Self-Similarity of Network Traffic

Presented by Wei Lu

Supervised by Niclas Meier

05/06 2004

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Table of Content

• Network Traffic Study– Motivation– Measurement– Modeling

• Classic Model, Poisson or Markovian• Self-Similar Model

– What’s Self-Similarity– Definition of Self-Similarity– Explanation of Self-Similarity– Impact on network performance– Adapting to Self-Similarity

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• Understanding network traffic behavior is essential for all aspects of network design and operation– Component design– Protocol design– Provisioning– Management– Modeling and simulation

Motivation for Network Traffic Study

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Network Traffic Measurement

• Collect data or packet traces showing packet activity on the network for different network applications

• Purpose– Understand the traffic characteristics of existing

networks– Develop models of traffic for future networks– Useful for simulations, planning studies

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• Traffic modeling in the world of telephony was the basis for initial network models– Assumed Poisson arrival process– Assumed Exponential call duration– Well established queuing literature based on

these assumptions– Enabled very successful engineering of

telephone networks

Network Traffic ModelingIn the past…

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Classic Model

• Poisson Process

• Markov Chain

• ON-OFF model Interrupted Poisson Process

tn

n en

ttp

!

)()(

0 1

ONFixed rate arrival

OFF

ActivePoisson arrival

Idle

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The Story Begins with Measurement

• In 1989, Leland and Wilson begin taking high resolution traffic traces at Bellcore – Ethernet traffic from a large research lab

– Mostly IP traffic (a little NFS)

– Four data sets over three year period

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Actual Network Traffic v.s. Poisson

[Chun Zhang 2003]

Network Traffic Measurement

Poisson Traffic Model

5,8,2 mean 5

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What’s Self-Similarity

• Self-similarity describes the phenomenon where a certain property of an object is preserved with respect to scaling in space and/or time. (also called fractals)

• If an object is self-similar, its parts, when magnified, resemble the shape of the whole.

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Definition of Self-Similarity

• Self-similarSelf-similar processes are the simplest way to model processes with long-range dependencelong-range dependence

• The autocorrelation function k of a process with lon

g-range dependence is not summable: – k .

• e.g. k k- as k . for 0 < < 1

• Autocorrelation function follows a power law

• Slower decay than exponential process

– If k < .

Long Range Dependence

Short Range Dependence

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Self-Similarity contd.

• Zero-mean stationary time series X = (Xt;t = 1,2,3,…), m-aggregated series X(m) = (Xk

(m);k = 1,2,3,…) by summing X over blocks of size m.

• X is H-self-similar (distributional self-similarity), if for all positive m, X(m) has the same distribution as X rescaled by mH.– PDF{Xat}=PDF{ mH{Xt} }.

• X is Second-order-self-similar, if (m)(k) of the series X(m) for all m. – Var(X(m) ) = 2 m-β , and– (m) (k) = (k), k0 [Asymptotically: (m) (k) (k), m

• Degree of self-similarity is expressed as the speed of decay of series autocorrelation function using the Hurst parameter

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=1,H=0.5 SRD

=0.6,H=0.7 LRD

Log( Var(X(m) ) ) = log(2m-β) =2log - βlog m

Y X

Graphic Tests, e.g. Variance-time plots• The variance of X(m)

is plotted v.s. m on log-log plot

• Slope (- > –1 indicates of SS

• H = 1 - /2– LRD, ½ < H < 1

– Degree of SS\LRD increases as H 1

H increases, more bursty

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Modeling Self-Similarity

• Superposition of High Variability ON-OFF Sources– Extension to traditional ON-OFF models by allowing

the ON and OFF periods to have infinite variance (high variability or Noah Effect)

X1(t) off on

X2(t) on

X3(t) off

S3(t)

3

02 2 2

1 1 1

time

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Explanation of Self-Similarity

• Consider a set of processes which are either ON or OFF– The distribution of ON time is heavy tailed (wide range

of different values, including large values with non-negligible probability)

• The size of files on a server are heavy-tail

• The transfer times also have the same type of characteristics.

– The distribution of OFF time is heavy tailed• Since some source model phenomena that are triggered by

humans (e.g. HTTP sessions) have extremely long period of latency.

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Impact on Network Performance

• Self-similar burstiness can lead to the amplification of packet loss.

• The burstiness cannot be smoothed.

• Limited effectiveness of buffering– queue length distribution decays slower than expone

ntially v.s. the exponential decay associated with Markovian input

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[Kihong Park, Walter Willinger]

•Mean queue length v.s. buffer capacity at a bottleneck router when fed with self-similar input with varying degrees of LRD but equal traffic intensity

2 : weak Long Range Correlation, buffer capacity of about 60kB suffices to contain the input’s variability, the average buffer occupancy remains below 5kB

1:strong LRC,increase in buffer capacity accompanied by increase in buffer occupancy

Impact, contd.

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Adapt to self-similarity

• Flexible resource allocation– Increase bandwidth to accommodate periods of “bur

stiness”. Could be wasteful in times of low traffic intensity adaptive adjustment can be effective counter measure.

– Increase the buffer size to absorb periods of “burstiness”.

– Tradeoff, increase both appropriately.

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Current Status

• Many people (vendors) chose to ignore self-similarity

• People want to blame the protocols for observed behavior

• Multi-resolution analysis may provide a means for better models

• Lots of opportunity!!

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Questions?