IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v12y1964i5p736-752.html
   My bibliography  Save this article

On a Generalized M / G /1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service

Author

Listed:
  • Peter D. Welch

    (IBM Watson Research Center, Yorktown Heights, New York)

Abstract

The following generalization of the M / G /1 queue is considered. If a customer arrives when the server is busy, his service time has a distribution function, G b ( x ); while if he arrives when the server is idle, his service time has a different distribution function, G e ( x ). Results are obtained that characterize the transient and asymptotic distributions of the queue size, waiting time, and waiting-plus-service time. These results are then applied to the special case of a queue with a single service time distribution function, but with additional independent delay times that have one distribution function for the customers arriving when the server is idle and another for the customers arriving when the server is busy.

Suggested Citation

  • Peter D. Welch, 1964. "On a Generalized M / G /1 Queuing Process in Which the First Customer of Each Busy Period Receives Exceptional Service," Operations Research, INFORMS, vol. 12(5), pages 736-752, October.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:5:p:736-752
    DOI: 10.1287/opre.12.5.736
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.12.5.736
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.12.5.736?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. Bozer, Yavuz A. & Hsieh, Ying-Jiun, 2004. "Expected waiting times at loading stations in discrete-space closed-loop conveyors," European Journal of Operational Research, Elsevier, vol. 155(2), pages 516-532, June.
    2. Meier, Christian & Li, Lingfei & Zhang, Gongqiu, 2023. "Simulation of multidimensional diffusions with sticky boundaries via Markov chain approximation," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1292-1308.
    3. uit het Broek, Michiel A.J. & Van der Heide, Gerlach & Van Foreest, Nicky D., 2020. "Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs," European Journal of Operational Research, Elsevier, vol. 287(3), pages 916-928.
    4. Balcıõglu, Barış & Varol, Yãgız, 2022. "Fair and profitable: How pricing and lead-time quotation policies can help," European Journal of Operational Research, Elsevier, vol. 299(3), pages 977-986.
    5. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    6. Lillo, Rosa E., 2005. "Ergodicity and analysis of the process describing the system state in polling systems with two queues," European Journal of Operational Research, Elsevier, vol. 167(1), pages 144-162, November.

    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:12:y:1964:i:5:p:736-752. 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.