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Self-Similarity in Network Traffic. Kevin Henkener 5/29/2002. 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.

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self similarity in network traffic

Self-Similarity in Network Traffic

Kevin Henkener


what is self similarity
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.
the famous data
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 LAN’s at the Bellcore Morristown Research and Engineering Center at different times over the course of approximately 4 years.
why is self similarity important
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.
problems with current models
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
problems with current models cont d
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
definitions and properties
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 < H < 1
    • H increases as traffic increases
definitions and properties cont d
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
self similar measures
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-βL(t), as k∞where 0 < β < 1
      • limt∞ L(tx) / L(t) = 1, for all x > 0
second order self similar
Second-order Self-Similar
  • Exactly
    • A process X is called (exactly) self-similar with self-similarity parameter H = 1 – β/2 if
    • for all m = 1, 2, …. var(X(m)) = σ2m-β
    • r(m)(k) = r(k), k ≥ 0
  • Asymptotically
    • r(m)(k) = r(k), as m∞
    • aggregated processes are the same
  • Current model shows aggregated processes tending to pure noise
measuring self similarity
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
methods of modeling self similar traffic
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
  • 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
results cont d
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
results cont d1
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.
problems with packet loss
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.
possible methods for dealing with the self similar property of traffic
Possible Methods for Dealing with the Self-Similar Property of Traffic
  • Dynamic Control of Traffic Flow
  • Structural resource allocation
dynamic control of traffic flow
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
dynamic control of traffic flow cont d
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
structural resource allocation
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
structural resource allocation cont d
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 router’s buffer and create a bottleneck
  • tradeoff
    • increase both until they complement each other and begin curtailing the effects of self-similarity