IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v6y1958i1p96-105.html
   My bibliography  Save this article

Discrete-Time Queuing Theory

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.6.1.96
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.6.1.96?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. 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.
    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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:6:y:1958:i:1:p:96-105. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.