Internet Traffic Modeling
Poisson Model vs. Self-Similar Model
By
Srividhya Chandrasekaran
Dept of CS
University of Houston
Outline
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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 timeseries, 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 SelfSimilar
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:
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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..
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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