IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i6p917-927.html
   My bibliography  Save this article

The Nonpreemptive Priority MAP/G/1 Queue

Author

Listed:
  • Tetsuya Takine

    (Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan)

Abstract

This paper considers the nonpreemptive priority queue with MAP (Markovian Arrival Process) arrivals. Since MAP is weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.

Suggested Citation

  • Tetsuya Takine, 1999. "The Nonpreemptive Priority MAP/G/1 Queue," Operations Research, INFORMS, vol. 47(6), pages 917-927, December.
  • Handle: RePEc:inm:oropre:v:47:y:1999:i:6:p:917-927
    DOI: 10.1287/opre.47.6.917
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.6.917
    Download Restriction: no

    File URL: https://libkey.io/10.1287/opre.47.6.917?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. Gagan L. Choudhury & David M. Lucantoni, 1996. "Numerical Computation of the Moments of a Probability Distribution from its Transform," Operations Research, INFORMS, vol. 44(2), pages 368-381, April.
    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. Sofian De Clercq & Joris Walraevens, 2020. "Delay analysis of a two-class priority queue with external arrivals and correlated arrivals from another node," Annals of Operations Research, Springer, vol. 293(1), pages 57-72, October.
    2. 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.
    3. Joris Walraevens & Thomas Giel & Stijn Vuyst & Sabine Wittevrongel, 2022. "Asymptotics of waiting time distributions in the accumulating priority queue," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 221-244, August.

    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. Svetlana Boyarchenko & Sergei Levendorskiu{i}, 2024. "Efficient inverse $Z$-transform and Wiener-Hopf factorization," Papers 2404.19290, arXiv.org, revised May 2024.
    2. Brignone, Riccardo & Gonzato, Luca, 2024. "Exact simulation of the Hull and White stochastic volatility model," Journal of Economic Dynamics and Control, Elsevier, vol. 163(C).
    3. Steve Derkic & James E. Stafford, 2002. "Symbolic Computation of Moments in Priority Queues," INFORMS Journal on Computing, INFORMS, vol. 14(3), pages 261-277, August.
    4. Dasu, Sriram, 1998. "Class dependent departure process from multiclass phase queues: Exact and approximate analyses," European Journal of Operational Research, Elsevier, vol. 108(2), pages 379-404, July.
    5. Boxma, O. J. & Down, D. G., 1997. "Dynamic server assignment in a two-queue model," European Journal of Operational Research, Elsevier, vol. 103(3), pages 595-609, December.
    6. Wu-Lin Chen, 2019. "Computing the Moments of Polling Models with Batch Poisson Arrivals by Transform Inversion," INFORMS Journal on Computing, INFORMS, vol. 31(3), pages 515-526, July.

    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:47:y:1999:i:6:p:917-927. 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: 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.