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On infinite-server queues with cyclically dependent service times. (English) Zbl 0601.60095

The author considers an infinite-server queue with Poisson arrivals and with service times which are cyclically dependent in the sense that the service times of the customers served during the same busy period are assumed to be independent, and on the other hand, concerning service times being realized on different busy periods no independence assumptions are made.
For this queue the author shows that the stationary distribution of the number of customers in the system is also Poisson with parameter being equal to the arrival intensity multiplied by the mean service time. Moreover, if the service times satisfy a strong mixing condition this stationary distribution can be approximated by the corresponding time- dependent distributions under the condition that a busy period starts at time zero.
Reviewer: Wang Zhenpeng

MSC:

60K25 Queueing theory (aspects of probability theory)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research
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