IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v36y1990i8p928-937.html
   My bibliography  Save this article

Queues with Slowly Varying Arrival and Service Processes

Author

Listed:
  • Erol Gelenbe

    (EHEI, Université Paris V (René Descartes), 45 rue des Saints-Pères, 75006 Paris, France)

  • Catherine Rosenberg

    (Ecole Polytechnique de Montréal, Département de Génie Electrique, C.P. 6079, Succ. A, Montréal, Québec H3C 3A7, Canada)

Abstract

We examine a generalisation of the M/G/1 queue. The arrival and service processes are governed by a Markov chain which determines the rate of arrival and the service time distribution from a finite set. This Markov chain is assumed to vary "slowly", so that we are able to derive analytical results for the stationary distribution of the queue length using an approach based on decomposability. The practical interest of this model stems from the numerous applications where the parameters of queueing systems are time varying, such as inventory models, telephone systems, time-sharing systems, computer networks with bursty traffic, etc. We also show how this approach can be extended to arbitrary networks of queues and in particular to those with product form solution.

Suggested Citation

  • Erol Gelenbe & Catherine Rosenberg, 1990. "Queues with Slowly Varying Arrival and Service Processes," Management Science, INFORMS, vol. 36(8), pages 928-937, August.
    • Handle: RePEc:inm:ormnsc:v:36:y:1990:i:8:p:928-937
    DOI: 10.1287/mnsc.36.8.928
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.36.8.928
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.36.8.928?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. Balsamo, Simonetta & Marin, Andrea, 2013. "Separable solutions for Markov processes in random environments," European Journal of Operational Research, Elsevier, vol. 229(2), pages 391-403.

    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:ormnsc:v:36:y:1990:i:8:p:928-937. 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.