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A fundamental identity in the theory of queues

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Summary

The main result of this paper is a fundamental identity for single-server queueing processes. By using the fundamental identity it is possible to find the mathematical laws describing the behavior of a queue in continuous time if we know the mathematical laws describing the behavior of the same queue in discrete time. The case of single-server queues with recurrent input and general service times is discussed in detail.

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Reference

  1. Pollaczek, F. (1957). Problèmes stochastiques posés par le phénomène de formation d'une queue d'attente a un guichet et par des phénomènes apparentés, Mémorial des Sciences Mathématiques, Fasc.136, Gauthier-Villars, Paris.

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Authors and Affiliations

  1. Case Western Reserve University, Cleveland, USA

    Lajos Takács

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  1. Lajos Takács
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Additional information

This research was supported by the National Science Foundation under Contract No. GP-7847.

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Takács, L. A fundamental identity in the theory of queues. Ann Inst Stat Math 22, 339–348 (1970). https://doi.org/10.1007/BF02506349

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  • DOI: https://doi.org/10.1007/BF02506349

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