IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v87y2014icp98-104.html
   My bibliography  Save this article

A time-dependent busy period queue length formula for the M/Ek/1 queue

Author

Listed:
  • Baek, Jung Woo
  • Moon, Seung Ki
  • Lee, Ho Woo

Abstract

In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M/Ek/1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M/M/1 queue is also presented as a special case.

Suggested Citation

  • Baek, Jung Woo & Moon, Seung Ki & Lee, Ho Woo, 2014. "A time-dependent busy period queue length formula for the M/Ek/1 queue," Statistics & Probability Letters, Elsevier, vol. 87(C), pages 98-104.
    • Handle: RePEc:eee:stapro:v:87:y:2014:i:c:p:98-104
    DOI: 10.1016/j.spl.2014.01.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715214000157
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2014.01.004?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Leonenko, G.M., 2009. "A new formula for the transient solution of the Erlang queueing model," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 400-406, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. B. H. Margolius, 2023. "The periodic steady-state solution for queues with Erlang arrivals and service and time-varying periodic transition rates," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 45-94, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. B. H. Margolius, 2023. "The periodic steady-state solution for queues with Erlang arrivals and service and time-varying periodic transition rates," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 45-94, February.
    2. Xiaoyuan Liu & Brian Fralix, 2019. "On Lattice Path Counting and the Random Product Representation, with Applications to the Er/M/1 Queue and the M/Er/1 Queue," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1119-1149, December.
    3. Jung Woo Baek & Yun Han Bae, 2019. "Exact Time-Dependent Queue-Length Solution to a Discrete-Time Geo / D /1 Queue," Mathematics, MDPI, vol. 7(8), pages 1-8, August.
    4. Jain, Madhu & Bhagat, Amita & Shekhar, Chandra, 2015. "Double orbit finite retrial queues with priority customers and service interruptions," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 324-344.

    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:eee:stapro:v:87:y:2014:i:c:p:98-104. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.