Self-Similarity in Network Traffic

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Self-Similarity in Network Traffic

• Kevin Henkener
• 5/29/2002

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

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Pictorial View of Self-Similarity
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The Famous Data

• Leland and Wilson collected hundreds of millions
  of Ethernet packets without loss and with
  recorded time-stamps accurate to within 100µs.
• Data collected from several Ethernet LANs at the
  Bellcore Morristown Research and Engineering
  Center at different times over the course of
  approximately 4 years.

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Why is Self-Similarity Important?

• Recently, network packet traffic has been
  identified as being self-similar.
• Current network traffic modeling using Poisson
  distributing (etc.) does not take into account
  the self-similar nature of traffic.
• This leads to inaccurate modeling which, when
  applied to a huge network like the Internet, can
  lead to huge financial losses.

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Problems with Current Models

• Current modeling shows that as the number of
  sources (Ethernet users) increases, the traffic
  becomes smoother and smoother
• Analysis shows that the traffic tends to become
  less smooth and more bursty as the number of
  active sources increases

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Problems with Current Models Cont.d

• Were traffic to follow a Poisson or Markovian
  arrival process, it would have a characteristic
  burst length which would tend to be smoothed by
  averaging over a long enough time scale. Rather,
  measurements of real traffic indicate that
  significant traffic variance (burstiness) is
  present on a wide range of time scales

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Pictorial View of Current Modeling
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Side-by-side View
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Definitions and Properties

• Long-range Dependence
• covariance decays slowly
• Hurst Parameter
• Developed by Harold Hurst (1965)
• H is a measure of burstiness
• also considered a measure of self-similarity
• 0 lt H lt 1
• H increases as traffic increases

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Definitions and Properties Cont.d

• low, medium, and high traffic hours
• as traffic increases, the Hurst parameter
  increases
• i.e., traffic becomes more self-similar

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Self-Similar Measures

• Background
• Let time series X (Xt t 0, 1, 2, .) be a
  covariance stationary stochastic process
• autocorrelation function r(k), k 0
• assume r(k) k-ß L(t), as k?8 where 0 lt ß lt 1
• limt?8 L(tx) / L(t) 1, for all x gt 0

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Second-order Self-Similar

• Exactly
• A process X is called (exactly) self-similar with
  self-similarity parameter H 1 ß/2 if
• for all m 1, 2, . var(X(m)) s2m-ß
• r(m)(k) r(k), k 0
• Asymptotically
• r(m)(k) r(k), as m?8
• aggregated processes are the same
• Current model shows aggregated processes tending
  to pure noise

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Measuring Self-Similarity

• time-domain analysis based on R/S statistic
• analysis of the variance of the aggregated
  processes X(m)
• periodogram-based analysis in the frequency
  domain

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Methods of Modeling Self-Similar Traffic

• Two formal mathematical models that yield elegant
  representations of self-similarity
• fractional Gaussian noise
• fractional autoregressive integrated
  moving-average processes

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Results

• Ethernet traffic is self-similar irrespective of
  time
• Ethernet traffic is self-similar irrespective of
  where it is collected
• The degree of self-similarity measured in terms
  of the Hurst parameter h is typically a function
  of the overall utilization of the Ethernet and
  can be used for measuring the burstiness of the
  traffic
• Current traffic models are not capable of
  capturing the self-similarity property

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Results Cont.d

• There exists the presence of concentrated periods
  of congestion at a wide range of time scales
• This implies the existence of concentrated
  periods of light network load
• These two features cannot be easily controlled by
  traffic control.
• i.e., burstiness cannot be smoothed

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Results Cont.d

• These two implications make it difficult to
  allocated services such that QOS and network
  utilization are maximized.
• Self-similar burstiness can lead to the
  amplification of packet loss.

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Problems with Packet Loss

• Effects in TCP
• TCP guarantees that packets will be delivered and
  will be delivered in order
• When packets are lost in TCP, the lost packets
  must be retransmitted
• This wastes valuable resources
• Effects in UDP
• UDP sends packets as quickly as possible with no
  promise of delivery
• When packets are lost, they are not retransmitted
• Repercussions for packet loss in UDP include
  jitter in streaming audio/video etc.

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Possible Methods for Dealing with the
Self-Similar Property of Traffic

• Dynamic Control of Traffic Flow
• Structural resource allocation

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Dynamic Control of Traffic Flow

• Predictive feedback control
• identify the on-set of concentrated periods of
  either high or low traffic activity
• adjust the mode of congestion control
  appropriately from conservative to aggressive

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Dynamic Control of Traffic Flow Cont.d

• Adaptive forward error correction
• retransmission of lost information is not viable
  because of time-constraints (real-time)
• adjust the degree of redundancy based on the
  network state
• increase level of redundancy when traffic is high
• could backfire as too much of an increase will
  only further aggrevate congestion
• decrease level of redundancy when traffic is low

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Structural Resource Allocation

• Two types
• bandwidth
• buffer size
• Bandwidth
• increase bandwidth to accommodate periods of
  burstiness
• could be wasteful in times of low traffic
  intensity

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Structural Resource Allocation Cont.d

• buffer size
• increase the buffer size in routers (et. al.)
  such that they can absorb periods of burstiness
• still possible to fill a given routers buffer
  and create a bottleneck
• tradeoff
• increase both until they complement each other
  and begin curtailing the effects of
  self-similarity