Saint-Petersburg State University of Telecommunications

1. 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

2. 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

3. 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

4. Why IP ? 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)

5. Why IP ? • 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

6. Why IP ? 2001 year - Conceptual regulations about multiservice networks structure in Russian communication networks NGN architecture Management 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

7. Why IP ? IP oriented networks Multiservice IP network applications classification of traffic types

8. Why self-similarity ? 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”

9. 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 • Fractals • Some mathematics • Hurst parameter OUTLINE

10. Self-similarity, what is it? 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

11. Self-similarity, what is it? 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

12. Self-similarity, what is it? 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), kZ+, 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, mN 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

13. Self-similarity, what is it? 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

14. 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 • Parameters of distributions • Heavy tails • Pareto • Weibull • Log-normal

15. 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

16. 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

17. 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)

18. Heavy-tailed distributions 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

19. Heavy-tailed distributions Log-normal distribution It has a finite dispersion but has a subexponential decrease of a tail It used for call-centers, LANs, etc.

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

21. Self-similarity and networks 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

22. Self-similarity and networks 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

23. 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

24. 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

25. Self-similarity and networks 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

26. Self-similarity and networks 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

27. Self-similarity and networks 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

28. Self-similarity and networks Insertion of limitation for real values of random quantities Restricted distribution has a finite parameters Mx and Dx Then - finite value For Pareto law

29. Self-similarity and networks 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

30. Self-similarity and networks 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

31. Self-similarity and networks 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 !!!

32. 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

33. Results of modeling • Animation • Trace file Ploss for P/P/m

34. 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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