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A second-order Markov-modulated fluid queue with linear service rate

Published online by Cambridge University Press:  14 July 2016

Landy Rabehasaina
Affiliation:
IRISA-INRIA, Rennes
Bruno Sericola*
Affiliation:
IRISA-INRIA, Rennes
*
∗∗ Postal address: IRISA-INRIA, Campus de Beaulieu, 35042 Rennes Cedex, France. Email address: bruno.sericola@irisa.fr

Abstract

We consider an infinite-capacity second-order fluid queue governed by a continuous-time Markov chain and with linear service rate. The variability of the traffic is modeled by a Brownian motion and a local variance function modulated by the Markov chain and proportional to the fluid level in the queue. The behavior of this second-order fluid-flow model is described by a linear stochastic differential equation, satisfied by the transient queue level. We study the transient level's convergence in distribution under weak assumptions and we obtain an expression for the stationary queue level. For the first-order case, we give a simple expression of all its moments as well as of its Laplace transform. For the second-order model we compute its first two moments.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Current address: LMC-IMAG, 51, Rue des Mathématiques, BP53, 38043 Grenoble Cedex 9, France. Email address: landy.rabehasaina@imag.fr

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