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Optimal control of noncollaborative servers in two‐stage tandem queueing systems

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  • Dimitrios G. Pandelis

Abstract

We consider two‐stage tandem queueing systems with dedicated servers in each station and a flexible server that is trained to serve both stations. We assume no arrivals, exponential service times, and linear holding costs for jobs present in the system. We study the optimal dynamic assignment of servers to jobs assuming a noncollaborative work discipline with idling and preemptions allowed. For larger holding costs in the first station, we show that (i) nonidling policies are optimal and (ii) if the flexible server is not faster than the dedicated servers, the optimal server allocation strategy has a threshold‐type structure. For all other cases, we provide numerical results that support the optimality of threshold‐type policies. Our numerical experiments also indicate that when the flexible server is faster than the dedicated server of the second station, the optimal policy may have counterintuitive properties, which is not the case when a collaborative service discipline is assumed. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 435–446, 2014

Suggested Citation

  • Dimitrios G. Pandelis, 2014. "Optimal control of noncollaborative servers in two‐stage tandem queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(6), pages 435-446, September.
    • Handle: RePEc:wly:navres:v:61:y:2014:i:6:p:435-446
    DOI: 10.1002/nav.21594
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    References listed on IDEAS

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    1. Ramesh Arumugam & Maria Mayorga & Kevin Taaffe, 2009. "Inventory based allocation policies for flexible servers in serial systems," Annals of Operations Research, Springer, vol. 172(1), pages 1-23, November.
    2. Hoda Parvin & Mark Van Oyen & Dimitrios Pandelis & Damon Williams & Junghee Lee, 2012. "Fixed task zone chaining: worker coordination and zone design for inexpensive cross-training in serial CONWIP lines," IISE Transactions, Taylor & Francis Journals, vol. 44(10), pages 894-914.
    3. Sigrún Andradóttir & Hayriye Ayhan, 2005. "Throughput Maximization for Tandem Lines with Two Stations and Flexible Servers," Operations Research, INFORMS, vol. 53(3), pages 516-531, June.
    4. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2012. "Flexible Servers in Understaffed Tandem Lines," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 761-777, July.
    5. Dimitrios Pandelis, 2007. "Optimal use of excess capacity in two interconnected queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 179-192, February.
    6. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2001. "Server Assignment Policies for Maximizing the Steady-State Throughput of Finite Queueing Systems," Management Science, INFORMS, vol. 47(10), pages 1421-1439, October.
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