service of traffic demand

Tájékoztatáshttp://digitus.itk.ppke.hu/~gosztony/

2.1 Loss systems2.2 Network traffic management

Highway tunnel

Infocomm networks’ planningtraffic aspects

PPKE ITK

2011/12tanév

ŐsziFélév

Service of traffic demandIncoming demands (intensity, holding time)

no free resourceservice principle:

loss limited delay delay

redirection loss

free waiting place

no waitingplace

waiting

Simplified scheme:human factors,

queue management, etc.

are missing.

Infocomm networks' planning - traffic aspects - 2011.09.21

Erlang’s formula and its’ calculation

(The intensity of incoming demands is constant)

• Structure: n identical channels (servers, trunks, slots) – homogeneous group

• Strategy: full accessibility, one demand – one channel if all channels are busy the demand is lost

without any after effect (lost calls cleared) Erlang’s loss model – Lost Calls Cleared (LCC

model)• Traffic:

exp. holding time distribution. μ intensity (1/μ mean value, „holding time”)

arrival rate: intensity (Poisson process) pure birth and death process Pure Chance

Traffic type One PCT-1

Erlang’s model –1.

Infocomm networks' planning - traffic aspects - 2011.09.21See the Textbook: Chapter 4

• Offered traffic: offered traffic = carried traffic, if n∞

• Considered cases: (n = ∞ Poisson distribution) n < ∞ truncated Poisson distribution

• Performance measures E (time congestion) B (call congestion) C (traffic congestion)The model is insensitive to the

holding time distribution

that is: mean arrival rate x mean holding time

Insensitivity:

A system is insensitive to the holding time distribution

if the state probabilities of the system only depend on the

mean value of the holding time.

The model is insensitive to the holding time distribution

Erlang’s distribution -1.Traffic: PCT-1

Erlang’s distribution (truncated Poisson)

[conditional Poisson p(i i n) – see: Textbook]

Time congestionAll n channels are occupied in a random point of time

Call congestionRejection of a random demand

Erlang B formula

Erlang’s distribution -2.

Carried trafficMean value or expectation

Lost traffic

Traffic congestionE = B = Csince the intensity of demands is state independent

PASTA – Poisson arrivals see time averages

Erlang’s distribution -3.

Tabular calculation aid:GG Honlap, GyakorlatokErlang B táblázat

A (traffic), from anyN (number of channels two theErlang B (congestion) third

Erlang’s distribution - 4.

Generalisation of Erlang B• It is valid for any holding time distribution

(formulas depend only on the average holding time which is included in A, the offered traffic).

• The deduction assumed a Poisson arrival process. According to Palm’s theorem this is fulfilled, if the traffic is offered by many indpendent sources.

• Mathematical generalization is possible for fractional number of channels.

Erlang B formula is robust

Evaluation of Erlang’s B formula - 1.

For large state spaces numerical difficulties may occur in calculating state probabilities.

Easily applicable methods and recursion formulas are available.[See: Textbook, Chapter 4.5)

Not easy to handlesince n! and An increase rapidly

Useful recursion formula:

where:

Evaluation of Erlang’s B formula - 2.

BPP-traffic models

(Generalization of Erlang’s classical loss system)

BPP-traffic models -1.

BPPThese models are all insensitive to the service time distribution. Engset and Pascal models are even insensitive to the distribution of the idle time of sources. It is important always to use traffic congestion as the most important performance metric.

See the Textbook: Chapter 5

For these models the relationship between E, B and C congestion values and Z peakedness is well defined.

Erlang distribution

n=number of channels

Arrival intensity: λ

Engset distribution

Arrival intensity: (S-i)

Arrival intensity: (S+i)

Z, peakedness Peakedness (Z) The peakedness has dimension: [number of channels]

Poissondistribution:

Erlangdistribution:

„Number representation” Index of Dispersion for Counts – IDC= peakedness

Gives a characterization for the probability distribution of occupiedservers (lines, channels).

Binomial and Engsetdistribution:

In the case of binomial and Engset distribution β (offered traffic of free traffic sources), takes congestion already into account.

For applications the traffic congestion C is the most important, as it is almost a linear function of the peakedness.

Textbook:Fig. 5.7

Engset’s formula and its’ calculation

(The intensity of incoming demands depends on

the number of occupied traffic sources)

Engset’s model -1.

• Structure: n identical channels (servers, trunks, slots) – homogeneous group

• Strategy: full accessibility, one demand – one channel if all channels are busy the demand is lost without

any after effect – LCC (lost calls cleared) model• Traffic:

exp. holding time distribution. μ intensity (1/μ mean value, „holding time”)

offered traffic, A = carried traffic, if the number of channels is not limited (independent of the number of channels)

pure birth and death process Pure Chance Traffic type Two PCT-2

Results are independent from the holding time distribution they depend on its’ average value.

S traffic sources offer demands to n fully available channels. The arrival intensity of new demands is: (S-i)

exponentially distributedtime intervals(assumption required for themathematical deduction)

Possiblestates of atraffic source

The traffic source

Engset distribution - 1.

Cut equations exist for 0 ≤ i ≤ n .

(See: Textbook Chapter 5.3) Normalization:

Distribution:(truncatedbinomial)

Engset, 1918 !!

offered trafficof free trafficsource

Time congestion

Call congestion

After some transformations:

As if the remaining S-1 traffic sources had occupiedall channels.

When S increases E is increasing too, therefore:

Interpretation:

Carriedtraffic:

transformation withcut equations

Traffic congestion:designation:

Number of calls (traffic demands) per time unit

(S – Y) the number of free traffic sources

SaArelationshipwas applied

Lost traffic:

Duration of state [i]

Improvement function

Relations between E, B and CDesignation:

Alreadyderived

There are numerical problems for large values of S and n. Various numerically stable recursive formulae have been elaborated.

Evaluation of Engset’s formula - 1.

recursion according n:

recursion according S :

(See details in Chapter 5.5 of the Textbook)

Tabular calculation aid:GG Honlap, GyakorlatokEngset táblázat

S (number of sources), n (number of channels γ (call intesity)μ (release intensíty)

Engset E, B, CAA-Y

recursion according n and S :

Based on the previous calculations

Evaluation: If the parameter is increasing recursions by n and by n and S are both good, but not acceptable for decreasing parameters. Recursion by decreasing S is however acceptable.

(See details in Chapter 5.5 of the Textbook)

Overflow traffic

PeakednessSmooth and bursty traffic

Overflow traffic - model Basic problem: traffic from node A to nodes B or C are directed on different „first choice” routes and if these are fully occupied the overflow traffic might use the „overflow” route

Nowadays these type of arrangements are used only in networks.

Overflow traffic – Example 1a.

……10 erlPCT-I

8 81. 10 erl, 16 channels, E16=2,23%, lost traffic 0,223 erl.

PCT-ICould this be calculated in two steps ??

If yes,how ?

PCT-I ??

2. 10 erl, 8 channels, E8 =33,832%, Alost = 3,3832 erl A’ =3,3832 erl, 8 channels, E8’=0,1457 A’lost= 3,3832 x 0,1457 = 0,0483 erl. 0,223 erl = 0,0483 erl What is the reason ???

Overflow traffic does not have PCT-I/PCT-II character

Overflow traffic – Example 1b.

1. Peakedness Z is a good indicator for the relative loss probabilities of traffics with the same average value (A).

2. For a given A traffic Z has a maximum as a function of n, the number of channels.

3. For PCT-I Z = 1.4. If Z < 1, the traffic is smooth.5. If Z > 1, tha traffic is bursty.6. Congestion: smooth < PCT-I < bursty.

Overflow traffic - peakedness –1.

Peakedness Z of overflow traffic as a function of the offered PCT-1 traffic (A) and the number of channels (n)

Overflow traffic - peakedness –2.

Textbook:Fig. 6.8

IPP principleIPP = Interrupted Poisson Process

Principle: the process is in theoff state, if there are free channels in the primary route;if there isn’t any free channel it is in the in state.

For practical applications of the method one has to determine the actual values of the parameters involved.

Dimensioning overflow systems

ERT (Equivalent Random Theory)• an equivalent random traffic is applied which is derived

from the average value (expected value) and the variance of the overflow traffic

Modified ERT• calculation is based on a Z peakedness value which is

derived from the average value (expected value) and the variance of the overflow traffic

IPP (Interrupted Poisson Process)• If the primary route is occupied, a random (Poisson)

traffic appears temporarily (in an interrupted way) on the secondary route.

Textbook: Chapter 6.

Multi-dimensional loss systems

Example:multi-dimensional Erlang-B loss formula

• Structure: n uniform channels (trunks, slots) – homogenous group• Strategy:

full accessibility LCC - lost calls cleared

• Input process: two independent PCT-I traffic streams with 1 and 2 intensity holding times: exp. distribution. μ1 and μ2 intensity

• Offered traffic A1= 1/μ1 and A2 = 2/μ2

Model – 1.

In state (i,j) i channels are occupied by the first,j channels are occupied by the secondtraffic stream.

Restrictions:

Statistical equilibrium, (n+1)(n+2)/2 node equations.

Model – 2.

One demand occupies one channel.

Number of states:(n+1)(n+2)/2

Example of node equation:

p(0,1)[1+2+μ2]=p(0,0) 2 +p(1,1) μ1 +p(0,2)2μ2

Model – 3.

Multi dimensional Erlang distr. – 1.The state space diagram depicts a reversible Markov process with local balance and with product form solution.

It can be shown that the solution is: where: p(i) and p(j) are one dimensional, truncated Poisson distributions and Q is the normalisation constant

Poisson Arrivals See Time Averages – PASTA !!

Időtorlódás Hivástorlódás P(i+j=n)Forgalmi torlódás

0 )!()(

!!)()(

ji jiAAQ

jiAAQjpip

)2,0()0,2()1,1()1,0()0,1()0,0()()(

AAAAAAQ

ppppppjpip

n22n1nnn bnn

...ba2n

Generalization by

Newton’s binomiallaw

Multi dimensional Erlang distr. – 2.

It can be found, that:

This is a truncated Poisson distribution, with offer traffic

Generalization for N traffic streams:

Course of calculation:

Time congestion, etc.

PASTA !

q(x) relativ state probabilityp(x) absolute state probability

TTE – in networks

Network traffic management

TTE in networks – 1.

Traffic engineering functions

ITU-T Rec. E.360.1 (02/05) – Framework for QoS routing and related traffic engineering methods for IP ......

regulates the service provided by the network through capacity and routing adjustments.

„noisy”traffic load

unkownforecast

predicted average demand instantaneoushour-to-hourday-to-day

week-to weekseasonal

load variations

Feedback

the time constants of the feedback controls are matched to the load variations

ITU-T Rec. E.360.1 (02.05) – Framework for QoS routing and related traffic engineering methods for IP ......

Traffic engineering functions include:

traffic management, capacity management, and network planning. Traffic management ensures that network performance is maximized under all conditions, including load shifts and failures.

Capacity management ensures that the network is designed and provisioned to meet performance objectives for network demands at minimum cost.

Network planning ensures that node and transport capacity is planned and deployed in advance of forecasted traffic growth. Figure 1 illustrates traffic management, capacity management, and network planning as three interacting feedback loops around the network.

3.35 traffic engineering: Encompasses traffic management, capacity management, traffic measurement and modelling, network modelling, and performance analysis.

3.36 traffic engineering methods: Network functions which support traffic engineering and include call routing; connection routing, QoS resource management, routing table management, and capacity management.

3.37 traffic stream: A class of connection requests with thesame traffic characteristics

3.27 QoS (Quality of Service): A set of service requirements to be met by the network while transporting a Connection or flow; the collective effect of service performance which determine the Degree of satisfaction of a user of the service.

3.28 QoS resource management: Network functions which include class-of-service identification, routing table; derivation, connection admission, bandwidth allocation, bandwidth protection, bandwidth reservation, priority routing, and priority queuing.

3.29 QoS routing: See QoS Resource Management.

3.30 QoS variable: Any performance variable (such as congestion, delay, etc.) which is perceivable by a user.

TTE in IP networks - example a-1. Rec. ITU-T Y.1543 (2007.11.)Measurements in IP networks for inter-domainperformance assessment

The performance attributes that are used to characterize the network performance (inter-domain QoS) of a path are:

• Mean one-way delay.• One-way packet delay variation.• Packet loss ratio.• Path unavailability.

ITU-T Y.1543 (2007.11.) Measurements in IP networks for inter-domain performance assessment

TTE in IP networks - example a-2.

TTE in NGN networks - example b-1. Recommendation ITU-T Y.2173 (2008.09.)Management of performance measurement for NGN

SummaryThis Recommendation specifies requirements, reference measurement network model, high-level and functional architectures, and procedures for performance measurement management. This Recommendation together with [Recommendation ITU-T Y.1543] provides overall consistency for performance measurement and management of NGN.ScopeThis document specifies the management aspects of performance measurement:- Requirements for management of performance measurement....- A reference measurement network model....- A general and functional architecture for the management of performance measurement....- Management procedures covering various management scenarios.... - Application scenarios for management of performance measurement (MPM)

use cases.....

ABG = Access Border Gateway

IBG = Interconnection Border Gateway

CPNE =Customer Premises Network Edge

TTE in NGN networks - example b-2.

Recommendation ITU-T Y.2173 (2008.09.)

Traffic routing may be:• fixed

(Fixed Routing –FR)• time-dependent

(Time dependent Routing – TDR)• state dependent

(State Dependent Routing – SDR)• event dependent

(Event Dependent Routing – EDR)ITU-T Rec. E.350 (2000.03.)– Dynamic Routing Interworking(Framework for dynamic routing interworking in circuit-switched PSTN, narrow-band ISDN, and broadband ISDN networks)

Traffic routing (PSTN, ISDN) – 1.

Fixed Routing (FR) In a fixed routing (FR) method, a routing table is

fixed for a traffic stream. Hierarchical or non-hierarchical routing structures may be realized based on fixed routing. In both hierarchical or non-hierarchical structures, the route set and route selection sequence are determined on a preplanned basis and maintained over a long period of time.

ITU-T Rec. E.350 (2000/03.) – Dynamic Routing Interworking

Traffic routing (PSTN, ISDN) – 1a.

Time-Dependent Routing (TDR) Time-dependent routing (TDR) methods are a type

of dynamic routing in which the routing tables are altered at a fixed point in time during the day or week. TDR routing tables are determined on a preplanned basis and are implemented consistently over a time period. The TDR routing tables are determined considering the time variation of traffic load in the network. Typically, the TDR routing tables used in the network are coordinated by taking advantage of non-coincidence of busy hours among the traffic streams.

ITU-T Rec. E.350 (2000.03.) – Dynamic Routing Interworking

Traffic routing (PSTN, ISDN) – 1b.

State-Dependent Routing (SDR)

In state-dependent routing (SDR), the routes in the routing tables are altered automatically according to the state of the network. For a given SDR method, the routing table rules are implemented to determine the route choices in response to changing network status, and are used over a relatively short time period. Information on network status may be collected at a central processor or distributed to exchanges in the network. The information exchange may be performed on a periodic or on-demand basis. SDR methods use the principle of routing calls on the best available route on the basis of network state information.

Traffic routing (PSTN, ISDN) – 1c.

Event-dependent routing (EDR)

In event-dependent routing (EDR), the routing tables are updated locally on the basis of whether calls succeed or fail on a given route choice. In EDR, for example, a call is offered first to a fixed, preplanned route often encompassing only a direct route, if it exists. If no circuit is available on the preplanned routes, the overflow traffic is offered to a currently selected alternate route. If a call is blocked on the current alternate route choice, another alternate route is selected from a set of available alternate routes for the traffic stream according to the given EDR routing table rules. For example, the current alternate route choice can be updated randomly, cyclically, or by some other means, and may be maintained as long as a call is established successfully on the route.

Traffic routing (PSTN, ISDN) – 1d.

Traffic routing - MPLS (IP, ….) - 1 Multiprotocol Label Switching (MPLS) is a mechanism in

high-performance telecommunications networks which directs and carries data from one network node to the next. MPLS makes it easy to create "virtual links" between distant nodes. It can encapsulate packets of various network protocols.

MPLS is a highly scalable, protocol agnostic, data-carrying mechanism. In an MPLS network, data packets are assigned labels. Packet-forwarding decisions are made solely on the contents of this label, without the need to examine the packet itself. This allows one to create end-to-end circuits across any type of transport medium, using any protocol. The primary benefit is to eliminate dependence on a particular Data Link Layer technology, such as ATM, frame relay, SONET or Ethernet, and eliminate the need for multiple Layer 2 networks to satisfy different types of traffic. MPLS belongs to the family of packet-switched networks.

http://en.wikipedia.org/wiki/MPLS - 2011.09. Infocomm networks' planning - traffic aspects - 2011.09.21

Traffic routing MPLS (IP, ….) - 2 MPLS operates at an OSI Model layer

that is generally considered to lie between traditional definitions of Layer 2 (Data Link Layer) and Layer 3 (Network Layer), and thus is often referred to as a "Layer 2.5" protocol. It was designed to provide a unified data-carrying service for both circuit-based clients and packet-switching clients which provide a datagram service model. It can be used to carry many different kinds of traffic, including IP packets, as well as native ATM, SONET, and Ethernet frames.

http://en.wikipedia.org/wiki/MPLS - 2011.09.

Traffic calculationsApproximate end-to-end calculationmethods:

Assumptions:• If trunk groups of the networks are

independent

• If congestion probabilities are small

Multidimensional convolution algorithm(number of dimension equals to the number of trunk groups)

worst case

Number of states if state probabilities are applied

Service protection – 1.

For preferential subscribers (priority for e.g. first aid,) Depending from traffic load

• normal load cca. same congestion for all types of demands

• overload preference for some types of demands In digital switches

• call-gapping• priority (e.g. for hand overs in mobile networks)

In networks• trunk reservation• virtual channels protection

see next slides

Trunk reservation

Service protection – 2a.

Trunk reservation

Service protection – 2b. previous slide

In systems with integrated services all services have to be protected against each other.

This can be obtained by e.g.:• a certain minimum allocation of bandwidht which

ensures a certain minimum service,• a maximum allocation which both allows for the

advantages of statistical multiplexing and ensures that a single service do not dominate.

Virtual channel protection

Service protection – 3.

service of traffic demand

offered traffic

congestionc traffic

holding time distributionthat

time congestionall n

erlangs formula

intensity of demands

poisson arrival process

n identical channels

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