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The Joint Stationary Multivariate Queue Length Distribution in a Single Server Queueing System with N Queues, Arbitrary Priorities, and a General Probabilistic Inter-Queue Transition Matrix

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  • T. K. Wignall

    (University of Calgary)

  • E. G. Enns

    (University of Calgary)

Abstract

In modern telephone systems utilizing computers, the realization of a single server feedback queueing system often arises. In this paper, it is assumed that an originating or transferred call to such a system requires a number of different services before leaving the system as a completed or rejected call. A customer may also repeat a portion of his services, omit some services, or leave the system after any service with some assigned probabilities. In this paper, we present a theorem on the joint multi-variate queue length distribution, in a system with N services or queues, arbitrary priorities, and a general probabilistic transition matrix inter-connecting the various queues.

Suggested Citation

  • T. K. Wignall & E. G. Enns, 1973. "The Joint Stationary Multivariate Queue Length Distribution in a Single Server Queueing System with N Queues, Arbitrary Priorities, and a General Probabilistic Inter-Queue Transition Matrix," Management Science, INFORMS, vol. 19(7), pages 778-782, March.
    • Handle: RePEc:inm:ormnsc:v:19:y:1973:i:7:p:778-782
    DOI: 10.1287/mnsc.19.7.778
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