# Asymptotic Behavior of a Multiplexer Fed by a Long-Range Dependent Process

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 «$M/G/\infty$ 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., $G$ corresponding to either the Pareto or lognormal distribution and $c-\rho<1$, where $\rho$ is the arrival rate to the buffer.
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Type de document :
Rapport
RR-3230, INRIA. 1997
Domaine :

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https://hal.inria.fr/inria-00073459
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Soumis le : mercredi 24 mai 2006 - 12:51:45
Dernière modification le : jeudi 11 janvier 2018 - 16:41:50
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:47:15

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• HAL Id : inria-00073459, version 1

### Citation

Zhen Liu, Philippe Nain, Don Towsley, Zhi-Li Zhang. Asymptotic Behavior of a Multiplexer Fed by a Long-Range Dependent Process. RR-3230, INRIA. 1997. 〈inria-00073459〉

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