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Exact overflow asymptotics for queues with many Gaussian inputs

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Krzysztof Dębicki  and
Michel Mandjes
Krzysztof Dębicki*
Affiliation:
CWI, Amsterdam, and University of Wrocław
Michel Mandjes*
Affiliation:
CWI, Amsterdam, and University of Twente
*
∗Postal address: Mathematical Institute, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland. Email address: [email protected]
∗∗Postal address: CWI, PO Box 94079, 1090 GB Amsterdam, The Netherlands
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Abstract

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

Keywords

Gaussian processfluid queueextremesoverflow probabilityexact asymptoticsintegrated Gaussian processfractional Brownian motion

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 704 - 720
Copyright
Copyright © Applied Probability Trust 2003 

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