Optimal control of the MX/G/1/K queue with multiple server vacations

Abstract We consider an M X / G /1/ K queue in which the removable server applies the following (ν, N ) policy: Every time the server completes service and finds ν customers in the system, the server takes a sequence of vacations. At the end of each vacation, the server inspects the length of the queue. If the queue length is greater than or equal to N , the server begins service until the number of customers drops to ν. Under a classical cost structure, we characterize an optimal policy and develop an algorithm to find an optimal policy which minimizes the expected cost per unit time.

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