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Asymptotic bounds for the fluid queue fed by sub-exponential On/Off sources

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

V. Dumas  and
A. Simonian
V. Dumas*
Affiliation:
MAB, Université Bordeaux I
A. Simonian*
Affiliation:
France Télécom CNET
*
∗ Postal address: MAB, Université Bordeaux I, 351, cours de la Libération, 33405 Talence Cedex, France.
∗∗ Postal address: France Télécom/CNET, 38/40 rue du Général Leclerc, 92794 Issy-les-Moulineaux Cedex 9, France.
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Abstract

We consider a fluid queue fed by a superposition of a finite number of On/Off sources, the distribution of the On period being subexponential for some of them and exponential for the others. We provide general lower and upper bounds for the tail of the stationary buffer content distribution in terms of the so-called minimal subsets of sources. We then show that this tail decays at exponential or subexponential speed according as a certain parameter is smaller or larger than the ouput rate. If we replace the subexponential tails by regularly varying tails, the upper bound and the lower bound are sharp in that they differ only by a multiplicative factor.

Keywords

Fluid queueOn/Off sourcesbuffer contentstationaritytail-behavioursubexponential distributionsregular variationlong-range dependence

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 1 , March 2000 , pp. 244 - 255
Copyright
Copyright © Applied Probability Trust 2000 

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