Abstract
SUMMARY In this paper we set forth an approach to queueing and inventory problems which is based on the theory of semi-Markov processes. The method is applicable to a wide variety of models in continuous or discrete time. After developing two basic theorems, we illustrate the method by determining the limiting distribution of a “batch service” queue, in which K customers are always served at a time. The batch service queue is also shown to be equivalent to a classical single-server queue with gamma interarrival distribution and general service distribution, and to an inventory model of the popular “s, S” type. Waiting-time distributions and expected lengths of busy periods are shown for the queues, and the application of the method to finite queues is indicated.
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