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A sample path analysis of the M t /M t /c queue

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Abstract

The exact transient distribution of the queue length of the M t /M t /1 single server queue with time‐dependent Poisson arrival rate and time‐dependent exponential service rate was recently obtained by Zhang and Coyle [63] in terms of a solution to a Volterra equation. Their method involved the use of generating functions and complex analysis. In this paper, we present an approach that ties the computation of these transient distributions directly to the random sample path behavior of the M t /M t /1 queue. We show the versatility of this method by applying it to the M t /M t /c multiserver queue, and indicating how it can be applied to queues with time‐dependent phase arrivals or time‐dependent phase service.

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  1. Cleveland State University, Euclid Avenue at East 24th Street, Cleveland, Ohio, 44115, USA

    Barbara Haas Margolius

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Margolius, B.H. A sample path analysis of the M t /M t /c queue. Queueing Systems 31, 59–93 (1999). https://doi.org/10.1023/A:1019145927891

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