The Annals of Applied Probability

Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?

Thomas Mikosch, Sidney Resnick, Holger Rootzén, and Alwin Stegeman

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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.

Article information

Source
Ann. Appl. Probab., Volume 12, Number 1 (2002), 23-68.

Dates
First available in Project Euclid: 12 March 2002

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1015961155

Digital Object Identifier
doi:10.1214/aoap/1015961155

Mathematical Reviews number (MathSciNet)
MR1890056

Zentralblatt MATH identifier
1021.60076

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F05: Central limit and other weak theorems 60F10: Large deviations 60F17: Functional limit theorems; invariance principles 60G18: Self-similar processes 60G55: Point processes

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

Citation

Mikosch, Thomas; Resnick, Sidney; Rootzén, Holger; Stegeman, Alwin. Is Network Traffic Appriximated by Stable Lévy Motion or Fractional Brownian Motion?. Ann. Appl. Probab. 12 (2002), no. 1, 23--68. doi:10.1214/aoap/1015961155. https://projecteuclid.org/euclid.aoap/1015961155


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