Abstract
This paper investigates an M[x]/G/1 queueing system with an unreliable server, where the server may take an additional vacation after the essential vacation. If the system becomes empty, the server leaves the system and takes the essential vacation. At the end of the essential vacation, the server may return to the system with probability p or take another vacation with probability 1-p. When the additional vacation is completed, the server returns from the vacation. If there are no customers waiting for service in the system, the server waits idly for the first arrival and starts working. It is assumed that the server is subject to break down according to a Poisson process and the repair time obeys a general distribution. For such a system, we derive the system size distribution at a random epoch, as well as various system characteristics. Finally, we develop an iterative procedure to find the optimal threshold values under a linear cost structure. Some numerical experiments are also presented. Key words: Cost, optimization, server breakdowns, vacation queue.
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