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

In: Computations with Markov Chains

Author

Listed:
  • Guy Latouche

    (Université Libre de Bruzelles, Département d’Informatique)

  • Paul J. Schweitzer

    (University of Rochester Graduate School of Business)

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.

Suggested Citation

  • Guy Latouche & Paul J. Schweitzer, 1995. "A Markov Modulated, Nearly Completely Decomposable M/M/1 Queue," Springer Books, in: William J. Stewart (ed.), Computations with Markov Chains, chapter 3, pages 39-48, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-2241-6_3
    DOI: 10.1007/978-1-4615-2241-6_3
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