Abstract
This paper predicts the performance of an unreliable Mx/G/1 G-queue with delayed repair. The negative customers stop functioning of the server and force the server to undergo repair. The failed server takes a random amount of time called delay time before going for repair. It is assumed that the positive customers arrive in batches and negative customers arrive singly, according to Poisson process. The server provides first phase of regular service to all arriving customers whereas it provides l types of optional services to only those who demand the same. The working vacation period of the server starts either if queue becomes empty or repairing of the server finishes. Numerical experiments are provided to show the effects of various critical system parameters on performance measures.
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