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December 2009 Conditional limit theorems for regulated fractional Brownian motion
Hernan Awad, Peter Glynn
Ann. Appl. Probab. 19(6): 2102-2136 (December 2009). DOI: 10.1214/09-AAP605

Abstract

We consider a stationary fluid queue with fractional Brownian motion input. Conditional on the workload at time zero being greater than a large value b, we provide the limiting distribution for the amount of time that the workload process spends above level b over the busy cycle straddling the origin, as b→∞. Our results can be interpreted as showing that long delays occur in large clumps of size of order b2−1/H. The conditional limit result involves a finer scaling of the queueing process than fluid analysis, thereby departing from previous related literature.

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Hernan Awad. Peter Glynn. "Conditional limit theorems for regulated fractional Brownian motion." Ann. Appl. Probab. 19 (6) 2102 - 2136, December 2009. https://doi.org/10.1214/09-AAP605

Information

Published: December 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1204.60084
MathSciNet: MR2588241
Digital Object Identifier: 10.1214/09-AAP605

Subjects:
Primary: 60K25
Secondary: 60F99, 68M20, 90B22

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.19 • No. 6 • December 2009
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