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Batch arrival queue with \(N\)-policy and at most \(J\) vacations. (English) Zbl 1185.90049

Summary: We study the operating characteristics of an \(M^{[x]}/G/1\) queueing system with \(N\)-policy and at most \(J\) vacations. The server takes at most \(J\) vacations repeatedly until at least \(N\) customers returning from a vacation are waiting in the queue. If no customer arrives by the end of the \(J\)th vacation, the server becomes idle in the system until the number of arrivals in the queue reaches \(N\). We derive the system size distribution at a random epoch and departure epoch, as well as various system characteristics.

MSC:

90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
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References:

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