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A two-queue, one-server model with priority for the longer queue

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Abstract

The queueing model studied consists of one server and two queues. Each queue has its own Poisson arrival stream and service time distribution. After a service completion, the server proceeds with a customer from the longer queue, if the queues are unequal; if the queues are equal, the server chooses with some probability a customer from one of the queues. The model is of practical interest in performance analysis, but also of theoretical interest because the functional equation to be solved has not yet been studied in the queueing literature. A basic analysis of this functional equation is presented. Some numerical results are given to assess the influence of the present service discipline. Some new properties of L.S. transforms of service time distributions are discussed in the appendix.

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References

  1. J.W. Cohen and O.J. Boxma,Boundary Value Problems in Queueing System Analysis (North-Holland, Amsterdam, 1983).

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  2. J.W. Cohen,The Single Server Queue (North-Holland, Amsterdam, 1982), revised edition.

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  3. M.A. Evgrafov,Analytic Functions (Dover Publ., New York, 1966).

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  4. F.D. Gakhov,Boundary Value Problems (Pergamon Press, Oxford, 1966).

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  5. E.C. Titchmarsh,Theory of Functions (Oxford University Press, London, 1952).

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Authors and Affiliations

  1. Mathematical Institute, University of Utrecht, Utrecht, The Netherlands

    J. W. Cohen

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  1. J. W. Cohen
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Additional information

Dr. T. Katayama has formulated the present problem and brought it to the author's attention during his visit in October/November 1984 to the NTT-Electr. Comm. Lab.'s Musashino, Tokyo 180.

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Cohen, J.W. A two-queue, one-server model with priority for the longer queue. Queueing Syst 2, 261–283 (1987). https://doi.org/10.1007/BF01158902

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  • DOI: https://doi.org/10.1007/BF01158902

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