doi:10.1016/j.peva.2004.07.017
Copyright © 2004 Published by Elsevier B.V.
Network traffic behaviour in switched Ethernet systems
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Tony Field
, Uli Harder
, and Peter Harrison
Department of Computing, Imperial College, Huxley Building, 180 Queen's Gate, London SW72AZ, UK
Available online 15 September 2004.
Abstract
Measurements on a high-performance Ethernet are shown to match well a truncated Cauchy probability distribution, with a much better fit over smaller file/request sizes than the commonly used Pareto distribution. We observe self-similar characteristics in the traffic at both file servers and at a CPU server elsewhere in the network, which targets, predominantly, file and web servers. This suggests propagation of self-similarity. A simulation model of a single server with Poisson arrivals and Cauchy service demands yields a departure process that follows a power law and matches closely the observed traffic. The simulation is also used to investigate the link between the power laws in the request size distribution and the network traffic by using Lévy distributions for the request sizes. This suggests a link between file/request size distribution and self-similarity in traffic, leading to the possibility of using conventional queueing network performance models with processor sharing queueing discipline. This idea is further supported by an additional simulation experiment and suitable models are proposed.
Keywords: Self-similarity; Network traffic; Lévy distribution; Traffic model
Fig. 1. The departmental network.
Fig. 2. The first plot shows the inter arrival time histogram for the outgoing network traffic on a log–log scale. For comparison, we have drawn an exponential pdf with the same mean as that measured. The second plot shows the power spectrum of the outgoing network traffic time series.
Fig. 3. The plot compares power-spectra resulting from /proc/net/dev and tcpdump measurements.
Fig. 4. The plot displays the distribution of the changes in the packet arrival rate, measured over 2 h for both methods.
Fig. 5. Power spectrum of the network traffic time series measured in packets per second, aggregated over 5 s intervals. As described in the text, the /proc/net/dev measurement lasted 12 days on the CPU server, starting on 1 February 2002 at 16:24:47.
Fig. 6. (a) Probability distribution function of the changes in the arrival rates of packets. (b) Probability distribution function of the changes in the arrival rates of packets of the entire traffic compared to a Cauchy distribution.
Fig. 7. Probability distribution function of the changes in the arrival rates of packets of the entire traffic at different aggregation levels.
Fig. 8. File size distributions on a departmental LINUX machine on the local disk and external request size distribution.
Fig. 9. A sketch of our model.
Fig. 10. This plot compares the power spectra of the simulation using Cauchy distributions to ones using exponential distributions for the request sizes at different network speeds.
Fig. 11. The request size density distribution using different Lévy distributions.
Fig. 12. The power spectrum of the simulation for different Lévy distributions.
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