Is network traffic approximated by stable Lévy motion or fractional Brownian motion?
Journal article, 2002

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.

ON/OFF process

Heavy tails

infinite variance

regular variation

input rate

workload process

Pareto tails

Gaussian approximation

cumulative input process

stable Lévy motion


fractional Brownian motion


large deviations


Thomas Mikosch

Sidney Resnick

Holger Rootzen

University of Gothenburg

Department of Mathematics

Alwin Stegeman

Annals of Applied Probabability

Vol. 12 23-68

Subject Categories

Probability Theory and Statistics

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