Abstract
Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of γ each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.
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Altman, E., Nain, P. Optimality of a Threshold Policy in theM/M/ queue with repeated vacations. Mathematical Methods of Operations Research 44, 75–96 (1996). https://doi.org/10.1007/BF01246330
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DOI: https://doi.org/10.1007/BF01246330