A hierarchical product model seeks to model network
traffic as a
product of independent on/off processes. Previous studies have
assumed a Markovian structure for component processes amounting to
assuming that exponential distributions govern on and off periods, but this is not in good agreement with traffic
measurements. However,
if the number of factor processes grows and input rates are stabilized
by allowing the on period distribution to change suitably, a
limiting on/off process can be obtained which has exponentially
distributed on periods and whose off periods are equal
in distribution to the busy period of an $M/G/\infty$ queue. We give a
fairly complete study of the possible limits of the product process
as the number of factors
grows and offer various characterizations of the approximating
processes. We also study the dependence structure of the approximations.
Publié le : 2003-11-14
Classification:
Fluid queue,
$M/G/\infty$ queue,
heavy tales,
long-range dependence,
steady state distribution,
product models,
infinite divisibility,
renewal theorems,
90B15,
60K25
@article{1069786502,
author = {Resnick, Sidney and Samorodnitsky, Gennady},
title = {Limits of on/off hierarchical product models for data transmission},
journal = {Ann. Appl. Probab.},
volume = {13},
number = {1},
year = {2003},
pages = { 1355-1398},
language = {en},
url = {http://dml.mathdoc.fr/item/1069786502}
}
Resnick, Sidney; Samorodnitsky, Gennady. Limits of on/off hierarchical product models for data transmission. Ann. Appl. Probab., Tome 13 (2003) no. 1, pp. 1355-1398. http://gdmltest.u-ga.fr/item/1069786502/