IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v189y2008i3p1403-1408.html
   My bibliography  Save this article

Discrete time GI/Geom/1 queueing system with priority

Author

Listed:
  • Ndreca, Sokol
  • Scoppola, Benedetto

Abstract

We study a discrete time single server system with generic distribution of the number of arrivals in a time slot, geometric distribution of the service time and two classes of customers. The customers can be served only when each time slot begins. The customers of the second class can be served only if the customers of the first class are absent. The model is motivated by the description of the congestion in the information networks. We give a complete description of this systems: we are able to compute the expected waiting time of the customers of the two classes, and solving a boundary value problem we are able to write the probability distribution of the length of the queue. To obtain these results, we use judiciously the standard technique of the generating function of the probability distribution. Although the boundary value problem is relatively easy, it is has to be pointed out that the generating function is not simply the product of two independent generating functions for the two classes.

Suggested Citation

  • Ndreca, Sokol & Scoppola, Benedetto, 2008. "Discrete time GI/Geom/1 queueing system with priority," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1403-1408, September.
  • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1403-1408
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00626-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dave Worthington & A Wall, 1999. "Using the discrete time modelling approach to evaluate the time-dependent behaviour of queueing systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(8), pages 777-788, 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. I. Atencia, 2015. "A discrete-time queueing system with server breakdowns and changes in the repair times," Annals of Operations Research, Springer, vol. 235(1), pages 37-49, December.
    2. Sofian De Clercq & Koenraad Laevens & Bart Steyaert & Herwig Bruneel, 2013. "A multi-class discrete-time queueing system under the FCFS service discipline," Annals of Operations Research, Springer, vol. 202(1), pages 59-73, January.
    3. Walraevens, Joris & Maertens, Tom & Bruneel, Herwig, 2013. "A semi-preemptive priority scheduling discipline: Performance analysis," European Journal of Operational Research, Elsevier, vol. 224(2), pages 324-332.
    4. Mu-Song Chen & Hao-Wei Yen, 2016. "A two-stage approach in solving the state probabilities of the multi-queue //1 model," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(5), pages 1230-1244, April.

    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. Xi Chen & Dave Worthington, 2017. "Staffing of time-varying queues using a geometric discrete time modelling approach," Annals of Operations Research, Springer, vol. 252(1), pages 63-84, May.
    2. Justus Schwarz & Judith Stoll née Matzka & Eda Özden, 2015. "A general model for batch building processes under the timeout and capacity rules," Annals of Operations Research, Springer, vol. 231(1), pages 5-31, August.
    3. Wall, A.D. & Worthington, D.J., 2007. "Time-dependent analysis of virtual waiting time behaviour in discrete time queues," European Journal of Operational Research, Elsevier, vol. 178(2), pages 482-499, April.
    4. Schwarz, Justus Arne & Selinka, Gregor & Stolletz, Raik, 2016. "Performance analysis of time-dependent queueing systems: Survey and classification," Omega, Elsevier, vol. 63(C), pages 170-189.
    5. D Worthington, 2009. "Reflections on queue modelling from the last 50 years," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 83-92, May.

    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:eee:ejores:v:189:y:2008:i:3:p:1403-1408. 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/locate/eor .

    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.