Traffic with an fBm Limit: Convergence of the Stationary Workload Process

Highly-aggregated traffic in communication networks is often modeled as fractional Brownian motion (fBm). This is justified by the theoretical result that the sum of a large number of on-off inputs, with either on-times or off-times having a heavy-tailed distribution with infinite variance, converge...

Full description

Saved in:
Bibliographic Details
Published in:Queueing systems 2004-01, Vol.46 (1/2), p.113-127
Main Authors: Dębicki, Krzysztof, Mandjes, Michel
Format: Article
Language:English
Subjects:
Brownian motion
Communications networks
Convergence
Mathematical models
Normal distribution
Queuing theory
Random variables
Workloads
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Highly-aggregated traffic in communication networks is often modeled as fractional Brownian motion (fBm). This is justified by the theoretical result that the sum of a large number of on-off inputs, with either on-times or off-times having a heavy-tailed distribution with infinite variance, converges to fBm, after rescaling time appropriately. For performance analysis purposes, the key question is whether this convergence carries over to the stationary buffer content process. In this paper it is shown that, in a heavy-traffic queueing environment, this property indeed holds.[Publication Abstract]
ISSN:0257-0130
1572-9443
DOI:10.1023/B:QUES.0000021144.61749.aa