IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v39y1993i2p241-252.html
   My bibliography  Save this article

Mt/G/\infty Queues with Sinusoidal Arrival Rates

Author

Listed:
  • Stephen G. Eick

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636)

  • William A. Massey

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636)

  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974-0636)

Abstract

In this paper we describe the mean number of busy servers as a function of time in an M t /G/\infty queue (having a nonhomogeneous Poisson arrival process) with a sinusoidal arrival rate function. For an M t /G/\infty model with appropriate initial conditions, it is known that the number of busy servers at time t has a Poisson distribution for each t, so that the full distribution is characterized by its mean. Our formulas show how the peak congestion lags behind the peak arrival rate and how much less is the range of congestion than the range of offered load. The simple formulas can also be regarded as consequences of linear system theory, because the mean function can be regarded as the image of a linear operator applied to the arrival rate function. We also investigate the quality of various approximations for the mean number of busy servers such as the pointwise stationary approximation and several polynomial approximations. Finally, we apply the results for sinusoidal arrival rate functions to treat general periodic arrival rate functions using Fourier series. These results are intended to provide a better understanding of the behavior of the M t /G/\infty model and related M t /G/s/r models where some customers are lost or delayed.

Suggested Citation

  • Stephen G. Eick & William A. Massey & Ward Whitt, 1993. "Mt/G/\infty Queues with Sinusoidal Arrival Rates," Management Science, INFORMS, vol. 39(2), pages 241-252, February.
    • Handle: RePEc:inm:ormnsc:v:39:y:1993:i:2:p:241-252
    DOI: 10.1287/mnsc.39.2.241
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.39.2.241
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.39.2.241?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. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    2. Rouba Ibrahim & Mor Armony & Achal Bassamboo, 2017. "Does the Past Predict the Future? The Case of Delay Announcements in Service Systems," Management Science, INFORMS, vol. 63(6), pages 1762-1780, June.
    3. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    4. Vijayalakshmi Chetlapalli & K. S. S. Iyer & Himanshu Agrawal, 2020. "Modelling time-dependent aggregate traffic in 5G networks," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 73(4), pages 557-575, April.
    5. Song-Hee Kim & Ward Whitt, 2013. "Statistical Analysis with Little's Law," Operations Research, INFORMS, vol. 61(4), pages 1030-1045, August.
    6. Yang, Feng & Liu, Jingang, 2012. "Simulation-based transfer function modeling for transient analysis of general queueing systems," European Journal of Operational Research, Elsevier, vol. 223(1), pages 150-166.
    7. Eugene Furman & Alex Cressman & Saeha Shin & Alexey Kuznetsov & Fahad Razak & Amol Verma & Adam Diamant, 2021. "Prediction of personal protective equipment use in hospitals during COVID-19," Health Care Management Science, Springer, vol. 24(2), pages 439-453, June.
    8. Linda V. Green & Peter J. Kolesar, 1998. "A Note on Approximating Peak Congestion in Mt/G/\infty Queues with Sinusoidal Arrivals," Management Science, INFORMS, vol. 44(11-Part-2), pages 137-144, November.
    9. Ward Whitt, 2016. "Heavy-traffic fluid limits for periodic infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 111-143, 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:ormnsc:v:39:y:1993:i:2:p:241-252. 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.