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Monotonic and Insensitive Optimal Policies for Control of Queues with Undiscounted Costs

Author

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  • Shaler Stidham

    (University of North Carolina, Chapel Hill, North Carolina)

  • Richard R. Weber

    (Queens' College, Cambridge, England)

Abstract

We consider the problem of controlling the service and/or arrival rates in queues, with the objective of minimizing the total expected cost to reach state zero. We present a unified, simple method for proving that an optimal policy is monotonic in the number of customers in the system. Applications to average-cost minimization over an infinite horizon are given. Both exponential and nonexponential models are considered; the essential characteristic is a left-skip-free transition structure and a nondecreasing (not necessarily convex) holding-cost function. Some of our results are insensitive to service-time distributions.

Suggested Citation

  • Shaler Stidham & Richard R. Weber, 1989. "Monotonic and Insensitive Optimal Policies for Control of Queues with Undiscounted Costs," Operations Research, INFORMS, vol. 37(4), pages 611-625, August.
    • Handle: RePEc:inm:oropre:v:37:y:1989:i:4:p:611-625
    DOI: 10.1287/opre.37.4.611
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    Cited by:

    1. De Munck, Thomas & Chevalier, Philippe & Tancrez, Jean-Sébastien, 2023. "Managing priorities on on-demand service platforms with waiting time differentiation," International Journal of Production Economics, Elsevier, vol. 266(C).
    2. Ying Xu & Alan Scheller-Wolf & Katia Sycara, 2015. "The Benefit of Introducing Variability in Single-Server Queues with Application to Quality-Based Service Domains," Operations Research, INFORMS, vol. 63(1), pages 233-246, February.
    3. Diwas S. KC & Bradley R. Staats & Maryam Kouchaki & Francesca Gino, 2020. "Task Selection and Workload: A Focus on Completing Easy Tasks Hurts Performance," Management Science, INFORMS, vol. 66(10), pages 4397-4416, October.
    4. Barιş Ata, 2005. "Dynamic Power Control in a Wireless Static Channel Subject to a Quality-of-Service Constraint," Operations Research, INFORMS, vol. 53(5), pages 842-851, October.
    5. Piotr Więcek & Eitan Altman & Arnob Ghosh, 2016. "Mean-Field Game Approach to Admission Control of an M/M/ $$\infty $$ ∞ Queue with Shared Service Cost," Dynamic Games and Applications, Springer, vol. 6(4), pages 538-566, December.
    6. Bradley, James R., 2005. "Optimal control of a dual service rate M/M/1 production-inventory model," European Journal of Operational Research, Elsevier, vol. 161(3), pages 812-837, March.
    7. Johansen, Soren Glud & Larsen, Christian, 2001. "Computation of a near-optimal service policy for a single-server queue with homogeneous jobs," European Journal of Operational Research, Elsevier, vol. 134(3), pages 648-663, November.
    8. Wallace J. Hopp & Seyed M. R. Iravani & Gigi Y. Yuen, 2007. "Operations Systems with Discretionary Task Completion," Management Science, INFORMS, vol. 53(1), pages 61-77, January.
    9. Jillian A. Berry Jaeker & Anita L. Tucker, 2017. "Past the Point of Speeding Up: The Negative Effects of Workload Saturation on Efficiency and Patient Severity," Management Science, INFORMS, vol. 63(4), pages 1042-1062, April.
    10. Diwas S. Kc & Christian Terwiesch, 2009. "Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations," Management Science, INFORMS, vol. 55(9), pages 1486-1498, September.
    11. 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.
    12. Peter Whittle, 2002. "Applied Probability in Great Britain," Operations Research, INFORMS, vol. 50(1), pages 227-239, February.
    13. Pengfei Guo & Refael Hassin, 2011. "Strategic Behavior and Social Optimization in Markovian Vacation Queues," Operations Research, INFORMS, vol. 59(4), pages 986-997, August.
    14. Jingqi Wang & Yong-Pin Zhou, 2018. "Impact of Queue Configuration on Service Time: Evidence from a Supermarket," Management Science, INFORMS, vol. 64(7), pages 3055-3075, July.
    15. Jennifer M. George & J. Michael Harrison, 2001. "Dynamic Control of a Queue with Adjustable Service Rate," Operations Research, INFORMS, vol. 49(5), pages 720-731, October.
    16. Wei, Yihua & Xu, Chen & Hu, Qiying, 2013. "Transformation of optimization problems in revenue management, queueing system, and supply chain management," International Journal of Production Economics, Elsevier, vol. 146(2), pages 588-597.
    17. Delasay, Mohammad & Ingolfsson, Armann & Kolfal, Bora & Schultz, Kenneth, 2019. "Load effect on service times," European Journal of Operational Research, Elsevier, vol. 279(3), pages 673-686.
    18. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    19. Diwas Singh KC & Christian Terwiesch, 2012. "An Econometric Analysis of Patient Flows in the Cardiac Intensive Care Unit," Manufacturing & Service Operations Management, INFORMS, vol. 14(1), pages 50-65, January.
    20. Li Xia & Zhe George Zhang & Quan‐Lin Li, 2022. "A c/μ‐Rule for Job Assignment in Heterogeneous Group‐Server Queues," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1191-1215, March.
    21. Erim Kardeş & Fernando Ordóñez & Randolph W. Hall, 2011. "Discounted Robust Stochastic Games and an Application to Queueing Control," Operations Research, INFORMS, vol. 59(2), pages 365-382, April.

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