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November 2000 On the maximum workload of a queue fed by fractional Brownian motion
Peter W. Glynn, Assaf J. Zeevi
Ann. Appl. Probab. 10(4): 1084-1099 (November 2000). DOI: 10.1214/aoap/1019487607


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.


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Peter W. Glynn. Assaf J. Zeevi. "On the maximum workload of a queue fed by fractional Brownian motion." Ann. Appl. Probab. 10 (4) 1084 - 1099, November 2000.


Published: November 2000
First available in Project Euclid: 22 April 2002

zbMATH: 1073.60089
MathSciNet: MR1810865
Digital Object Identifier: 10.1214/aoap/1019487607

Primary: 60K25
Secondary: 60G70

Keywords: Extreme values , fractional Brownian motion , long-range dependence , queues

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 4 • November 2000
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