## Is Network Traffic Approximated By Stable Lévy Motion Or Fractional Brownian Motion? (1999)

Citations: | 69 - 9 self |

### BibTeX

@MISC{Mikosch99isnetwork,

author = {Thomas Mikosch and Sidney Resnick and Holger Rootzén and Alwin Stegeman},

title = { Is Network Traffic Approximated By Stable Lévy Motion Or Fractional Brownian Motion? },

year = {1999}

}

### Years of Citing Articles

### OpenURL

### Abstract

Cumulative broadband network traffic is often thought to be well modelled by fractional Brownian motion. 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 L'evy 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.