1. Internet Traffic Modeling Poisson Model vs. Self-Similar Model By Srividhya Chandrasekaran Dept of CS University of Houston

2. Outline Introduction Poisson model Self-Similar model Poisson model vs. Self-Similar model Experimental Result Co-Existence Remarks References

3. Introduction What is a model? Why do we need modeling? What are the kinds of models available? What are the models that I have discussed?

4. Poisson Model Poisson Process : Describes the number of times that some known event has occurred as a function of time, where events can occur at random times. Network traffic : Considered as a random arrival process under Poisson modeling.

5. Packet arrival is considered as 1 or ON state and the inter arrival time is 0 or OFF state

7. Self-Similar Model Self-Similarity: Something that feels the same irrespective of the scale. In case of stochastic objects like time- series, self-similarity is used in the distributional sense Long Range Dependence (LRD): The traffic is similar in longer spans of time.

9. Poisson Model vs. Self-Similar Model Poisson model considers network arrival as a random process. Self-similarity uses autocorrelation and does not consider the network traffic to be random.

10. Poisson Model vs. Self-Similar Model Poisson Model: –Does not scale the Bursty Traffic properly. –In fine scale, Bursty Traffic Appears Bursty, while in Coarse scale, Bursty Traffic appears smoothed out and looks like random noise.

11. Poisson Model vs. Self-Similar Model Self-Similar Model –Scales Bursty traffic well, because it has similar characteristics on any scale. –Gives a more accurate pictures due to Long Range Dependence in the network traffic

12. Experimental Results Researchers from UCal Berkeley, found that Poisson model could not accurately capture the network traffic.

13. Bellcode research group’s experiments show that traffic is Self- Similar

14. Co-Existence Bell labs research shows that both the models can co-exist. In a low congestion link, Long Range Dependence characteristics are observed. As load increases, the model is pushed to Poisson. As load decreases, model pushed to Self-Similarity.

15. Remarks Two models to describe network traffic: –Poisson model –Self-Similar model Each has its own advantage. Both the models can co-exist to give a more exact picture.

16. References: A Nonstationary Poisson view of Internet Traffic; TKaragiannis, M.Molle, M.Falautsos, A.Broido; Infocom in 2004 On Internet traffic Dynamics and Internet Topology II: Inter Model Validation; W.Willinger; AT&T Labs-Research Internet Traffic Tends Towards Poisson and Independent as the Load Increases; J.Cio, W.S.Cleveland, D.Lin, D.X.Sun; Nonlinear Estimation and Classification eds, 2002 On the Self-Similar Nature of Ethernet Traffic; W.Leland, M.s. Taqqu W.Willingfer, D.V.Wilson; ACM Sigcomm Proof of a fundamental Result in Self-Similar Traffic Modeling; M.S.Taqqu, W.Willinger, R.Sherman. ACMCCR: Computer Communication Review Self-Similarity; http://students.cs.byu.eduhttp://students.cs.byu.edu Traffic modeling of IP Networks Using the Batch Markovian Arrival Process; A.Klemm, C.Lindemann, M Lohmann; ACM 2003 Modelling and control of broadband traffic using multiplicative fractal cascades; P.M.Krishna,V.M.Gadre, U.B.Desai; IIT, Bombay

17. References Contd.. http://www.hyperdictionary.com/dictionary/stochastic+process http://www.sics.se/~aeg/report/node9.html http://www.sics.se/~aeg/report/node23.html The Effect of Statistical Multiplexing on the Long-Range Dependence of Internet Packet Traffic; Jin Cao, William S. Cleveland, Dong Lin, Don X. Su; Bell Labs Technical Report http://mathworld.wolfram.com/PoissonDistribution.html http://mathworld.wolfram.com/PoissonProcess.html http://www.itl.nist.gov/div898/handbook/eda/section3/eda366j.htm http://www.itl.nist.gov/div898/handbook/eda/section3/eda35c.htm Wide-Area Traffic: The Failure of Poisson Modeling; Vern Paxson and Sally Floyd; University of California, Berkeley Mathematical Modeling of the internet; F.Kelly, Statistical Laboratory, Univ of Cambridge. Internet Traffic modeling: Markovian Approach to self similarity traffic and prediction of Loss Probability for Finite Queues; S.Kasahara; IEICE Trans Communications, 2001

18. Questions