Abstract

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 y(log t)1/(2-2H), where H > 1/2 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{b2(1-H)}.We also discuss the implication of these results for statistical estimation of the tail probabilities associated with the steady-state workload distribution.

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Authors
Peter Glynn and Assaf Zeevi
Format
Journal Article
Publication Date
Journal
The Annals of Applied Probability

Full Citation

Glynn, Peter and Assaf Zeevi
. “On the maximum workload of a queue fed by fractional Brownian motion.”
The Annals of Applied Probability
vol.
10
, (January 01, 2000):
1084
-
1099
.