Consider a queue with a stochastic fluid input process modeled as
fractional Brownian motion (fBM).When the queue is stable, we prove that the
maximum of the workload process observed over an interval of length $t$
grows like $\gamma(\log t)^{1/(2-2H)}, where $H > ½$ is the
self-similarity index (also known as the Hurst parameter) that characterizes
the fBM and can be explicitly computed. Consequently, we also have that the
typical time required to reach a level $b$ grows like $\exp{b^{2(1-H)}}.We
also discuss the implication of these results for statistical estimation of the
tail probabilities associated with the steady-state workload distribution.
@article{1019487607,
author = {Zeevi, Assaf J. and Glynn, Peter W.},
title = {On the maximum workload of a queue fed by fractional Brownian
motion},
journal = {Ann. Appl. Probab.},
volume = {10},
number = {2},
year = {2000},
pages = { 1084-1099},
language = {en},
url = {http://dml.mathdoc.fr/item/1019487607}
}
Zeevi, Assaf J.; Glynn, Peter W. On the maximum workload of a queue fed by fractional Brownian
motion. Ann. Appl. Probab., Tome 10 (2000) no. 2, pp. 1084-1099. http://gdmltest.u-ga.fr/item/1019487607/