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On the Self-Similar Nature of Ethernet Traffic

This presentation explores the self-similar nature of Ethernet LAN traffic and studies the degree of self-similarity in various data sets. It discusses traffic measurements, self-similar stochastic processes, source models, and implications. The analysis demonstrates the significance of self-similarity in Ethernet traffic and its implications for congestion and queueing.

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On the Self-Similar Nature of Ethernet Traffic

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  1. On the Self-Similar Nature of Ethernet Traffic - Leland, et. Al Presented by Sumitra Ganesh

  2. Overview • Demonstrate the self-similar nature of Ethernet LAN traffic • Study the degree of self-similarity in various data sets using the Hurst parameter as a measure of “burstiness” • High resolution data collected over several years and across several networks • Discusses models for traffic sources, methods for measuring self-similarity and simulating self-similar traffic.

  3. Structure of presentation • Traffic Measurements • Self-Similar Stochastic Processes • Analysis of Ethernet Traffic Measurements • Source Models • Implications and Conclusions • Comments

  4. Traffic Measurements • Traffic monitor records for each packet a timestamp (accurate to within 100-20 microsec, packet length, header information • Study conducted from 1989-1992 • Network underwent changes during this period • Data sets with External traffic analyzed separately

  5. Relevant Network Changes • Aug 89/Oct 89 – host to host workgroup traffic • Jan 1990 – host-host and router-to-router • Feb 1992 – predominantly router-to-router traffic

  6. Self-similarity • Slowly Decaying Variances : Variance of the sample mean decreases slower than the reciprocal of the sample size. • Long Range Dependence : The autocorrlations decay hyperbolically rather than exponentially. • Power Law: Spectral density obeys a power law near the origin

  7. Hurst parameter For a given set of observations

  8. Mathematical Models • Fractional Gaussian noise – rigid correlation structure • ARIMA processes – more flexible for simultaneous modeling of short-term and long-term behavior • Construction by Mandelbrot : aggregation of renewal reward processes with inter-arrival times exhibiting infinite variances

  9. Estimating the Hurst parameter H • Time domain analysis based on the R/S statistic – robust against changes in the marginal distributions • Analysis of the variances for the aggregated processes • Periodogram based Maximum Likelihood Estimate analysis in the frequency domain – yields confidence intervals

  10. Ethernet traffic (27 hour) • Compare variance-time plot, R/S plot and periodogram for number of bytes during normal hour in Aug 89. H is approx. 0.8 • Estimate is constant over different levels of aggregation Conclusion : The Ethernet traffic over a 24-hour period is self-similar with the degree of self-similarity increasing as the utilization of the Ethernet increases.

  11. R/S plot • Variance-time • Periodogram • Different levels • Analysis for data set • AUG89.MB

  12. Four Year period • Estimate for H is quite stable (0.85-0.95) • Ethernet traffic during normal traffic hours is exactly self-similar • Estimates from R/S and variance-time plots are accurate

  13. (a)-(d) Aug 89, Oct 89, Jan 90, Feb 92. Analysis for packet count Normal hour traffic

  14. – packet count • - number of bytes • Low-Normal-High for each

  15. Observations (4-year) • H increases from low to normal to high traffic hours • As number of sources increased the aggregate traffic does not get smoother – rather the burstiness increases • Low traffic hours : gets smoother in 90s because of router-to-router traffic • Confidence intervals wider for low traffic hours – process is asymptotically self-similar

  16. External Traffic • Normal/High – H is slightly smaller • Low traffic hours – H is 0.55 and confidence interval contains 0.5. Therefore coventional short-range Poisson based models describe this traffic accurately • 87 % of the packets were TCP

  17. Source Model • Renewal reward process in which the inter-arrival times are heavy-tailed • With relatively high probability the active-inactive periods are very long • The heavier the tail -> the greater the variability -> Burstier the traffic • Not analyzed the traffic generated by individual Ethernet users.

  18. Conclusions • Ethernet LAN traffic is statistically self-similar • Degree of self-similarity (the Husrt parameter H) is typically a function of the overall utilization of the Ethernet • Normal and Busy hour traffic are exactly self-similar. Low hour traffic is asymptotically self-similar • External traffic / TCP traffic share the same characteristics • Conventional packet traffic models are not able to capture the self-similarity

  19. Implications • Congestion ? • Queueing ? • … • …

  20. Comments • Convincing analysis and interpretation of results • Poor graphs for a paper that relies on them so heavily

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