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Discrete-Time Queuing Theory

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  • Torben Meisling

    (Division of Engineering Research, Stanford Research Institute, Menlo Park, California)

Abstract

This paper contains an analysis of a single-server queuing system for which time is treated as a discrete variable. The number of customers arriving within a fixed time interval is assumed to obey a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent but are not otherwise restricted. It is furthermore assumed that customers are served in their order of arrival. Formulas for the mean queue length and the mean waiting time are derived for the general case and it is shown how the previously obtained results for the corresponding continuous-time system may be derived from the results given here by a limiting process. The results are applied to two special cases, (1) a service-time distribution, which has the form of a geometrical progression, and (2) a fixed service-time distribution.

Suggested Citation

  • Torben Meisling, 1958. "Discrete-Time Queuing Theory," Operations Research, INFORMS, vol. 6(1), pages 96-105, February.
    • Handle: RePEc:inm:oropre:v:6:y:1958:i:1:p:96-105
    DOI: 10.1287/opre.6.1.96
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    Cited by:

    1. Upadhyaya, Shweta, 2016. "Performance prediction of a discrete-time batch arrival retrial queue with Bernoulli feedback," Applied Mathematics and Computation, Elsevier, vol. 283(C), pages 108-119.
    2. Sofian Clercq & Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2016. "Analysis of a discrete-time queue with time-limited overtake priority," Annals of Operations Research, Springer, vol. 238(1), pages 69-97, March.
    3. I. Atencia & A. Pechinkin, 2013. "A discrete-time queueing system with optional LCFS discipline," Annals of Operations Research, Springer, vol. 202(1), pages 3-17, January.
    4. Sofian Clercq & Bart Steyaert & Sabine Wittevrongel & Herwig Bruneel, 2016. "Analysis of a discrete-time queue with time-limited overtake priority," Annals of Operations Research, Springer, vol. 238(1), pages 69-97, March.

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