IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v192y2009i1p151-172.html
   My bibliography  Save this article

Analysis of a finite buffer model with two servers and two nonpreemptive priority classes

Author

Listed:
  • Feng, Wei
  • Umemura, Masataka

Abstract

In this paper, we analyze a finite buffer queueing model with two servers and two nonpreemptive priority service classes. The arrival streams are independent Poisson processes, and the service times of the two classes are exponentially distributed with different means. One of the two servers is reserved exclusively for one class with high priority and the other server serves the two classes according to a nonpreemptive priority service schedule. For the model, we describe its dynamic behavior by a four-dimensional continuous-time Markov process. Applying recursive approaches we present the explicit representation for the steady-state distribution of this Markov process. Then, we calculate the Laplace-Stieltjes Transform and the steady-state distribution of the actual waiting times of two classes of customers. We also give some numerical comparison results with other queueing models.

Suggested Citation

  • Feng, Wei & Umemura, Masataka, 2009. "Analysis of a finite buffer model with two servers and two nonpreemptive priority classes," European Journal of Operational Research, Elsevier, vol. 192(1), pages 151-172, January.
    • Handle: RePEc:eee:ejores:v:192:y:2009:i:1:p:151-172
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(07)00940-X
    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. 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.
    2. Feng, Wei & Adachi, Kouichi & Kowada, Masashi, 2002. "A two-queue and two-server model with a threshold-based control service policy," European Journal of Operational Research, Elsevier, vol. 137(3), pages 593-611, March.
    3. H. R. Gail & S. L. Hantler & B. A. Taylor, 1992. "On a Preemptive Markovian Queue with Multiple Servers and Two Priority Classes," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 365-391, May.
    4. Dietmar Wagner, 1998. "A finite capacity multi-server multi-queueing priority model with non-renewal input," Annals of Operations Research, Springer, vol. 79(0), pages 63-82, January.
    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. Bruneel, Herwig & Maertens, Tom & Walraevens, Joris, 2014. "Class clustering destroys delay differentiation in priority queues," European Journal of Operational Research, Elsevier, vol. 235(1), pages 149-158.
    2. 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.
    3. Herwig Bruneel & Tom Maertens & Bart Steyaert & Dieter Claeys & Dieter Fiems & Joris Walraevens, 2018. "Analysis of a two-class single-server discrete-time FCFS queue: the effect of interclass correlation," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 403-436, October.

    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. Chen, Shih-Pin, 2004. "Parametric nonlinear programming for analyzing fuzzy queues with finite capacity," European Journal of Operational Research, Elsevier, vol. 157(2), pages 429-438, September.
    2. Bedford, A. & Zeephongsekul, P., 2005. "On a dual queueing system with preemptive priority service discipline," European Journal of Operational Research, Elsevier, vol. 161(1), pages 224-239, February.
    3. Zeephongsekul, P. & Bedford, A., 2006. "Waiting time analysis of the multiple priority dual queue with a preemptive priority service discipline," European Journal of Operational Research, Elsevier, vol. 172(3), pages 886-908, August.
    4. Seyed Khodadadi & Fariborz Jolai, 2012. "A fuzzy based threshold policy for a single server retrial queue with vacations," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(2), pages 281-297, June.
    5. Ivanovs, Jevgenijs & Boxma, Onno & Mandjes, Michel, 2010. "Singularities of the matrix exponent of a Markov additive process with one-sided jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(9), pages 1776-1794, August.
    6. Feng, Wei & Adachi, Kouichi & Kowada, Masashi, 2002. "A two-queue and two-server model with a threshold-based control service policy," European Journal of Operational Research, Elsevier, vol. 137(3), pages 593-611, March.
    7. Andrei Sleptchenko & M. Eric Johnson, 2015. "Maintaining Secure and Reliable Distributed Control Systems," INFORMS Journal on Computing, INFORMS, vol. 27(1), pages 103-117, February.

    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:192:y:2009:i:1:p:151-172. 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.