Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?
Thomas Mikosch, Sidney Resnick, Holger Rootzén, and Alwin Stegeman
Source: Ann. Appl. Probab. Volume 12, Number 1
(2002), 23-68.
Abstract
Cumulative broadband network traffic is often thought to be well modeled by fractional Brownian motion (FBM). However, some traffic measurements do not show an agreement with the Gaussian marginal distribution assumption. We show that if connection rates are modest relative to heavy tailed connection length distribution tails, then stable Lévy motion is a sensible approximation to cumulative traffic over a time period. If connection rates are large relative to heavy tailed connection length distribution tails, then FBM is the appropriate approximation. The results are framed as limit theorems for a sequence of cumulative input processes whose connection rates are varying in such a way as to remove or induce long range dependence.
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Keywords: Heavy tails; regular variation; Pareto tails; self-similarity; scaling; infinite variance; stable Lévy motion; fractional Brownian motion; Gaussian approximation; ON/OFF process; workload process; cumulative input process; input rate; large deviations
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1015961155
Digital Object Identifier: doi:10.1214/aoap/1015961155
Mathematical Reviews number (MathSciNet): MR1890056
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