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TECHNICAL NOTE---Queueing Systems with Synergistic Servers

Author

Listed:
  • Sigrún Andradóttir

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Hayriye Ayhan

    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

  • Douglas G. Down

    (Department of Computing and Software, McMaster University, Hamilton, Ontario L8S 4L7, Canada)

Abstract

We consider tandem lines with finite buffers and flexible, heterogeneous servers that are synergistic in that they work more effectively in teams than on their own. Our objective is to determine how the servers should be assigned dynamically to tasks in order to maximize the long-run average throughput. In particular, we investigate when it is better to take advantage of synergy among servers, rather than exploiting the servers' special skills, to achieve the best possible system throughput. We show that when there is no trade-off between server synergy and servers' special skills (because the servers are generalists who are equally skilled at all tasks), the optimal policy has servers working in teams of two or more at all times. Moreover, for Markovian systems with two stations and two servers, we provide a complete characterization of the optimal policy and show that, depending on how well the servers work together, the optimal policy either takes full advantage of servers' special skills, or full advantage of server synergy (and hence there is no middle ground in this case). Finally, for a class of larger Markovian systems, we provide sufficient conditions that guarantee that the optimal policy should take full advantage of server synergy at all times.

Suggested Citation

  • Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2011. "TECHNICAL NOTE---Queueing Systems with Synergistic Servers," Operations Research, INFORMS, vol. 59(3), pages 772-780, June.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:3:p:772-780
    DOI: 10.1287/opre.1110.0934
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    References listed on IDEAS

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    1. Sennott, Linn I. & Van Oyen, Mark P. & Iravani, Seyed M.R., 2006. "Optimal dynamic assignment of a flexible worker on an open production line with specialists," European Journal of Operational Research, Elsevier, vol. 170(2), pages 541-566, April.
    2. 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.
    3. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    4. 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.
    5. John A. Buzacott, 1996. "Commonalities in Reengineered Business Processes: Models and Issues," Management Science, INFORMS, vol. 42(5), pages 768-782, May.
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    Cited by:

    1. Emmett J. Lodree & Nezih Altay & Robert A. Cook, 2019. "Staff assignment policies for a mass casualty event queuing network," Annals of Operations Research, Springer, vol. 283(1), pages 411-442, December.
    2. Hyun-Soo Ahn & Mark E. Lewis, 2013. "Flexible Server Allocation and Customer Routing Policies for Two Parallel Queues When Service Rates Are Not Additive," Operations Research, INFORMS, vol. 61(2), pages 344-358, April.
    3. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2022. "Synchronous resource allocation: modeling, capacity, and optimization," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(4), pages 1287-1310, December.

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