## Assaf Zeevi

*On the maximum workload of a queue fed by fractional Brownian motion*

Coauthor(s): Peter Glynn.

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**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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**Source:** *The Annals of Applied Probability*

**Exact Citation:**

Glynn, Peter, and Assaf Zeevi. "On the maximum workload of a queue fed by fractional Brownian motion." *The Annals of Applied Probability* 10, no. 4 (2000): 1084-1099.

**Volume:** 10

**Number:** 4

**Pages:** 1084-1099

**Date:**
2000