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February 2002 Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?
Thomas Mikosch, Sidney Resnick, Holger Rootzén, Alwin Stegeman
Ann. Appl. Probab. 12(1): 23-68 (February 2002). DOI: 10.1214/aoap/1015961155

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.

Citation

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Thomas Mikosch. Sidney Resnick. Holger Rootzén. Alwin Stegeman. "Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?." Ann. Appl. Probab. 12 (1) 23 - 68, February 2002. https://doi.org/10.1214/aoap/1015961155

Information

Published: February 2002
First available in Project Euclid: 12 March 2002

zbMATH: 1021.60076
MathSciNet: MR1890056
Digital Object Identifier: 10.1214/aoap/1015961155

Subjects:
Primary: 60K25
Secondary: 60F05, 60F10, 60F17, 60G18, 60G55

Rights: Copyright © 2002 Institute of Mathematical Statistics

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Vol.12 • No. 1 • February 2002
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