IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v27y1979i6p1168-1179.html
   My bibliography  Save this article

Qualitative Properties and Bounds for the Serial Covariances of Waiting Times in Single-Server Queues

Author

Listed:
  • Reinhard Bergmann

    (Karl-Marx-University, Leipzig, German Democratic Republic)

Abstract

For the stationary waiting time process of a GI / G /1 queue we prove the empirically obvious fact that if the service times are increased and the interarrival times decreased, then the correlation of waiting times of successive customers is increased. If the service and interarrival times are respectively larger or smaller than for given exponential service or interarrival times, then the serial covariances of waiting times are bounded by the known covariances for the given exponential case. Also, some general bounds for the covariances are given, and the heavy traffic case is considered. The results are very useful in simulation problems where the mean stationary waiting time is estimated by a sample and it is sought to determine the mean square error of the sample mean.

Suggested Citation

  • Reinhard Bergmann, 1979. "Qualitative Properties and Bounds for the Serial Covariances of Waiting Times in Single-Server Queues," Operations Research, INFORMS, vol. 27(6), pages 1168-1179, December.
    • Handle: RePEc:inm:oropre:v:27:y:1979:i:6:p:1168-1179
    DOI: 10.1287/opre.27.6.1168
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.27.6.1168
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.27.6.1168?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
    ---><---

    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:27:y:1979:i:6:p:1168-1179. 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.