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Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server

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  • Colin E. Bell

    (University of California, Irvine, California)

Abstract

This paper studies the optimal operation of an M / G /1 queuing system with removable server and the following cost structure: a holding cost per customer in the system per unit time, a cost per unit time of keeping the server running, and fixed charges for turning the server on or off. The server can be turned on at arrival epochs or off at service-completion epochs. The paper characterizes an optimal policy for the infinite-horizon discounted problem, offers an optimality proof, and presents a computational algorithm.

Suggested Citation

  • Colin E. Bell, 1971. "Characterization and Computation of Optimal Policies for Operating an M / G /1 Queuing System with Removable Server," Operations Research, INFORMS, vol. 19(1), pages 208-218, February.
    • Handle: RePEc:inm:oropre:v:19:y:1971:i:1:p:208-218
    DOI: 10.1287/opre.19.1.208
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    Cited by:

    1. K.-H. Wang & C.-C. Kuo & W. L. Pearn, 2007. "Optimal Control of an M/G/1/K Queueing System with Combined F Policy and Startup Time," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 285-299, November.
    2. Ke, Jau-Chuan & Wang, Kuo-Hsiung, 2002. "A recursive method for the N policy G/M/1 queueing system with finite capacity," European Journal of Operational Research, Elsevier, vol. 142(3), pages 577-594, November.
    3. Tirdad, Ali & Grassmann, Winfried K. & Tavakoli, Javad, 2016. "Optimal policies of M(t)/M/c/c queues with two different levels of servers," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1124-1130.
    4. Cigdem Gurgur, 2013. "Optimal configuration of a decentralized, market-driven production/inventory system," Annals of Operations Research, Springer, vol. 209(1), pages 139-157, October.
    5. Shaler Stidham, 2002. "Analysis, Design, and Control of Queueing Systems," Operations Research, INFORMS, vol. 50(1), pages 197-216, February.
    6. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
    7. Shaler Stidham, 2005. "On the optimality of a full-service policy for a queueing system with discounted costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 485-497, December.
    8. Tayfur Altiok & Goang An Shiue, 1995. "Single‐stage, multi‐product production/inventory systems with lost sales," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(6), pages 889-913, September.
    9. Wei Li & Attahiru Sule Alfa, 2000. "Optimal policies for M/M/m queue with two different kinds of (N, T)‐policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(3), pages 240-258, April.
    10. Jau-Chuan Ke, 2006. "An M/G/1 queue under hysteretic vacation policy with an early startup and un-reliable server," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(2), pages 357-369, May.
    11. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.
    12. Vasiliki Kostami, 2020. "Price and Lead time Disclosure Strategies in Inventory Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2760-2788, December.
    13. Niño-Mora, José, 2012. "Towards minimum loss job routing to parallel heterogeneous multiserver queues via index policies," European Journal of Operational Research, Elsevier, vol. 220(3), pages 705-715.
    14. R.E. Lillo, 2001. "Optimal control of an M/G/1 queue with impatient priority customers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(3), pages 201-209, April.

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