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The discrete-time single-server queue

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Abstract

In this paper we consider the discrete-time single server queueing model with exceptional first service. For this model we cannot define the steady-state waiting-time distribution simply as the limiting distribution of the waiting times, since this limit does not always exist. Instead, we use the Cesaro limit to define the limiting waiting-time distribution. We give an exact relation between the generating functions of the steady-state waiting-time distribution and of the idle-time distribution in the case of general interarrival-time and service-time distributions. Once we have this relation, we can give more explicit results when the generating function of either the interarrival-time distribution or the service-time distribution is rational. We also derive some results on the asymptotic behaviour of the waiting-time distribution.

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  1. Faculty of Applied Mathematics, University Twente, P.O. Box 217, 7500 AE, Enschede, The Netherlands

    J. C. W. van Ommeren

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  1. J. C. W. van Ommeren
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van Ommeren, J.C.W. The discrete-time single-server queue. Queueing Syst 8, 279–294 (1991). https://doi.org/10.1007/BF02412256

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  • DOI: https://doi.org/10.1007/BF02412256

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