1000.868 1014.327 1027.364 1040.173 1052.899 1065.659 1078.488 1218.854

980 885.727 910.911 936.125 951.235 971.599 987.600 1001.910 1015.380 1028.428 1041.219 1053.986 1066.758 1079.599 1220.104

981 886.672 911.884 937.102 952.245 972.591 988.631 1002.951 1016.433 1029.462 1042.294 1055.072 1067.857 1080.710 1221.354

982 887.644 912.857 938.107 953.255 973.611 989.662 1003.993 1017.485 1030.526 1043.369 1056.159 1068.956 1081.821 1222.604

983 888.589 913.830 939.084 954.237 974.632 990.693 1005.035 1018.538 1031.590 1044.444 1057.246 1070.055 1082.932 1223.854

984 889.533 914.804 940.061 955.247 975.652 991.724 1006.076 1019.591 1032.654 1045.520 1058.333 1071.154 1084.043 1225.104

985 890.506 915.777 941.066 956.229 976.644 992.755 1007.118 1020.643 1033.717 1046.595 1059.420 1072.222 1085.154 1226.354

986 891.450 916.722 942.044 957.239 977.664 993.757 1008.160 1021.696 1034.781 1047.670 1060.507 1073.321 1086.265 1227.604

987 892.395 917.695 943.021 958.221 978.685 994.788 1009.201 1022.749 1035.845 1048.746 1061.594 1074.420 1087.377 1228.854

988 893.367 918.669 944.026 959.231 979.705 995.819 1010.214 1023.801 1036.909 1049.821 1062.681 1075.519 1088.488 1230.104

989 894.312 919.642 945.003 960.213 980.697 996.850 1011.256 1024.825 1037.973 1050.896 1063.768 1076.618 1089.599 1231.354

990 895.284 920.615 945.980 961.223 981.718 997.881 1012.297 1025.877 1039.037 1051.971 1064.855 1077.717 1090.710 1232.604

Erlang Tables

.

9-34

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


991 896.229 921.588 946.985 962.233 982.738 998.912 1013.339 1026.930 1040.100 1053.047 1065.912 1078.816 1091.821 1233.854

992 897.173 922.561 947.962 963.215 983.759 999.914 1014.381 1027.982 1041.164 1054.122 1066.999 1079.915 1092.932 1235.104

993 898.145 923.535 948.967 964.226 984.751 1000.945 1015.422 1029.035 1042.228 1055.197 1068.086 1081.013 1094.043 1236.354

994 899.090 924.508 949.944 965.208 985.771 1001.976 1016.464 1030.088 1043.292 1056.272 1069.173 1082.112 1095.154 1237.604

995 900.062 925.481 950.921 966.218 986.791 1003.007 1017.506 1031.140 1044.356 1057.348 1070.260 1083.211 1096.265 1238.854

996 901.007 926.454 951.926 967.200 987.812 1004.038 1018.547 1032.193 1045.420 1058.423 1071.347 1084.310 1097.377 1240.104

997 901.951 927.400 952.903 968.210 988.804 1005.069 1019.560 1033.246 1046.483 1059.498 1072.434 1085.409 1098.488 1241.354

998 902.924 928.373 953.881 969.220 989.824 1006.100 1020.602 1034.298 1047.547 1060.573 1073.521 1086.508 1099.599 1242.604

999 903.868 929.346 954.886 970.202 990.845 1007.102 1021.644 1035.351 1048.582 1061.649 1074.607 1087.607 1100.710 1243.854

1000 904.840 930.319 955.863 971.212 991.865 1008.133 1022.685 1036.404 1049.645 1062.724 1075.694 1088.706 1101.821 1245.104

1100 1000.517 1027.500 1054.662 1071.044 1093.226 1110.796 1126.563 1141.462 1155.881 1170.131 1184.300 1198.535 1212.870 1370.069

1200 1096.387 1124.847 1153.573 1170.988 1194.671 1213.517 1230.469 1246.520 1262.145 1277.569 1292.935 1308.364 1323.920 1495.069

1300 1192.480 1222.333 1252.568 1270.988 1296.145 1316.237 1334.404 1351.637 1368.410 1385.006 1401.570 1418.223 1435.000 1620.069

1400 1288.740 1319.931 1351.647 1371.072 1397.647 1419.015 1438.368 1456.754 1474.675 1492.443 1510.205 1528.053 1546.080 1745.069

1500 1385.139 1417.640 1450.810 1471.184 1499.206 1521.821 1542.332 1561.871 1580.969 1599.910 1618.841 1637.912 1657.160 1870.069

1600 1481.676 1515.460 1550.056 1571.352 1600.822 1624.628 1646.325 1667.018 1687.264 1707.378 1727.506 1747.772 1768.241 1995.069

1700 1578.324 1613.363 1649.330 1671.577 1702.438 1727.463 1750.318 1772.164 1793.587 1814.845 1836.141 1857.631 1879.352 2120.069

1800 1675.112 1711.350 1748.688 1771.857 1804.082 1830.326 1854.340 1877.339 1899.882 1922.312 1944.807 1967.491 1990.432 2245.069

1900 1771.983 1809.421 1848.074 1872.138 1905.754 1933.219 1958.362 1982.515 2006.206 2029.809 2053.472 2077.350 2101.512 2370.035

2000 1868.937 1907.546 1947.515 1972.475 2007.426 2036.082 2062.413 2087.690 2112.530 2137.276 2162.138 2187.210 2212.623 2495.035

2100 1965.974 2005.728 2046.985 2072.840 2109.155 2139.003 2166.435 2192.865 2218.853 2244.773 2270.803 2297.070 2323.704 2620.035

2200 2063.095 2103.965 2146.482 2173.204 2210.884 2241.896 2270.486 2298.041 2325.207 2352.270 2379.469 2406.960 2434.815 2745.035

2300 2160.299 2202.258 2246.036 2273.625 2312.613 2344.817 2374.566 2403.246 2431.531 2459.767 2488.134 2516.819 2545.895 2870.035

2400 2257.559 2300.606 2345.617 2374.074 2414.371 2447.738 2478.617 2508.450 2537.855 2567.264 2596.830 2626.709 2657.006 2995.035

2500 2354.902 2399.010 2445.226 2474.523 2516.128 2550.687 2582.697 2613.655 2644.208 2674.761 2705.495 2736.569 2768.086 3120.035

2600 2452.301 2497.442 2544.863 2575.000 2617.914 2653.637 2686.777 2718.860 2750.561 2782.258 2814.161 2846.459 2879.198 3245.035

2700 2549.755 2595.929 2644.528 2675.505 2719.700 2756.586 2790.856 2824.064 2856.885 2889.755 2922.856 2956.319 2990.309 3370.035

2800 2647.265 2694.444 2744.221 2776.010 2821.514 2859.536 2894.936 2929.269 2963.239 2997.252 3031.522 3066.209 3101.389 3495.035

2900 2744.802 2792.987 2843.942 2876.543 2923.328 2962.514 2999.016 3034.474 3069.592 3104.749 3140.217 3176.068 3212.500 3620.035

3000 2842.423 2891.586 2943.663 2977.076 3025.142 3065.493 3103.125 3139.708 3175.946 3212.276 3248.883 3285.958 3323.611 3745.035

Erlang Tables

9-35

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


3100 2940.072 2990.185 3043.412 3077.637 3126.956 3168.471 3207.234 3244.912 3282.299 3319.773 3357.579 3395.849 3434.722 3870.035

3200 3037.748 3088.839 3143.188 3178.227 3228.798 3271.449 3311.314 3350.146 3388.652 3427.270 3466.244 3505.708 3545.802 3995.035

3300 3135.480 3187.521 3242.965 3278.816 3330.641 3374.427 3415.422 3455.351 3495.006 3534.797 3574.940 3615.598 3656.914 4120.035

3400 3233.268 3286.231 3342.797 3379.405 3432.511 3477.405 3519.531 3560.585 3601.359 3642.294 3683.605 3725.488 3768.025 4245.035

3500 3331.083 3384.968 3442.602 3480.022 3534.354 3580.412 3623.640 3665.819 3707.742 3749.821 3792.301 3835.348 3879.136 4370.035

3600 3428.926 3483.734 3542.462 3580.640 3636.224 3683.419 3727.749 3771.053 3814.096 3857.318 3900.966 3945.238 3990.216 4495.035

3700 3526.797 3582.499 3642.295 3681.257 3738.095 3786.426 3831.858 3876.287 3920.449 3964.845 4009.662 4055.128 4101.327 4620.035

3800 3624.696 3681.320 3742.183 3781.902 3839.966 3889.404 3935.966 3981.491 4026.803 4072.342 4118.357 4165.018 4212.438 4745.035

3900 3722.650 3780.141 3842.071 3882.548 3941.837 3992.411 4040.104 4086.725 4133.186 4179.869 4227.023 4274.908 4323.549 4870.035

4000 3820.632 3878.990 3941.960 3983.221 4043.736 4095.447 4144.213 4191.959 4239.539 4287.366 4335.719 4384.768 4434.660 4995.035

4100 3918.642 3977.867 4041.876 4083.866 4145.607 4198.454 4248.351 4297.222 4345.892 4394.892 4444.414 4494.658 4545.772 5120.035

4200 4016.652 4076.743 4141.792 4184.568 4247.506 4301.460 4352.459 4402.456 4452.275 4502.389 4553.110 4604.548 4656.852 5245.035

4300 4114.717 4175.648 4241.709 4285.241 4349.405 4404.496 4456.597 4507.690 4558.629 4609.916 4661.775 4714.438 4767.963 5370.035

4400 4212.810 4274.580 4341.653 4385.915 4451.304 4507.503 4560.706 4612.924 4665.012 4717.443 4770.471 4824.328 4879.074 5495.035

4500 4310.903 4373.540 4441.625 4486.616 4553.231 4610.538 4664.844 4718.158 4771.365 4824.940 4879.167 4934.188 4990.185 5620.035

4600 4409.052 4472.500 4541.569 4587.318 4655.130 4713.545 4768.981 4823.392 4877.748 4932.467 4987.862 5044.078 5101.296 5745.035

4700 4507.201 4571.460 4641.541 4688.047 4757.029 4816.581 4873.090 4928.626 4984.102 5039.994 5096.528 5153.968 5212.407 5870.035

4800 4605.377 4670.476 4741.541 4788.749 4858.957 4919.616 4977.228 5033.889 5090.485 5147.491 5205.223 5263.858 5323.519 5995.035

4900 4703.581 4769.464 4841.513 4889.478 4960.884 5022.652 5081.366 5139.123 5196.838 5255.018 5313.919 5373.748 5434.630 6120.035

5000 4801.814 4868.507 4941.513 4990.208 5062.812 5125.687 5185.503 5244.357 5303.221 5362.545 5422.615 5483.639 5545.710 6245.035

5100 4900.046 4967.523 5041.541 5090.937 5164.739 5228.723 5289.641 5349.620 5409.574 5470.042 5531.310 5593.498 5656.821 6370.035

5200 4998.305 5066.594 5141.541 5191.695 5266.667 5331.758 5393.779 5454.854 5515.957 5577.569 5639.976 5703.388 5767.932 6495.035

5300 5096.593 5165.638 5241.569 5292.424 5368.594 5434.794 5497.917 5560.088 5622.340 5685.096 5748.671 5813.278 5879.043 6620.035

5400 5194.908 5264.737 5341.625 5393.182 5470.522 5537.829 5602.025 5665.351 5728.694 5792.622 5857.367 5923.168 5990.154 6745.035

5500 5293.224 5363.808 5441.653 5493.939 5572.449 5640.865 5706.163 5770.585 5835.077 5900.119 5966.063 6033.059 6101.265 6870.035

5600 5391.567 5462.907 5541.709 5594.697 5674.405 5743.900 5810.330 5875.848 5941.460 6007.646 6074.758 6142.949 6212.377 6995.035

5700 5489.910 5562.034 5641.764 5695.455 5776.332 5846.964 5914.468 5981.082 6047.813 6115.173 6183.454 6252.839 6323.488 7120.000

5800 5588.281 5661.161 5741.820 5796.240 5878.288 5950.000 6018.605 6086.345 6154.196 6222.700 6292.120 6362.729 6434.599 7245.000

5900 5686.680 5760.288 5841.876 5897.026 5980.215 6053.036 6122.743 6191.579 6260.579 6330.227 6400.815 6472.589 6545.710 7370.000

6000 5785.079 5859.443 5941.960 5997.783 6082.171 6156.100 6226.881 6296.842 6366.933 6437.724 6509.511 6582.479 6656.821 7495.000

Erlang Tables

.

9-36

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


6100 5883.477 5958.597 6042.044 6098.569 6184.127 6259.135 6331.019 6402.076 6473.316 6545.251 6618.207 6692.369 6767.932 7620.000

6200 5981.932 6057.752 6142.127 6199.355 6286.083 6362.199 6435.156 6507.339 6579.699 6652.778 6726.902 6802.259 6879.012 7745.000

6300 6080.358 6156.935 6242.211 6300.140 6388.039 6465.235 6539.323 6612.573 6686.052 6760.305 6835.598 6912.149 6990.123 7870.000

6400 6178.840 6256.117 6342.323 6400.954 6489.994 6568.299 6643.461 6717.836 6792.435 6867.832 6944.293 7022.039 7101.235 7995.000

6500 6277.322 6355.328 6442.406 6501.740 6591.950 6671.334 6747.598 6823.070 6898.818 6975.329 7052.959 7131.929 7212.346 8120.000

6600 6375.804 6454.538 6542.518 6602.525 6693.906 6774.399 6851.736 6928.333 7005.201 7082.855 7161.655 7241.819 7323.457 8245.000

6700 6474.314 6553.748 6642.630 6703.339 6795.862 6877.463 6955.903 7033.567 7111.554 7190.382 7270.350 7351.709 7434.568 8370.000

6800 6572.824 6652.986 6742.769 6804.153 6897.817 6980.498 7060.041 7138.830 7217.937 7297.909 7379.046 7461.600 7545.679 8495.000

6900 6671.334 6752.197 6842.881 6904.966 6999.773 7083.562 7164.178 7244.094 7324.320 7405.436 7487.742 7571.490 7656.790 8620.000

7000 6769.899 6851.463 6943.021 7005.780 7101.757 7186.627 7268.345 7349.327 7430.703 7512.963 7596.437 7681.380 7767.901 8745.000

7100 6868.437 6950.701 7043.132 7106.594 7203.713 7289.691 7372.483 7454.591 7537.057 7620.460 7705.133 7791.239 7879.012 8870.000

7200 6967.002 7049.967 7143.272 7207.407 7305.669 7392.726 7476.620 7559.825 7643.440 7727.987 7813.829 7901.129 7990.123 8995.000

7300 7065.595 7149.233 7243.412 7308.221 7407.653 7495.790 7580.787 7665.088 7749.823 7835.514 7922.524 8011.020 8101.235 9120.000

7400 7164.161 7248.498 7343.579 7409.063 7509.609 7598.855 7684.925 7770.351 7856.206 7943.041 8031.220 8120.910 8212.346 9245.000

7500 7262.782 7347.792 7443.719 7509.877 7611.593 7701.919 7789.063 7875.585 7962.559 8050.568 8139.885 8230.800 8323.457 9370.000

7600 7361.375 7447.058 7543.886 7610.718 7713.577 7804.983 7893.229 7980.848 8068.942 8158.094 8248.581 8340.690 8434.568 9495.000

7700 7459.996 7546.352 7644.026 7711.532 7815.533 7908.047 7997.367 8086.111 8175.325 8265.621 8357.277 8450.580 8545.679 9620.000

7800 7558.645 7645.673 7744.193 7812.374 7917.517 8011.111 8101.534 8191.345 8281.708 8373.118 8465.972 8560.470 8656.790 9745.000

7900 7657.266 7744.967 7844.361 7913.215 8019.501 8114.175 8205.671 8296.608 8388.091 8480.645 8574.668 8670.360 8767.901 9870.000

8000 7755.942 7844.289 7944.528 8014.057 8121.457 8217.239 8309.838 8401.871 8494.444 8588.172 8683.364 8780.250 8878.981 9995.000

8100 7854.591 7943.610 8044.696 8114.899 8223.441 8320.304 8413.976 8507.135 8600.827 8695.699 8792.059 8890.140 8990.093 10120.000

8200 7953.268 8042.960 8144.891 8215.741 8325.425 8423.368 8518.142 8612.368 8707.210 8803.226 8900.755 9000.031 9101.204 10245.000

8300 8051.944 8142.281 8245.059 8316.582 8427.409 8526.432 8622.280 8717.632 8813.593 8910.753 9009.450 9109.921 9212.315 10370.000

8400 8150.621 8241.631 8345.254 8417.424 8529.393 8629.496 8726.447 8822.895 8919.976 9018.280 9118.146 9219.811 9323.426 10495.000

8500 8249.325 8340.980 8445.449 8518.294 8631.378 8732.560 8830.584 8928.129 9026.359 9125.806 9226.842 9329.701 9434.537 10620.000

8600 8348.029 8440.329 8545.617 8619.136 8733.362 8835.624 8934.751 9033.392 9132.713 9233.303 9335.537 9439.591 9545.648 10745.000

8700 8446.761 8539.679 8645.812 8719.978 8835.346 8938.688 9038.889 9138.655 9239.096 9340.830 9444.203 9549.451 9656.759 10870.000

8800 8545.493 8639.056 8746.036 8820.847 8937.330 9041.753 9143.056 9243.918 9345.479 9448.357 9552.899 9659.341 9767.870 10995.000

8900 8644.226 8738.433 8846.231 8921.689 9039.314 9144.817 9247.193 9349.152 9451.862 9555.884 9661.594 9769.231 9878.981 11120.000

9000 8742.958 8837.810 8946.427 9022.559 9141.298 9247.881 9351.360 9454.415 9558.245 9663.411 9770.290 9879.121 9990.093 11245.000

Erlang Tables

9-37

Blocking

Rate 0.01% 0.10% 0.50% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 20%


9100 8841.718 8937.187 9046.622 9123.429 9243.282 9350.974 9455.498 9559.678 9664.628 9770.938 9878.986 9989.011 10101.204 11370.000

9200 8940.477 9036.564 9146.845 9224.299 9345.266 9454.038 9559.664 9664.942 9771.011 9878.465 9987.681 10098.901 10212.315 11495.000

9300 9039.237 9135.969 9247.069 9325.140 9447.251 9557.102 9663.831 9770.175 9877.364 9985.992 10096.377 10208.791 10323.426 11620.000

9400 9137.997 9235.374 9347.264 9426.010 9549.235 9660.166 9767.969 9875.439 9983.747 10093.519 10205.072 10318.681 10434.537 11745.000

9500 9236.785 9334.779 9447.487 9526.880 9651.247 9763.230 9872.135 9980.702 10090.130 10201.045 10313.768 10428.571 10545.648 11870.000

9600 9335.572 9434.184 9547.711 9627.750 9753.231 9866.323 9976.273 10085.965 10196.513 10308.572 10422.464 10538.462 10656.759 11995.000

9700 9434.388 9533.589 9647.934 9728.620 9855.215 9969.387 10080.440 10191.199 10302.896 10416.069 10531.159 10648.352 10767.870 12120.000

9800 9533.176 9633.022 9748.157 9829.517 9957.228 10072.451 10184.606 10296.462 10409.279 10523.596 10639.855 10758.242 10878.981 12245.000

9900 9631.991 9732.427 9848.381 9930.387 10059.212 10175.515 10288.744 10401.725 10515.662 10631.123 10748.551 10868.132 10990.093 12370.000

10000 9730.806 9831.860 9948.632 10031.257 10161.196 10278.608 10392.911 10506.988 10622.015 10738.650 10857.246 10978.022 11101.204 12495.000

Erlang Tables

.

9-38

End of document

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