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Time-dependent behaviour of an alternating service queue. (English) Zbl 1135.90327

Summary: We consider a model describing the waiting time of a server alternating between two service points. This model is described by a Lindley-type equation. We are interested in the time-dependent behaviour of this system and derive explicit expressions for its time-dependent waiting-time distribution, the correlation between waiting times, and the distribution of the cycle length. As our model is closely related to Lindley’s recursion, we compare our results to those derived for Lindley’s recursion.

MSC:

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