A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue

Guy Latouche and Paul J. Schweitzer
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Guy Latouche: Université Libre de Bruzelles, Département d’Informatique
Paul J. Schweitzer: University of Rochester Graduate School of Business

Chapter 3 in Computations with Markov Chains, 1995, pp 39-48 from Springer

Abstract: Abstract We consider a positive recurrent M/M/1 queue in a slowly varying Markovian environment, such that in some environments, the arrival rate may be higher than the service rate. The system therefore may oscillate between stable and unstable modes of behaviour. We investigate the limiting distribution as the expected sojourn times in the various environments increase to infinity. We show that the limiting behaviour of the stationary distribution is significantly different when there are unstable environments.

Date: 1995
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DOI: 10.1007/978-1-4615-2241-6_3

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