IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v198y2012i1p25-5610.1007-s10479-011-0921-4.html
   My bibliography  Save this article

Polling models with multi-phase gated service

Author

Listed:
  • R. Mei

    ()

  • A. Roubos

Abstract

In this paper we introduce and analyze a new class of service policies called multi-phase gated service. This policy is a generalization of the classical single-phase and two-phase gated policies and works as follows. Each customer that arrives at queue i will have to wait K i ≥1 cycles before it receives service. The aim of this policy is to provide an interleaving scheme to avoid monopolization of the system by heavily loaded queues, by choosing the proper values of interleaving levels K i . In this paper, we analyze the effectiveness of the interleaving scheme on the queueing behavior of the system, and consider the problem of identifying the proper combination of interleaving levels ${\underline{K}}^{*}=(K_{1}^{*},\ldots,K_{N}^{*})$ that minimizes a weighted sum of the mean waiting times at each of the N queues. Obviously, the proper choice of the interleaving levels is most critical when the system is heavily loaded. For this reason, we explore the framework developed in Queueing Syst. 57, 29–46 ( 2007 ) to obtain closed-form expressions for the asymptotic waiting-time distributions in heavy traffic, and use these expressions to derive simple heuristics for approximating the optimal interleaving scheme ${\underline{K}}^{*}$ . Numerical results with simulations demonstrate that the accuracy of these approximations is extremely high. Copyright Springer Science+Business Media, LLC 2012

Suggested Citation

  • R. Mei & A. Roubos, 2012. "Polling models with multi-phase gated service," Annals of Operations Research, Springer, vol. 198(1), pages 25-56, September.
  • Handle: RePEc:spr:annopr:v:198:y:2012:i:1:p:25-56:10.1007/s10479-011-0921-4
    DOI: 10.1007/s10479-011-0921-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-011-0921-4
    Download Restriction: Access to full text is restricted to subscribers.

    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. E. G. Coffman & A. A. Puhalskii & M. I. Reiman, 1998. "Polling Systems in Heavy Traffic: A Bessel Process Limit," Mathematics of Operations Research, INFORMS, vol. 23(2), pages 257-304, May.
    2. Blanc, J.P.C. & van der Mei, R.D., 1992. "Optimization of polling systems with Bernoulli schedules," Research Memorandum FEW 563, Tilburg University, School of Economics and Management.
    3. S. C. Borst & O. J. Boxma, 1997. "Polling Models With and Without Switchover Times," Operations Research, INFORMS, vol. 45(4), pages 536-543, August.
    Full references (including those not matched with items on IDEAS)

    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:spr:annopr:v:198:y:2012:i:1:p:25-56:10.1007/s10479-011-0921-4. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Springer Nature Abstracting and Indexing). General contact details of provider: http://www.springer.com .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.