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

Content Provider	CiteSeerX
Author	Zeevi, J. Glynn, Peter W.
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 γlog t1/2−2H, 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 expb21−H. We also discuss the implication of these results for statistical estimation of the tail probabilities associated with the steady-state workload distribution. 1. Introduction. Triggered
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Journal	Snedecor Hall Department of Statistics Iowa State University Ames, IA 50011, USA apghosh@iastate.edu Alexander Roitershtein 420 Carver Hall Department of Mathematics Iowa State University Ames, IA 50011, USA roiterst@iastate.edu Ananda Weerasinghe 414 Car
Language	English
Access Restriction	Open
Subject Keyword	Fractional Brownian Motion Maximum Workload Stochastic Fluid Input Process Steady-state Workload Distribution Length Grows Hurst Parameter Self-similarity Index Statistical Estimation Tail Probability Level Grows Typical Time Workload Process
Content Type	Text
Resource Type	Article