IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v24y1976i4p760-773.html
   My bibliography  Save this article

The M / M /∞ Queue with Varying Arrival and Departure Rates

Author

Listed:
  • T. Collings

    (University of Strathclyde, Glasgow, Scotland)

  • C. Stoneman

    (University of Strathclyde, Glasgow, Scotland)

Abstract

This paper derives the queue size distribution for infinite server queues with Poisson arrivals and exponential service times when the parameters of both distributions are allowed to vary with time. Both continuous and discrete variation are examined. Infinite server queues realistically describe those queues in which sufficient service capacity exists to prevent virtually any customer waiting time. Such queues are not uncommon in the health services, when a delay in service can sometimes mean death. Specifically, we discuss the queuing problem of an intensive care unit and show that it is unlikely that the hourly variation in the arrival rate of patients to the unit will significantly affect the number of beds occupied.

Suggested Citation

  • T. Collings & C. Stoneman, 1976. "The M / M /∞ Queue with Varying Arrival and Departure Rates," Operations Research, INFORMS, vol. 24(4), pages 760-773, August.
    • Handle: RePEc:inm:oropre:v:24:y:1976:i:4:p:760-773
    DOI: 10.1287/opre.24.4.760
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.24.4.760
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.24.4.760?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. Anatoly Nazarov & Alexander Dudin & Alexander Moiseev, 2022. "Pseudo Steady-State Period in Non-Stationary Infinite-Server Queue with State Dependent Arrival Intensity," Mathematics, MDPI, vol. 10(15), pages 1-12, July.
    2. Tan, Xiaoqian & Knessl, Charles & Yang, Yongzhi (Peter), 2013. "On finite capacity queues with time dependent arrival rates," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2175-2227.
    3. 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.
    4. Amir Elalouf & Guy Wachtel, 2022. "Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies," SN Operations Research Forum, Springer, vol. 3(1), pages 1-46, March.
    5. Giorno, Virginia & Nobile, Amelia G., 2022. "On some integral equations for the evaluation of first-passage-time densities of time-inhomogeneous birth-death processes," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    6. Harris, K.R. & Trappeniers, N.J., 1980. "The density dependence of the self-diffusion coefficient of liquid methane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(1), pages 262-280.
    7. Michels, J.P.J. & Trappeniers, N.J., 1980. "Molecular dynamical calculations on the transport properties of a square-well fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(1), pages 243-254.

    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:inm:oropre:v:24:y:1976:i:4:p:760-773. 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.