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Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate

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  • Thomas B. Crabill

    (University of North Carolina)

Abstract

This paper derives the form of a minimal cost rate stationary operating policy for an M/M/I queueing system with K possible service rates. The two costs of the system are a general cost rate dependent on the state of the system and a cost rate associated with each of the possible service rates. The optimal policy is completely characterized by if K - 1 numbers. The optimal service rate is shown to be nondecreasing in the state of the system.

Suggested Citation

  • Thomas B. Crabill, 1972. "Optimal Control of a Service Facility with Variable Exponential Service Times and Constant Arrival Rate," Management Science, INFORMS, vol. 18(9), pages 560-566, May.
    • Handle: RePEc:inm:ormnsc:v:18:y:1972:i:9:p:560-566
    DOI: 10.1287/mnsc.18.9.560
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    Cited by:

    1. José Niño-Mora, 2022. "Multi-Gear Bandits, Partial Conservation Laws, and Indexability," Mathematics, MDPI, vol. 10(14), pages 1-31, July.
    2. Sergey Sinelnikov-Murylev & Alexandr Radygin (ed.), 2018. "Russian Economy in 2017. Trends and Outlooks. In Russian," Books, Gaidar Institute for Economic Policy, edition 1, volume 39, number re39-2017-ru, November.
    3. 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.
    4. 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.
    5. Nasuh Buyukkaramikli & J. Bertrand & Henny Ooijen, 2013. "Flexible hiring in a make to order system with parallel processing units," Annals of Operations Research, Springer, vol. 209(1), pages 159-178, October.
    6. 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.
    7. 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.
    8. Mohammad Delasay & Armann Ingolfsson & Bora Kolfal, 2016. "Modeling Load and Overwork Effects in Queueing Systems with Adaptive Service Rates," Operations Research, INFORMS, vol. 64(4), pages 867-885, August.
    9. 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.
    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. Barιş Ata & Deishin Lee & Erkut Sönmez, 2019. "Dynamic Volunteer Staffing in Multicrop Gleaning Operations," Operations Research, INFORMS, vol. 67(2), pages 295-314, March.
    12. 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.
    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. Robert J. Batt & Christian Terwiesch, 2017. "Early Task Initiation and Other Load-Adaptive Mechanisms in the Emergency Department," Management Science, INFORMS, vol. 63(11), pages 3531-3551, November.
    15. Saed Alizamir & Francis de Véricourt & Peng Sun, 2013. "Diagnostic Accuracy Under Congestion," Management Science, INFORMS, vol. 59(1), pages 157-171, December.
    16. S. D. Deshmukh & Suresh Jain, 1975. "Optimal Control of Service Quality in a Queueing System," Discussion Papers 176, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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