Internet Traffic ModelingPoisson Model vs. Self-Similar

Model

BySrividhya Chandrasekaran

Dept of CSUniversity of Houston

Outline

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

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?

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.

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

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.

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.

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.

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

Experimental Results

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

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

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.

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.

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.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

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

Questions