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

Part of: Markov processes Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Landy Rabehasaina  and
Bruno Sericola
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
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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.

Keywords

Fluid queueMarkov chainsecond-order modelrisk theory

MSC classification

Primary: 60K25: Queueing theory 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 90B05: Inventory, storage, reservoirs
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 3 , September 2004 , pp. 758 - 777
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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