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Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations

Author

Listed:
  • S. W. Fuhrmann

    (AT&T Bell Laboratories, Holmdel, New Jersey)

  • Robert B. Cooper

    (Florida Atlantic University, Boca Raton, Florida)

Abstract

This paper considers a class of M / G /1 queueing models with a server who is unavailable for occasional intervals of time. As has been noted by other researchers, for several specific models of this type, the stationary number of customers present in the system at a random point in time is distributed as the sum of two or more independent random variables, one of which is the stationary number of customers present in the standard M / G /1 queue (i.e., the server is always available) at a random point in time. In this paper we demonstrate that this type of decomposition holds, in fact, for a very general class of M / G /1 queueing models. The arguments employed are both direct and intuitive. In the course of this work, moreover, we obtain two new results that can lead to remarkable simplifications when solving complex M / G /1 queueing models.

Suggested Citation

  • S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:5:p:1117-1129
    DOI: 10.1287/opre.33.5.1117
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    Keywords

    681 queues; 691 feedback;

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