IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v43y1995i1p158-165.html
   My bibliography  Save this article

Approximation of the Mean Queue Length of an M/G/c Queueing System

Author

Listed:
  • Bobby N. W. Ma

    (Ryerson Polytechnical Institute, Toronto, Ontario, Canada)

  • Jon W. Mark

    (University of Waterloo, Waterloo, Ontario, Canada)

Abstract

A relatively robust method for the approximate analysis of the mean queue length of an M/G/c queueing system is proposed. The approximation method is developed based on the following assumptions: the residual service time of one busy server is independent of those of the other busy servers, and the system in which all the servers are busy is treated in the same way as a single-server system with c times the service rate of one of the servers. The application of these two assumptions is coupled through the introduction of a parameter n p . If the number of customers in the system is larger than n p , assumption 2 is used; otherwise assumption 1 is used. We found that certain properties of n p allow an estimation of the mean queue length of a large M/G/c queueing system through the approximate analysis of the mean queue length of a much smaller M/G/c queueing system. Numerical results show that the approximation is accurate even when the coefficient of variation of the service time and the number of channels of the system are as large as 20 and 200, respectively.

Suggested Citation

  • Bobby N. W. Ma & Jon W. Mark, 1995. "Approximation of the Mean Queue Length of an M/G/c Queueing System," Operations Research, INFORMS, vol. 43(1), pages 158-165, February.
    • Handle: RePEc:inm:oropre:v:43:y:1995:i:1:p:158-165
    DOI: 10.1287/opre.43.1.158
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.43.1.158
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.43.1.158?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
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Guodong & Liu, Aijun & Zhang, Jianghua & Sun, Huiping, 2021. "Optimal operations planning of electric autonomous vehicles via asynchronous learning in ride-hailing systems," Omega, Elsevier, vol. 103(C).
    2. Kleijnen, J.P.C. & Bettonvil, B.W.M. & van Groenendaal, W.J.H., 1996. "Validation of Simulation Models : Regression Analysis Revisited," Other publications TiSEM 4891f156-fe9c-4360-b82d-3, Tilburg University, School of Economics and Management.
    3. Evsey Morozov & Michele Pagano & Irina Peshkova & Alexander Rumyantsev, 2020. "Sensitivity Analysis and Simulation of a Multiserver Queueing System with Mixed Service Time Distribution," Mathematics, MDPI, vol. 8(8), pages 1-16, August.
    4. Muhammad El-Taha & Bacel Maddah, 2006. "Allocation of Service Time in a Multiserver System," Management Science, INFORMS, vol. 52(4), pages 623-637, April.
    5. Guo, Pengfei & Sun, Wei & Wang, Yulan, 2011. "Equilibrium and optimal strategies to join a queue with partial information on service times," European Journal of Operational Research, Elsevier, vol. 214(2), pages 284-297, October.

    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:43:y:1995:i:1:p:158-165. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.