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
scaling
fractional Brownian motion
self-similarity
large deviations
Author
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