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Asymptotic behavior of a multiplexer fed by a long-range dependent process

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Zhen Liu ,
Philippe Nain ,
Don Towsley  and
Zhi-Li Zhang
Zhen Liu*
Affiliation:
INRIA
Philippe Nain*
Affiliation:
INRIA
Don Towsley*
Affiliation:
University of Massachusetts
Zhi-Li Zhang*
Affiliation:
University of Minnesota
*
∗Postal address: INRIA, 2004, route de Lucioles, B.P. 93, 06902 Sophia Antipolis, France.
∗Postal address: INRIA, 2004, route de Lucioles, B.P. 93, 06902 Sophia Antipolis, France.
∗∗∗Postal address: Department of Computer Science, University of Massachusetts, Amherst, MA 01003, USA.
∗∗∗Postal address: Department of Computer Science and Engineering, University of Minnesota, 200 Union St. S.E., Minneapolis, MN 55455, USA.
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Abstract

In this paper we study the asymptotic behavior of the tail of the stationary backlog distribution in a single server queue with constant service capacity c, fed by the so-called M/G/∞ input process or Cox input process. Asymptotic lower bounds are obtained for any distribution G and asymptotic upper bounds are derived when G is a subexponential distribution. We find the bounds to be tight in some instances, e.g. when G corresponds to either the Pareto or lognormal distribution and c − ρ < 1, where ρ is the arrival rate at the buffer.

Keywords

Asymptotic self-similar processlong-range dependencesubexponential distributionsPareto distributionlarge deviationsqueues

MSC classification

Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 36 , Issue 1 , March 1999 , pp. 105 - 118
Copyright
Copyright © Applied Probability Trust 1999 

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