The Finite Capacity GI/M/1 Queue with Server Vacations

We consider the GI/M/1/K queue where the server takes exponentially distributed vacations when there are no customers left to serve in the queue. We obtain the queue length distribution at arrival epochs and random epochs for the multiple vacation case. We present heuristic algorithms to compute the blocking probability for this system. Several numerical examples are presented to analyze the behaviour of the blocking probability and to test the performance of the heuristics.

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