IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v22y1975i2p202-211.html
   My bibliography  Save this article

Utilization of Idle Time in an M/G/1 Queueing System

Author

Listed:
  • Yonatan Levy

    (Tel-Aviv University)

  • Uri Yechiali

    (Tel-Aviv University)

Abstract

This paper studies an M/G/1 queue where the idle time of the server is utilized for additional work in a secondary system. As usual, the server is busy as long as there are units in the main system. However, as soon as the server becomes idle he leaves for a "vacation." The duration of a vacation is a random variable with a known distribution function. Two models are considered. In the first, upon termination of a vacation the server returns to the main queue and begins to serve those units, if any, that have arrived during the vacation. If no units have arrived the server waits for the first arrival when an ordinary M/G/1 busy period is initiated. In the second model if the server finds the system empty at the end of a vacation, he immediately takes another vacation, etc. For both models Laplace-Stieltjes transforms of the occupation period, vacation period and waiting time are derived and generating functions of the number of units in the system are calculated. The two models are then compared to each other, and for some special cases the optimal mean vacation times are found.

Suggested Citation

  • Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    • Handle: RePEc:inm:ormnsc:v:22:y:1975:i:2:p:202-211
    DOI: 10.1287/mnsc.22.2.202
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.22.2.202
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.22.2.202?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:ormnsc:v:22:y:1975:i:2:p:202-211. 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.