IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v45y1998i1p23-50.html
   My bibliography  Save this article

Matrix‐geometric solution of discrete time MAP/PH/1 priority queue

Author

Listed:
  • Attahiru Sule Alfa

Abstract

We use the matrix‐geometric method to study the discrete time MAP/PH/1 priority queue with two types of jobs. Both preemptive and non‐preemptive cases are considered. We show that the structure of the R matrix obtained by Miller for the Birth‐Death system can be extended to our Quasi‐Birth‐Death case. For both preemptive and non‐preemptive cases the distributions of the number of jobs of each type in the system are obtained and their waiting times are obtained for the non‐preemptive. For the preemptive case we obtain the waiting time distribution for the high priority job and the distribution of the lower priority job's wait before it becomes the leading job of its priority class. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 23–50, 1998

Suggested Citation

  • Attahiru Sule Alfa, 1998. "Matrix‐geometric solution of discrete time MAP/PH/1 priority queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(1), pages 23-50, February.
    • Handle: RePEc:wly:navres:v:45:y:1998:i:1:p:23-50
    DOI: 10.1002/(SICI)1520-6750(199802)45:13.0.CO;2-N
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/(SICI)1520-6750(199802)45:13.0.CO;2-N
    Download Restriction: no
    File URL: https://libkey.io/10.1002/(SICI)1520-6750(199802)45:13.0.CO;2-N?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
    ---><---

    References listed on IDEAS

    as
    1. Edward P. C. Kao & Kumar S. Narayanan, 1990. "Computing Steady-State Probabilities of a Nonpreemptive Priority Multiserver Queue," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 211-218, August.
    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. Attahiru Sule Alfa & Bin Liu & Qi‐Ming He, 2003. "Discrete‐time analysis of MAP/PH/1 multiclass general preemptive priority queue," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(6), pages 662-682, September.

    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. Josef Zuk & David Kirszenblat, 2024. "Explicit results for the distributions of queue lengths for a non-preemptive two-level priority queue," Annals of Operations Research, Springer, vol. 341(2), pages 1223-1246, October.
    2. Mor Harchol-Balter & Takayuki Osogami & Alan Scheller-Wolf & Adam Wierman, 2005. "Multi-Server Queueing Systems with Multiple Priority Classes," Queueing Systems: Theory and Applications, Springer, vol. 51(3), pages 331-360, December.
    3. Elvin Coban & Aliza Heching & Alan Scheller‐Wolf, 2019. "Service Center Staffing with Cross‐Trained Agents and Heterogeneous Customers," Production and Operations Management, Production and Operations Management Society, vol. 28(4), pages 788-809, April.
    4. Kao, Edward P. C. & Wilson, Sandra D., 1999. "Analysis of nonpreemptive priority queues with multiple servers and two priority classes," European Journal of Operational Research, Elsevier, vol. 118(1), pages 181-193, October.
    5. Wagner, Dietmar, 1997. "Waiting times of a finite-capacity multi-server model with non-preemptive priorities," European Journal of Operational Research, Elsevier, vol. 102(1), pages 227-241, October.

    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:wly:navres:v:45:y:1998:i:1:p:23-50. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.