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Generalized product-form stationary distributions for Markov chains in random environments with queueing applications

Part of: Markov processes Special processes Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  01 July 2016

Antonis Economou
Antonis Economou*
Affiliation:
University of Athens
*
∗ Postal address: Department of Mathematics, University of Athens, Panepistemiopolis, Athens 15784, Greece. Email address: aeconom@math.uoa.gr
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Abstract

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Consider a continuous-time Markov chain evolving in a random environment. We study certain forms of interaction between the process of interest and the environmental process, under which the stationary joint distribution is tractable. Moreover, we obtain necessary and sufficient conditions for a product-form stationary distribution. A number of examples that illustrate the applicability of our results in queueing and population growth models are also included.

Keywords

Continuous-time Markov chainrandom environmentqueueingproduct-form stationary distributionpartial balancepotentialresolventESTA property

MSC classification

Primary: 60J22: Computational methods in Markov chains 65C40: Computational Markov chains
Secondary: 60K37: Processes in random environments 60J27: Continuous-time Markov processes on discrete state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 37 , Issue 1 , March 2005 , pp. 185 - 211
Copyright
Copyright © Applied Probability Trust 2005 

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