IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v41y1995i8p1353-1370.html
   My bibliography  Save this article

On the Accuracy of the Simple Peak Hour Approximation for Markovian Queues

Author

Listed:
  • Linda V. Green

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Peter J. Kolesar

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

We empirically explore the accuracy of the simple stationary peak hour approximation (SPHA) for estimating peak hour performance in multiserver queuing systems with exponential service times and periodic (sinusoidal) Poisson arrival processes. We show that the SPHA is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems. However, we do find and document that there are many situations in which this approximation will be very inaccurate. We postulate and then support empirically a set of hypotheses that link the accuracy of the SPHA and the related point-wise stationary approximation (PSA) to key parameter values and model characteristics. We also present results on the time-dependent behavior of these systems as a function of key parameters. Finally we present results which indicate that our findings, developed for models with sinusoidal input streams, may apply to a much broader range of Markovian models with more general cyclic inputs.

Suggested Citation

  • Linda V. Green & Peter J. Kolesar, 1995. "On the Accuracy of the Simple Peak Hour Approximation for Markovian Queues," Management Science, INFORMS, vol. 41(8), pages 1353-1370, August.
    • Handle: RePEc:inm:ormnsc:v:41:y:1995:i:8:p:1353-1370
    DOI: 10.1287/mnsc.41.8.1353
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.41.8.1353
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.41.8.1353?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. Pieter Smet & Annelies Lejon & Greet Vanden Berghe, 2021. "Demand smoothing in shift design," Flexible Services and Manufacturing Journal, Springer, vol. 33(2), pages 457-484, June.
    2. Linda V. Green & Peter J. Kolesar & João Soares, 2001. "Improving the Sipp Approach for Staffing Service Systems That Have Cyclic Demands," Operations Research, INFORMS, vol. 49(4), pages 549-564, August.
    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. Ravi Kumar & Mark E. Lewis & Huseyin Topaloglu, 2013. "Dynamic service rate control for a single‐server queue with Markov‐modulated arrivals," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 661-677, December.
    5. Samantha L. Zimmerman & Alexander R. Rutherford & Alexa Waall & Monica Norena & Peter Dodek, 2023. "A queuing model for ventilator capacity management during the COVID-19 pandemic," Health Care Management Science, Springer, vol. 26(2), pages 200-216, June.
    6. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    7. Huanan Zhang & Cong Shi & Chao Qin & Cheng Hua, 2016. "Stochastic regret minimization for revenue management problems with nonstationary demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(6), pages 433-448, September.
    8. Gabriel Zayas-Cabán & Mark E. Lewis, 2020. "Admission control in a two-class loss system with periodically varying parameters and abandonments," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 175-210, February.
    9. 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.
    10. Alnowibet, Khalid Abdulaziz & Perros, Harry, 2009. "Nonstationary analysis of the loss queue and of queueing networks of loss queues," European Journal of Operational Research, Elsevier, vol. 196(3), pages 1015-1030, August.

    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:41:y:1995:i:8:p:1353-1370. 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.