IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v47y1999i2p310-312.html
   My bibliography  Save this article

M/M/1 Queues with Switching Costs and Hysteretic Optimal Control

Author

Listed:
  • M. Yu. Kitaev

    (Moscow State University, Moscow, Russia)

  • Richard F. Serfozo

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

This paper considers an M / M /1 queueing system with dynamically controlled arrival and service rates. At each arrival or service completion epoch, a decision maker chooses a pair of arrival and service rates from a finite set, and the system operates under these rates until the next arrival or service completion. There is a switching cost for changing the rates, and there is a cost per unit time of holding customers and using the arrival and service rates. The results describe natural conditions on the costs under which an optimal policy for either the discounted-cost or average-cost criterion is a hysteretic policy. Such a policy increases the service rate and decreases the arrival rate as the queue length increases. Furthermore, the control exhibits a stickiness or resistance to change, called hysteresis, due to the switching costs.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:oropre:v:47:y:1999:i:2:p:310-312
    DOI: 10.1287/opre.47.2.310
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.47.2.310
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.47.2.310?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
    ---><---

    References listed on IDEAS

    as
    1. Richard F. Serfozo, 1979. "Technical Note—An Equivalence Between Continuous and Discrete Time Markov Decision Processes," Operations Research, INFORMS, vol. 27(3), pages 616-620, June.
    2. 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.
    3. Sabine K. Hipp & Ulrich D. Holzbaur, 1988. "Decision Processes with Monotone Hysteretic Policies," Operations Research, INFORMS, vol. 36(4), pages 585-588, August.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Eugene Furman & Adam Diamant & Murat Kristal, 2021. "Customer Acquisition and Retention: A Fluid Approach for Staffing," Production and Operations Management, Production and Operations Management Society, vol. 30(11), pages 4236-4257, November.
    2. Maria Mayorga & Kevin Taaffe & Ramesh Arumugam, 2009. "Allocating flexible servers in serial systems with switching costs," Annals of Operations Research, Springer, vol. 172(1), pages 231-242, November.
    3. O. Boxma & A. Löpker & D. Perry, 2016. "On a make-to-stock production/mountain modeln with hysteretic control," Annals of Operations Research, Springer, vol. 241(1), pages 53-82, June.
    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. Lingjiao Zhang & Jinting Wang & Yilin Wang, 2023. "Strategic Behavior and Optimization of an M/M/1 Queue with N-Policy and Hysteretic Control," Methodology and Computing in Applied Probability, Springer, vol. 25(4), pages 1-29, December.
    6. Batta, Rajan & Berman, Oded & Wang, Qian, 2007. "Balancing staffing and switching costs in a service center with flexible servers," European Journal of Operational Research, Elsevier, vol. 177(2), pages 924-938, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xiuli Chao & Frank Y. Chen, 2005. "An Optimal Production and Shutdown Strategy when a Supplier Offers an Incentive Program," Manufacturing & Service Operations Management, INFORMS, vol. 7(2), pages 130-143, March.
    2. 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.
    3. Dwi Ertiningsih & Sandjai Bhulai & Flora Spieksma, 2018. "A novel use of value iteration for deriving bounds for threshold and switching curve optimal policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 638-659, December.
    4. 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.
    5. Nicole Leder & Bernd Heidergott & Arie Hordijk, 2010. "An Approximation Approach for the Deviation Matrix of Continuous-Time Markov Processes with Application to Markov Decision Theory," Operations Research, INFORMS, vol. 58(4-part-1), pages 918-932, August.
    6. 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).
    7. 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.
    8. 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.
    9. repec:dgr:rugsom:10005 is not listed on IDEAS
    10. Kim, Eungab, 2004. "Stochastic vendor managed replenishment with demand dependent shipment," European Journal of Operational Research, Elsevier, vol. 152(3), pages 723-744, February.
    11. Jianmin Shi, 2025. "Superposed semi-Markov decision process with application to optimal maintenance systems," Journal of Combinatorial Optimization, Springer, vol. 49(3), pages 1-19, April.
    12. 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.
    13. Dinard van der Laan, 2015. "Assigning Multiple Job Types to Parallel Specialized Servers," Tinbergen Institute Discussion Papers 15-102/III, Tinbergen Institute.
    14. Sergei V. Savin & Morris A. Cohen & Noah Gans & Ziv Katalan, 2005. "Capacity Management in Rental Businesses with Two Customer Bases," Operations Research, INFORMS, vol. 53(4), pages 617-631, August.
    15. 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.
    16. 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.
    17. Xufeng Yang & Juliang Zhang & Wen Jiao & Hong Yan, 2023. "Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers," Management Science, INFORMS, vol. 69(3), pages 1468-1485, March.
    18. Han, Gain & Sohn, Keemin, 2016. "Activity imputation for trip-chains elicited from smart-card data using a continuous hidden Markov model," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 121-135.
    19. Gregory Dobson & Hsiao-Hui Lee & Arvind Sainathan & Vera Tilson, 2012. "A Queueing Model to Evaluate the Impact of Patient "Batching" on Throughput and Flow Time in a Medical Teaching Facility," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 584-599, October.
    20. Yoon, Soovin & Albert, Laura A., 2020. "A dynamic ambulance routing model with multiple response," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 133(C).
    21. Lode Li & Evan L. Porteus & Hongtao Zhang, 2001. "Optimal Operating Policies for Multiplant Stochastic Manufacturing Systems in a Changing Environment," Management Science, INFORMS, vol. 47(11), pages 1539-1551, November.

    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:47:y:1999:i:2:p:310-312. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.