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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
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    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.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    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.

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