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Analysis of the M/Gi/1 →/M/1 queueing model

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Abstract

An M/GI/1 queueing system is in series with a unit with negative exponential service times and infinite waiting room capacity. We determine a closed form expression for the generating function of the joint queue length distribution in steady state. This result is obtained via the solution of a new type of functional equation in two variables.

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Authors and Affiliations

  1. Department of Econometrics, Tilburg University, Postbox 90153, 5000, LE Tilburg, The Netherlands

    J. P. C. Blanc

  2. Département de Mathématiques, Université d'Orléans, 45100, La Source Orléans, France

    R. Iasnogorodski

  3. INRIA Centre de Sophia Antipolis, Route des Lucioles, 06560, Valbonne, France

    Ph. Nain

Authors
  1. J. P. C. Blanc
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  2. R. Iasnogorodski
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  3. Ph. Nain
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Blanc, J.P.C., Iasnogorodski, R. & Nain, P. Analysis of the M/Gi/1 →/M/1 queueing model. Queueing Syst 3, 129–156 (1988). https://doi.org/10.1007/BF01189046

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  • DOI: https://doi.org/10.1007/BF01189046

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