dimensioning atm networks

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Monash University, Australia

Dimensioning ATM

Networks

Dr. Milosh V. Ivanovich

e-mail: [email protected]

ISDN Networks and Applications

Week 9

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The Question The FUNDAMENTAL DILEMMA of Carriers and Service

Providers :

??? How ??? to provide telecommunications services

at minimal cost

Subject to -

meeting Quality Of Service (QoS) requirements. $

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The Answer lies in ... By applying sound NETWORK DESIGN principles

... but Network Design has conflicting

objectives !!

economic

robustnessQoS

fairness

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... Cleverly Exploiting ATM Network Features

ATM network = a collection ofpartially separatedlogical networks.

Physical

Virtual Path

Virtual Channel* Cell Priority Mgmt.

* VC Switching

* VP Switching

* Layered Network Architecture

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... First a Brief ATM RefresherWhat is ATM ?• Asynchronous Transfer Mode• Cell switching (relay)• Fixed cell size of 53 octets• Connection-oriented technology

48 Bytes

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ATM Flexibility

64 kbit/s

384 kbit/s (Nx64)

2 Mbit/s

34 Mbit/s

3.14 kbit/s

64 kbit/s

384 kbit/s

7.2 Mbit/s

34 Mbit/s

111 Mbit/s

Today Future

ATM Bearer(any bandwidth)

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Why is it called “ASYNCHRONOUS” ?

• Cells are transmitted continuously (idle cells are inserted)

• Supports bursty services, easily and efficiently• Header identifies information stream

Cell Travel (full link rate)Headers

IdleIdle Idle

Idle Idle

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The Roles of ATM Traffic Management• Call Level

– Connection Admission Control• point to point• broadcast

– Call Set-up

– Call Management (VC, VP)

– Routing

• Cell / Stream Level– Usage Parameter Control (Policing)

– Congestion Control; Selective Discard

• General– QoS Class– Transfer Capability

– Traffic Shaping

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ATM Transfer Capabilities ITU -T vs. ATM Forum

ITU-T ATM Transfer Capability ATM Forum Service Category

DBR - Deterministic Bit Rate

SBR - Statistical Bit Rate

CBR - Constant Bit Rate

VBR-RT - Real Time Variable Bit RateVBR-NRT - Non Real Time

Variable Bit Rate

ABT - ATM Block Transfer

ABR - Available Bit Rate

N/A

ABR - Available Bit Rate

UBR - Unspecified Bit RateN/A

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ATM Traffic Categories and Associated Applications

– Interactive Audio and Video (e.g. voice call, videoconference), Circuit Emulation:

» CBR, QoS Class 1

» VBR-rt, QoS Class 1

– Transfer for immediate use (e.g. image transfer, n.r.t. guaranteed constant bit rate applications, maybe some TCP applications - TELNET, HTTP).

» CBR, QoS Class 2/3

» VBR-nrt / ABR, QoS Class 2/3

– Transfer for later use (e.g most TCP applications - FTP, SMTP).

» ABR / UBR, QoS Class 2

Most StringentQoS Requirement

Least StringentQoS Requirement

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The Relationship Between Network Design and Dimensioning

Network Design

Dimensioning Structuring

“the engineer”

“thearchitect”

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ATM Network StructuringKey factors to consider :

• Distribution of user population.• Traffic: expected volume, type, and time

+ geographical distributions.• Flexibility and scalability• Reliability• Low overall {switching, transmission} cost.

Guiding principles :• Choose a flat or layered switching architecture based on the above factors.• Pre-emptive traffic segmentation - maintain QoS.

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ATM Network Structuring : Traffic Segregation

S

ws

ws

ws

ws

ws

ws

ws

ws

S

S

S

ws

ws wsws

ws

ws

ws ws

S

S

VBRonly VBR CBR

Architecture A: Segregation

Architecture B: Symmetry

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ATM Network Structuring : an “ATM LAN” example

ws

ws

ws

ws

ws

SVBR

CBRmesh

Station1

Station2

Station3

Station4

Avg. Video/VoiceCBRconn.

Normal st.

Mixed st.

System avg.

0.049

1.75

0.383

0.049

1.752

0.350

0.050

1.691

0.325

0.051

1.614

0.293

Delay(ms)

ImageVBRconn.

Mixed st.only

9.873 9.902 9.849 9.789

Mixing traffic types, while guaranteeing QoS may be achieved by:

– Architectural Traffic Segregation

– Traffic Shaping (Buffering!) and Policing VBR conns.

– “Throwing raw bandwidth at the problem”

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ATM Network Dimensioning Tradeoffs

(for a given QoS)

Bandwidth

Traffic Management

Buffering

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The Subject In a Nutshell : ... at the Burst Scale

What is the smallest bandwidth(service rate) we can use to servean SSQ fed by real traffic such thatrequired CLR is met ? (for a given buffer size).

ATM Network Dimensioning most commonly boils down to:

Link Dimensioning CLR PredictionOR

What is the predicted CellLoss Ratio (CLR) of asingle server queue fedby the modeled process?

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Hierarchy of Time Scales

Calls

Bursts

Cells- Randomness fromphase independence.

- Fluid flow models.- REM and RS.

- Effective BW concept.- Multi-rate C.S. network.

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The Call Scale : Effective Bandwidth EB - Necessary to enable associating a “fixed” amount of bandwidth with each inherently variable bit-rate call. Can then model ATM

network as a circuit switched network. No single formula - EB depends on model used. Example [GAN91], [KWC93] :We wish to determine the minimal required service rate CB() such that the

probability PB=Pr{X > B} that the buffer occupancy (X) exceeds some level B is

below . The buffer is part of a Single Server Queue (SSQ) system fed by a

Markov Modulated Rate Process (MMRP). Its complementary content

distribution is approximately given by the exponential,

– Q(x) = Pr{X > x} ~ e-x

Making the assumptions from [GAN91] (i.e. that ~ 1) we get the Effective

Bandwidth to be:

– CB () = -1(-log / B)

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The Call Scale : Review of some “Classical” Dimensioning Methods

Some Definitions:

Traffic Volume = Total of Service Times

Traffic Volume = Number of Calls x Average Service Time

Total of Service Times

Number of Calls

Average Service Time =

Traffic Volume___

Period of Observation

Average Traffic =

The unit of traffic is the “erlang”, symbolised by “E”

Erlangs

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Fundamental Relationship of Teletraffic Engineering

Number of Calls__ Period of Observation

Average Traffic = x Average Service Time

Average Arrival Rate,

(Avg. Departure Rate)

A

... and what about “congestion” ??A call encounters congestion or blocking if it can not proceed immediately due to lack of resources.

* Call Congestion* Time Congestion

* Traffic Congestion

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The Call Scale : Common Teletraffic Models

Sources Servers Model+ve Binomial-ve Negative Binomial Poisson

+ve finite Truncated Binomial - ENGSET-ve finite Truncated Negative Binomial finite Truncated Poisson - ERLANG-B

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The Call Scale : A Model of Repeat Call Attempts

Often a blocked call’s initiator will try again ...

TotalAttempts

First Attempts

RepeatAttempts

R1 - R

AbandonedCalls

IneffectiveAttempts

SuccessfulCalls

All possible causes ofIneffective Attempts

B1 - B

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The Call Scale : Modelling a Loss System (Erlang-B)

The first step is to construct a State Transition Diagram.

n

n

PPPP ... up to nDefine A = ... (Offered Traffic, or

alternatively, Utilisation).

Use the “Cut”Method to obtain

Balance Eqns.

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Comparison of Poisson & Erlang-B PDFs

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

State

P(S

tate

)

Poisson

Erlang-B

Arrival Rate, = 5; Service Rate, = 1Off. Traffic, A = 5 ; No. Circuits, n = 10 (Erlang-B), = infinite (Poisson).

Erlang-B Distribution is also called

Truncated Poisson

Erlang-B Distribution:Time Congestion

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Can we Really Use the Erlang-B Formula for ATM Network Dimensioning ?

YES, but ...

– Only in one very special, and not very useful case: when all connections sharing the ATM bearer are of the same rate (“?!But the whole point of ATM is ...”)

– For example, we could have 10 combined CBR and VBR VC connections, with EB = 2Mbit/s, sharing a 34Mbit/s ATM VP.

– Blocking Probability would be = E (10, 34 / 2)» where E(*, *) is the Erlang-B Loss Function.

Conclusion :

– WE NEED MORE SOPHISTICATED MODELS !

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The Answer: Multi-rate Models Basic Link Model for the Complete Sharing Policy

•N different traffic classes accessing an ATM Tx link with cap. c Mbps•Arrival process for class i calls is Poisson, rate i.•Holding time follows a general distribution function, mean 1/i. •During the lifetime of a class i call, a constant rate denoted by ci, is allocated to it, and released immediately after its departure.

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Kaufman and Roberts Recursive Solution Exact algorithm - not an approximation. Based on a mapping of the multi-dimensional state space into a one dimensional state space. Uses “proper bandwidth discretisation”. Prevents “State Explosion” by compressing many different states into one.

• Basic Bandwidth Unit, BBU : • gcd is the “greatest common divisor”. • In broadband networks, typical BBUs may be 64kbps or 2.048Mbps.• Max. No. of available BBUs :• No. of BBUs required for class i :• System states defined by one quantity - the no. of occupied BBUs : m

c c for i Ni gcd( ) 1

M c c /

m c ci i /

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An Example : A Four Class System Call Blocking Probabilities - note the UNFAIRNESS

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An Example : A Four Class System (cont.) Link utilisation sharing - related to UNFAIRNESS,

note the under-utilisation for greater BW classes.

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Equalisation and Fairness Issues Basic link model for Trunk Reservation (TR).

• Many different Connection Admission Control (CAC) strategies for achieving some form of fairness exist : complete sharing, partial sharing, class limitation, trunk reservation (TR). • For a comparson of such strategies, see [KW88].• Briefly consider TR - one of the simplest and most effective methods to adjust/equalise call blocking.• Aim is to influence performance parameters such as call blocking pr.

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Enhancements : Combined Call and Burst Scale Model

Similar to complete sharing model outlined on p25. Tx link capacity c, N traffic classes (CBR & VBR). CBR calls modelled at call level only. VBR calls modelled at both burst and call levels. Connection admission control and blocking behaviour is different for CBR and VBR calls:

– CBR calls of class i» Must be accepted at CALL level.» And at BURST level.

– VBR calls of class j» Must be accepted at CALL level only.

Call Blocking

Burst Blocking

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The Burst (Stream) Scale - What is it? A time scale typical of an:

– ON/OFF source’s activity period,

– Video Frame duration,

– IP packet (carrying say a UDP datagram),

– Or any other “interval” aggregating some cells, but not being as long as a call duration.

The discrete nature of cell arrivals can be ignored. Instead, we focus on the incoming “stream” of cells.

– Denoted by the continuous random variable An or A(t) representing the “amount of work” entering the system,

– An used for discrete time modelling, – A(t) used for continuous time modelling .

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The Burst Scale (cont.) Time can either be modelled as :

– Continuous: generally used for fluid flow based models.

– Discrete: time divided into fixed-length sampling intervals.

Burst scale congestion - modelled by :– Burst scale loss, in the form of Rate Envelope

Multiplexing (REM), and /or

– Burst scale delay, in the guise of Rate Sharing (RS).

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Three approaches for Link Dimensioning (and CAC) at the Burst Scale

• Peak Allocation• Rate Envelope Multiplexing

(REM)• Rate Sharing (RS)

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Three approaches for Link Dimensioning (and CAC) at the Burst Scale (cont .)

Approach BufferSharing?

Bandwidth Sharing?

Peak Rate Allocation No NoRate Envelope

Multiplexing (REM)No Yes

Rate Sharing (RS)

Yes Yes

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Burst Scale Link Dimensioning Example

• Want to dimension an ATM bearer,• Given 70 variable bit-rate 2 Mb/s connections,• How much capacity is needed?

70 x 2 = 140 Mb/s

A Simple Solution: Peak Rate Allocation

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Example Continued: Let’s Try REM• More information required for each connection:

Peak (p) = 2 Mb/s, Mean (m) = 0.2 Mb/s• Assume On/Off Model for each connection so:

Variance = (p - m) m = 1.8 x 0.2 = 0.36 • For 70 connections (linear superposition):

Aggregate Mean = 70 x 0.2 = 14Aggregate Variance = 70 x 0.36 = 25.2

• By the Central Limit Theorem, the Aggregate Traffic Rate (Mb/s) can be modelled by a Gaussian R.V. X :

= 14 and 2 = 25.2

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REM Example - Continued• Minimize Required Link Bandwidth, B (Mb/s)

• Subject to Bit Loss Ratio (BLR) < 10-5

• Where BLR is given by:

BLR = E [( X - B )+ ] / E [X]

Solution: (1) (X-B)+ = X-B if X >B and = 0 if X < B.

(2) If X has density f(x) then:

Bx

dxxfBxBXE )()(])[(

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REM Example - ContinuedSolution (cont.):

(3) The Bit Loss Ratio

is thus given by

(4) Using the bisection algorithm, this equation is then numerically solved (e.g. use C++ program, or tool such as Mathematica):

Bmin = 32.485376 Mb/s.

Bx

x

Bx

dxeBx

dxxfBx

BLR

2

2

1

2

1)(

)()(

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Rate Sharing

• More complex to model because :– Large buffers as well as bandwidth is

considered,

– Now correlation is important.

• Traffic Modelling

• Queueing Theory & Simulation

• Real traffic traces

• Two approaches: Classical and Direct.

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Gamma Loss Prediction Tool : SSQ Dimensioning by the Classical Method

Compute Cell Loss Rate (CLR)

Find new service rate

Input: * Queue information(service, buffer)* Traffic model or trace

CLR

service rate

Aim: Find Minimum service rateSubject to CLR

Method: Bisection

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Autocorrelation of a Traffic Stream

• Low autocorrelation – Low dependence between traffic arriving in intervals

separated in time.

High autocorrelation – High dependence between traffic arriving in intervals

separated in time.

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Real Life Example of RS versus REM (1)Link Utilisation vs. Buffer SizeMeasured Ethernet TRAFFIC -Loss Probability = 1/10,000

Buffer Size (cells)

100,00010,0001,000

Uti

lisa

tio

n %

0

100

80

60

40

20

100

REM

Rate Sharing

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Real Life Example of RS versus REM (2)Link Utilisation vs. Buffer SizeVBR Video TRAFFIC (MPEG)Loss Probability=1/10,000

Uti

lisa

tio

n %

Buffer Size (cells)

0

10

20

30

40

50

60

70

100 1,000 10,000 100,000

REM

RS

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Critical Statistical Characteristics of a Traffic Process

• Mean,

• Variance,

• Autocovariance Sum or Autocovariance Integral (equal to the Asymptotic Variance Rate).

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Arrival Process Autocovariance Sum / Integral

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 5.0

The Variance

v=Autocovariance Integral

Lag

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Common SRD Traffic Models ...

• Bernoulli Process• Geometric (or Binomial) Batch

Process• On-Off• n-state Markov Modulated Processes• Gaussian

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But what if the Autocovariance sum is infinite?

LONG RANGE DEPENDENCE (LRD) otherwise known as

SELF-SIMILAR (FRACTAL) TRAFFIC

lag

auto

corr

elat

ion

LRDSRD

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SRD Process : Poisson Traffic at Different Timescales

Interval = 1

303540455055606570

0 20 40 60 80 100

Interval = 10

300350400450500550600650700

0 20 40 60 80 100

Interval = 100

300035004000450050005500600065007000

0 20 40 60 80 100

Interval = 1000

300003500040000450005000055000600006500070000

0 20 40 60 80 100

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LRD Process : Ethernet Traffic (Self Similar)

1 Second Intervals 10 Second Intervals 60 Second Intervals

100 Second Intervals Half Hour Intervals 1 Hour Intervals

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Measuring Self-Similarity : the Hurst Parameter

Slope = 1: Non-fractal (SRD)

Slope > 1: Fractal (LRD)

Log V(A(t))

Log (t)

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Hurst Parameter Values for VBR Video Traffic

Video Application Hurst Parameter

Student sitting at workstation(videoconference)

0.53

Episode of “The Simpsons” 0.88

Movie: “Terminator 2” 0.80

Episode of “Mr Bean” 0.95

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Why is Real Traffic Bursty and Correlated on a Wide Range of Timescales (FRACTAL) ?

• Very diverse IP packet lengths– FTP, SMTP, IP Phone ... etc. packets have very

different size distributions.

• Large differences exist in WWW document sizes

• VBR Video streams found to be self similar

• People and business timing characteristics (meeting, holidays, etc.)

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A Wide Difference of Document Sizes Available Through the WWW

Data Entity Bytes

ASCII Page 103

X-Ray 107

Star War (JPEG coded) 5109

Word document (10 pages) 5104

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References 1/2[AZN98] R.G. Addie, M. Zukerman, and T. D. Neame, “Broadband Traffic Modelling: Simple

Solutions to Hard Problems”, IEEE Communications Magazine, p88-95, August, 1998.

[EGHS96] V. Elek, Z. Gal, P. L. Huong and C. Szabo, “ATM LAN Network Design”, Journal on Telecommunications, vol. XLVII, January-February, 1996.

[EM73] O. Enomoto and H. Miyamoto, “An analysis of mixtures of multiple bandwidth traffic on time division in switching networks”, In 7th Int. Teletraffic Congress Proceedings, pages 635.1-8, North Holland-Elsevier Science Publishers , 1973.

[HR93] F. Huebner and M. Ritter, “Blocking in multi-service broadband systems with CBR and VBR input traffic.”, In 7th ITG/GI Conference, pages 212-225, Aachen, September 1993.

[Hui88] J. Y. Hui, “Resource Allocation for Broadband Networks”, IEEE J. Sel. Areas in Comm., vol. 6 no. 9: p.1598-1608, 1988.

[Kau81] J. S. Kaufman, “Blocking in a shared resource environment”, IEEE Trans. Comm., vol. 29, no. 10 : 1474-1481, 1981.

[KW88] R. Kleinewillinghoefer-Kopp and E. Wollner, “Comparison of access control strategies for ISDN-traffic on common trunk groups”, In 12th Int. Teletraffic Congress Proceedings, pages 5.4A.2.1-7, North Holland-Elsevier Science Publishers, 1988.

[KWC93] G. Kesidis, J. Walrand, and C-S. Chang, “Effective bandwidth for multiclass Markov fluids and other ATM sources”, IEEE/ACM Trans. Networking, vol.1 no. 4: p424-428, August, 1993.

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References 2/2[LPTB93] J. Lubacz, M. Pioro, A. Tomaszewski and D. Bursztynowski, “A framework for

network design and management”, Internal Report, Institute of Telecommunications, Warsaw University of Technology, 1993.

[RMV96] J. Roberts, U. Mocci and J. Virtamo (Eds.), “Broadband Network Teletraffic”, Final Report of Action COST 242, Springer, Berlin, 1996.

[Rob81] J. W. Roberts, “Teletraffic models for the telecom 1 integrated services network”, In 10th Int. Teletraffic Congress Proceedings, page 1.1.2, North Holland-Elsevier Science Publishers, 1983.

[TGH93] P. Tran-Gia and F. Huebner, “An analysis of trunk reservation and grade of service balancing mechanisms in multiservice broadband networks.”, In IFIP Workshop TC6, Modeling and Performance Evaluation of ATM Technology, page 2.1, La Martinique, 1993.

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Acknowledgments

Thanks to the following people for ideas / illustrations / and selected references:

A. Prof. Moshe Zukerman, University of Melbourne

Dr. Robert Warfield, Telstra

Peter Black, Telstra Research Laboratories

dimensioning atm networks

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