ANALYSIS OF AN M/G/1//N QUEUE WITH MULTIPLE SERVER VACATIONS, AND ITS APPLICATION TO A POLLING MODEL

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Queues with a finite population of customers and the server's occasional unavailable periods (called vacations) are studied in detail. We first consider M/G/1//N queueing system where the server takes repeated vacations until it finds a customer in the queue after emptying the queue. For the steady state, we obtain the performance measures such as the system throughput and mean waiting time from the known analysis of a regenerative cycle of the busy and vacation periods. We also obtain the Laplace-Stieltjes transform of the distribution function for the waiting time of a customer by applying the method of supplementary variables to the joint distribution of the queue size and the elapsed service or vacation times at an arbitrary point in time. These resuts are then applied to the steady-state analysis of a multiple-queue, cyclic-service (polling) model with a finite population of customers, which can represent a token ring network for several computers each with a finite number of interactive users. Some numerical results for symmetric systems are shown.

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