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We consider in this paper a batch arrival queueing system with an unreliable server. If the queue is empty at a service completion, then the server becomes inactive and begins an idle period. However, if the queue is not empty, then the server will take at most vacation before serving the next customer. A linear cost structure is developed for the system and the optimal value of is obtained.

Note on a Binomial Schedule for an MX/G/1 Queueing System with an Unreliable Server

Note on a Binomial Schedule for an M^X/G/1 Queueing System with an Unreliable Server