IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v19y1971i2p447-452.html
   My bibliography  Save this article

On the Growth of the Maximum Queue Length in a Stable Queue

Author

Listed:
  • C. C. Heyde

    (Australian National University, Canberra, Australia)

Abstract

Even for a stable one-server queue with relative traffic intensity less than unity, the maximum queue length observed will tend to infinity in probability as the length of time for which the system has been observed becomes large. It is important to have information on the behavior of the maximum queue length to enable estimation of the congestion likely to be encountered in a system operating over a long period. The present paper studies the stable GI / M /1 system, and, interpreting the results obtained rather loosely, one can say that the maximum queue length attained by the time the n th customer has arrived ( n large) can be expected to be of the order of log n .

Suggested Citation

  • C. C. Heyde, 1971. "On the Growth of the Maximum Queue Length in a Stable Queue," Operations Research, INFORMS, vol. 19(2), pages 447-452, April.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:2:p:447-452
    DOI: 10.1287/opre.19.2.447
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.19.2.447
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.19.2.447?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. Waroquier, M. & Hayde, K. & Vincx, H., 1975. "A phase-consistent derivation of the electromagnetic multipole operators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 80(5), pages 465-489.

    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:19:y:1971:i:2:p:447-452. 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.