IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v32y1984i5p1116-1132.html
   My bibliography  Save this article

M / M /1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies

Author

Listed:
  • F. V. Lu

    (St. John's University, Jamaica, New York)

  • R. F. Serfozo

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

This paper studies an M / M /1 queueing decision process in which the arrival and service rates are chosen from a finite set whenever the queue length changes. Each choice has a switching cost depending on the chosen rates and those currently in use, and a usage cost depending on the chosen rates and the queue length; these switching and usage cost functions are submodular and satisfy additional technical conditions. The system objective is to find a policy for dynamically choosing the rates, based on the current rates and queue length, that minimizes the expected total discounted cost or average cost over an infinite horizon. We prove that there is a monotone hysteretic optimal policy in which the arrival and service rates are decreasing and increasing, respectively, in the queue length; there is a hysteresis (retardation) in the changing of the actions due to the switching costs. We establish this result by showing that such optimal policies exist for an equivalent discrete-time random walk decision process. Our results confirm a decade-old conjecture that the M / M /1 queue has a monotone hysteretic optimal control policy.

Suggested Citation

  • F. V. Lu & R. F. Serfozo, 1984. "M / M /1 Queueing Decision Processes with Monotone Hysteretic Optimal Policies," Operations Research, INFORMS, vol. 32(5), pages 1116-1132, October.
    • Handle: RePEc:inm:oropre:v:32:y:1984:i:5:p:1116-1132
    DOI: 10.1287/opre.32.5.1116
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.32.5.1116
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.32.5.1116?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. Terekhov, Daria & Christopher Beck, J., 2009. "An extended queueing control model for facilities with front room and back room operations and mixed-skilled workers," European Journal of Operational Research, Elsevier, vol. 198(1), pages 223-231, October.
    2. António Pacheco & Helena Ribeiro, 2008. "Consecutive customer losses in oscillating GI X /M//n systems with state dependent services rates," Annals of Operations Research, Springer, vol. 162(1), pages 143-158, September.
    3. Berman, Oded & Wang, Jiamin & Sapna, K. P., 2005. "Optimal management of cross-trained workers in services with negligible switching costs," European Journal of Operational Research, Elsevier, vol. 167(2), pages 349-369, December.
    4. J. R. Artalejo & A. Economou, 2005. "Markovian Controllable Queueing Systems with Hysteretic Policies: Busy Period and Waiting Time Analysis," Methodology and Computing in Applied Probability, Springer, vol. 7(3), pages 353-378, September.
    5. Foreest, N. D. van & Wijngaard, J., 2010. "On the Optimal Policy for the Single-product Inventory Problem with Set-up Cost and a Restricted Production Capacity," Research Report 10005, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    6. Kim, Eungab, 2005. "Optimal inventory replenishment policy for a queueing system with finite waiting room capacity," European Journal of Operational Research, Elsevier, vol. 161(1), pages 256-274, February.
    7. Sunggon Kim & Jongwoo Kim & Eui Lee, 2006. "Stationary distribution of queue length in G / M / 1 queue with two-stage service policy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 467-480, December.
    8. M. Yu. Kitaev & Richard F. Serfozo, 1999. "M/M/1 Queues with Switching Costs and Hysteretic Optimal Control," Operations Research, INFORMS, vol. 47(2), pages 310-312, April.
    9. Carri W. Chan & Mor Armony & Nicholas Bambos, 2016. "Maximum weight matching with hysteresis in overloaded queues with setups," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 315-351, April.
    10. Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.
    11. repec:dgr:rugsom:10005 is not listed on IDEAS
    12. Nicky D. Van Foreest & Jacob Wijngaard, 2014. "On Optimal Policies for Production-Inventory Systems with Compound Poisson Demand and Setup Costs," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 517-532, May.
    13. Boronico, Jess S. & Siegel, Philip H., 1998. "Capacity planning for toll roadways incorporating consumer wait time costs," Transportation Research Part A: Policy and Practice, Elsevier, vol. 32(4), pages 297-310, May.
    14. Kim, Eungab, 2004. "Stochastic vendor managed replenishment with demand dependent shipment," European Journal of Operational Research, Elsevier, vol. 152(3), pages 723-744, February.

    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:32:y:1984:i:5:p:1116-1132. 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.