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Saint-Petersburg State University of Telecommunications

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Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

Saint-Petersburg State University of Telecommunications

Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

Anatoly M. Galkin

galkinam@inbox.ru

Adviser: Dr., Professor Gennady G. Yanovsky

Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

- Why IP and why self-similarity?
- Self-similarity, what is it?
- Heavy-tailed Distributions
- Self-similarity and Networks
- Conclusions

OUTLINE

Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties

- Why IP and why self-similarity?
- Self-similarity, what is it?
- Heavy-tailed distributions
- Self-similarity and Networks
- Conclusions

- NGN
- IP Traffic types

OUTLINE

NGN – next generation network

Growth of data services

Active introduction of IP networks

Channel switching

Packet switching

NGN is united network

- Supports different types of traffic
- Built on the base of the universal technology
- Divides switching, signaling and management
- Provides mentioned QoS (quality of service)

- Data networks evolution to NGN: the problem of compatibility of technologies and standards (providing traffic transmission of different applications in united transport network)

- Voice networks evolution to NGN: the problem of conversion from Channel Switching to Packet Switching

2001 year - Conceptual regulations about multiservice networks structure in Russian communication networks

NGN architectureManagement system

Management

Application servers

Applications

Softswitches

Control

Packet network

Core

Media Gateway

Mobile network

PSTN

Separate networks

Broadband network

UTRAN

Access

LE

DSL

WLL

CS

Mobile subscribers

Home subscribers

Business subscribers

Remote office/SOHO

Problem of NGN is to provide QoS for all types of traffic

QoS depends on service model

Old Markovian models (memory-less), Poisson laws and Erlang formulas don’t work in new networks.

1993 year W. Lenard, M. Taqqu, W. Willinger, D. Wilson. “On the Self-Similar Nature of Ethernet Traffic”

- Why IP and why self-similarity?
- Self-similarity, what is it?
- Heavy-tailed distributions
- Self-similarity and Networks
- Conclusions

- Fractals
- Some mathematics
- Hurst parameter

OUTLINE

Fractals

1975 Benua Mandelbrot

fractus (lat.)– consisting of fragments

1.5D

Fern leaf

Fractals property – self-similarity

Fractals are determined by the equations of chaos

Chaos deterministic chaos

Stochastic fractal processes are described by self-similarity of statistical characteristics of the second order

Notations

Aggregated process

Semi-infinite segment of second-order-stationary stochastic process

Its discrete argument

Its parameters

Letr(k)k-L1(k), k

L1 – is function slowly varying at infinity

Three definitions

Process is

1.Exactly second-order self-similar (es-s) with the parameter H=1 (/ 2), 0< <1

If rm(k) = r(k), kZ+, m {2,3,…}

2.Second-order asymptotical self-similar (as-s) with the parameter H=1 (/ 2), 0< <1

If

3.Strictly self-similar (ss-s) with the parameter H=1 (/ 2), 0< <1

If m1-H X(m) = X, mN

In other words

X is es-s, if the aggregated process X(m) is indistinguishable from the initial process X at least in term of statistical characteristics in second order.

X is as-s, if it meets es-s process after it is averaged on blocks of length m and m

The relation between ss-s and es-s processes is analogous to relation between second-order stationary process and strictly stationary process

Hurst parameter

Harold Edwin Hurst detected that foodless andfertile years are not random

0<H<1 – Hurst parameter (exponent)

H=0.5 – Brownian Motion

0<H<0.5 – antipersistence of the process

0.5<H<1 – persistent behaviour of the process or the process has long memory

- Why IP and why self-similarity?
- Self-similarity, what is it?
- Heavy-tailed distributions
- Self-similarity and Networks
- Conclusions

OUTLINE

- Parameters of distributions
- Heavy tails
- Pareto
- Weibull
- Log-normal

Probability distributions

X – random value

F(x)=P(X<x) – distribution function

It determines probability of random value X<x, where x is certain value 0≤F(x)≤1

f(x)=dF(x)/dx – probability destiny f(x)≥0

M[x] – mathematical expectation

D[x] – dispersion,σ – root-mean-square deviation

- quadratic coefficient of variation

Heavy-tailed distributions

Heavy-tailed distributions

Self-similar processes could be described by so-called Heavy-tailed distributions

Definition

The random variable is considered to have heavy-tailed distribution if with 0<a<2

a – shape parameter , c – a positive constant

Light-tailed distributions (Exponential, Gaussian) have exponential decrease tails

Heavy-tailed distributions have power law decrease tails

0<a<2 infinite dispersion

0<a≤1 also infinite average

Network interest is the case 1<a<2

Then H=(3-a)/2

Pareto distribution

Heavy-tailed distributions

a is the shape parameter,

b is minimum value of x

Pareto distribution is most frequently used (VoIP, FTP, HTTP)

Weibull distribution

a is the shape parameter,

β is the averaged weight speed

x0 is the minimum value of x

Weibull distribution is used for FTP

Log-normal distribution

It has a finite dispersion but has a subexponential decrease of a tail

It used for call-centers, LANs, etc.

- Kendall classification
- Researches of networks
- Limitations for real networks
- QoS parameters calculation
- Network modeling

- Why IP and why self-similarity?
- Self-similarity, what is it?
- Heavy-tailed distributions
- Self-similarity and Networks
- Conclusions

OUTLINE

Kendallclassification

Model of servicing

A/B/V/K/N

Classic teletraffic models

M/M/1, M/M/V/K , M/D/V etc.

M – Poisson law

A – law of incoming traffic

B – law of servicing traffic

S – queue size

V – number of severs

K – number of places in system

N – number of sources

D – determinate F(x)=const

If N=∞ then A/B/V/K

Often S=∞ → K=∞ then A/B/V

Poisson

Measured

1993 year W. Lenard, M. Taqqu, W. Willinger, D. Wilson. “On the Self-Similar Nature of Ethernet Traffic”

The period is 4 years

From 3 pieces of Bellcore network

It has been shown that 0.7<H<0.98

Further researches

M. Taqqu, W. Willinger, K. Park, M. Crowell - research on the network layer.

Now – about 10000 works about self-similarity

W. Willinger, M. Taqqu, R. Sherman, D. Wilson, A. Erramili, O. Narayan - research of the Ethernet traffic on data link layer

N. Sadek, A. Khotanzad, T. Chen- the АТМ traffic

K. Park, G. Kim, M. Crovella,V. Almeida, A. de Oliveira, A. B. Downey - research of TCP applications

In S. Molnar’s paper VoIP trafficis observed

Researches in Russia

The interest to self-similarity in Russia was initiated by

V.I. Neiman

Rigorous mathematics description of self-similar processes is given by B. Tsibakov

Applications of self-similar processes in telecommunications are presented in the book written by O. Sheluhin

Another works by A.J. Zaborovski, V.S. Gorodetski, V.V. Petrov

Further researches

DISTRIBUTION LAWS FOR DIFFERENT TYPES OF TRAFFIC IN IP NETWORKS

A is law of incoming traffic

B is law of of size of protocol data blocks

M is Poisson law

P is Pareto law

LN is lognormal law

F-ARIMA is

Fractal Auto-regressive Integrated moving Average

D is determinate

Even if one source generate self-similar traffic then aggregated traffic has self-similar properties.

At the network layer aggregated traffic is described with P/P/m most adequately

Insertion of limitation for real values of random quantities

If random value is the size of protocol data block then turn-down of value is [k; L]. k is minimum size L is maximum.

Restricted distribution

L

Insertion of limitation for real values of random quantities

Restricted distribution has a finite parameters

Mx and Dx

Then

- finite value

For Pareto law

Now we could calculate QoS parameters – delays and losses

Delays

Losses

nb – buffer size

- system load

- average time of the packet’s service

and

- average time of the packet’s staying in the buffer.

are quadratic coefficients of variation of incoming flow and service time distributions, correspondingly

- average value of the packets’ number in the queue

tm - average value of delay

parameter

Graphics

Loss probability in P/G/1 system for different distributions of service time

The average delay in P/G/1 system for different distribution laws of service time

Self-similarity boils down to packet losses, delays and congestions

Multiservice traffic modeling

Excel, MathCAD, MathLAB – non specialized

OPNET, COMNET ect.

GPSS General Purpose Simulating System

Allows to research discrete models of different types

NS2 network simulator 2

Object-oriented discrete event simulator. Useful for simulating local and wide area networks

The main advantage – it is free !!!

ns2

Network simulator 2 (ns2) 1996 year

Project VINT (Virtual InterNetwork Testbed), organized byDARPA (Defense research project agency)

- Specialized for existing modern technologies
- Open source code software
- Core modification availability
- Ns2 is free product
- Result visualization availability

Conclusions

- NGN is based on multiservice IP-oriented network
- Providing QoS is one of the main problem
- Multiservice IP traffic has a self-similarity properties
- Old distributions (Poisson) don’t work
- IP-traffic has Heavy-tailed distributions (the main is Pareto)
- Self-similarity makes worse QoS parameters

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