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On the Self-Similar Nature of Ethernet Traffic
- Leland, et. Al
Presented by Sumitra Ganesh
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.
Structure of presentation Traffic Measurements Self-Similar Stochastic Processes Analysis of Ethernet Traffic
Measurements Source Models Implications and Conclusions Comments
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
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
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
mX m )var( )( m 10
)(kr
Hurst parameter
For a given set of observations kX
)(/)],..,0min(),..,0[max()(/)( 11 nSWWWWnSnR nn
)()..( 1 nXkXXW kk
nk ,..1
HnnSnRE )](/)([
HnnSnRE )](/)([ n
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
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
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.
(a)R/S plot(b) Variance-time (c) Periodogram(d)Different levels
Analysis for data setAUG89.MB
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
(a)-(d) Aug 89, Oct 89,Jan 90, Feb 92.
Analysis for packet countNormal hour traffic
(a)– packet count(b)- number of bytes
Low-Normal-High for each
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
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
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.
2/)3( H 21
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
Implications Congestion ? Queueing ? … …
Comments Convincing analysis and
interpretation of results Poor graphs for a paper that relies
on them so heavily