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