SaintPetersburg State University of Telecommunications Analysis of IPoriented
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 OUTLINE • Why IP and why self-similarity? • Self-similarity, what is it? • Heavy-tailed Distributions • Self-similarity and Networks • Conclusions
Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties OUTLINE • Why IP and why self-similarity? • Self-similarity, what is it? ØNGN ØIP Traffic types • Heavy-tailed distributions • Self-similarity and Networks • Conclusions
Why IP ? Growth of data services Channel switching Active introduction of IP networks Packet switching NGN – next generation network NGN is united network ü Supports different types of traffic ü Built on the base of the universal technology ü Divides switching, signaling and management ü Provides mentioned Qo. S (quality of service)
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
Why IP ? 2001 year - Conceptual regulations about multiservice networks structure in Russian communication networks NGN architecture Management system Management Application servers Applications Softswitches Control Core Separate networks Access Packet network Mobile network UTRAN Business subscribers PSTN Broadband network DSL CS Remote office/SOHO Media Gateway WLL LE Home subscribers Mobile subscribers
Why IP ? IP oriented networks Multiservice IP network applications classification of traffic types Type of traffic Applications IP telephony, videoconference Delay sensitivity Delay jitter sensitivity Low losses sensitivity RSVP, RTCP, UDP Control processes, on-line games Delay sensitivity Delay jitter sensitivity Losses sensitivity UDP, TCP Audio on demand Video on demand Internet broadcasting Low delay sensitivity Delay jitter sensitivity Losses sensitivity RSVP, SCTP, UDP, TCP Real time Stream Elastic Requirements Transport layer protocols Conference of documentation Low delay sensitivity Low delay jitter sensitivity High losses sensitivity Animation, file transfer, E-mail Very low delay sensitivity Low delay jitter sensitivity High losses sensitivity TCP
Why self-similarity ? Problem of NGN is to provide Qo. S for all types of traffic Qo. S 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”
Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties OUTLINE • Why IP and why self-similarity? • Self-similarity, what is it? ØFractals distributions • Heavy-tailed ØSome mathematics • Self-similarity and Networks ØHurst parameter • Conclusions
Self-similarity, what is it? Fractals 1975 Benua Mandelbrot fractus (lat. )– consisting of fragments 1. 5 D Fern leaf Fractals property – self-similarity Fractals are determined by the equations of chaos Chaos deterministic chaos Stochastic fractal processes are described by selfsimilarity of statistical characteristics of the second order
Self-similarity, what is it? Notations Aggregated process Semi-infinite segment of second-order-stationary stochastic process Its discrete argument Its parameters Let r(k) k- L 1(k), k L 1 – is function slowly varying at infinity
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 m 1 -H X(m) = X, m N In other words (m) is indistinguishable from the initial process X at X is es-s, if the aggregated process X(m) 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 secondorder stationary process and strictly stationary process
Self-similarity, what is it? Hurst parameter Harold Edwin Hurst detected that foodless and fertile 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
Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties OUTLINE • Why IP and why self-similarity? • Self-similarity, what is it? • Heavy-tailed distributions ØParameters and of distributions • Self-similarity Networks ØHeavy tails • Conclusions ØPareto ØWeibull ØLog-normal
Heavy-tailed distributions 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)=d. F(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 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
Heavy-tailed distributions Pareto distribution a is the shape parameter, b is minimum value of x Pareto distribution is most frequently used (Vo. IP, FTP, HTTP)
Heavy-tailed distributions Weibull distribution a is the shape parameter, β is the averaged weight speed x 0 is the minimum value of x Weibull distribution is used for FTP
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.
Analysis of IP-oriented Multiservice Networks Characteristics with Consideration of Traffic’s Self-Similarity Properties OUTLINE ØKendall classification Ø Researches of networks • Why IP and why self-similarity? ØLimitations for real networks • Self-similarity, what is it? ØQo. S parameters calculation • Heavy-tailed distributions ØNetwork modeling • Self-similarity and Networks • Conclusions
Self-similarity and networks Kendall classification A/ B/ V / K/ N Model of servicing 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 If N=∞ then A/B/V/K Often S=∞ → K=∞ then A/B/V Classic teletraffic models M/M/1, M/M/V/K , M/D/V etc. M – Poisson law D – determinate F(x)=const
Self-similarity and networks 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 Poisson Measured
Further researches Now – about 10000 works about self-similarity M. Taqqu, W. Willinger, K. Park, M. Crowell - research on the network layer. 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 Vo. IP traffic is 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
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 Traffic type Vo. IP FTP/TCP SMTP/TCP Distribution law M is Poisson law Authors А В P Р Molnar P W and LN Van Mieghem Downey М Molnar М P is Pareto law HTTP/TCP P LN and P Crovella Van Mieghem IP P P Paxson Ethernet P P Taqqu ATM D F-ARIMA Sadek LN is lognormal law F-ARIMA is Fractal Auto-regressive Integrated moving Average D is determinate
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
Self-similarity and networks Insertion of limitation for real values of random quantities If random value is the size of protocol data block then turndown of value is [k; L]. k is minimum size L is maximum. Restricted distribution L
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
Self-similarity and networks Now we could calculate Qo. S parameters – delays and losses Delays Losses nb – buffer size - average time of the packet’s service - average time of the packet’s staying - system load in the buffer. are quadratic coefficients of and variation of incoming flow and service time - average value of the packets’ number in the queue distributions, correspondingly tm - average value of delay parameter
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
Self-similarity and networks Multiservice traffic modeling Excel, Math. CAD, Math. LAB – non specialized OPNET, COMNET ect. GPSS General Purpose Simulating System Allows to research discrete models of different types NS 2 network simulator 2 Object-oriented discrete event simulator. Useful for simulating local and wide area networks The main advantage – it is free !!!
ns 2 Network simulator 2 (ns 2) 1996 year Project VINT (Virtual Inter. Network Testbed), organized by DARPA (Defense research project agency) • Specialized for existing modern technologies • Open source code software • Core modification availability • Ns 2 is free product • Result visualization availability
Results of modeling • • Animation Trace file Ploss for P/P/m
Conclusions • NGN is based on multiservice IP-oriented network • Providing Qo. S 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 Qo. S parameters
THANK YOU !
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