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Moments of a Markov-modulated, irreducible network of fluid queues

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Landy Rabehasaina
Landy Rabehasaina*
Affiliation:
ENSSAT
*
∗Postal address: ENSSAT, 6 rue de Kerampont, BP 805, 22305 Lannion, France. Email address: landy.rabehasaina@enssat.fr
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Abstract

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We study a network of fluid queues in which exogenous arrivals are modulated by a continuous-time Markov chain. Service rates in each queue are proportional to the queue size, and the network is assumed to be irreducible. The queue levels satisfy a linear, vector-valued differential equation. We obtain joint moments of the queue sizes recursively, and deduce the Laplace transform of the queue sizes in the stationary regime.

Keywords

Linear fluid networkMarkov modulation

MSC classification

Primary: 60K25: Queueing theory 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 510 - 522
Copyright
© Applied Probability Trust 2006 

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