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Compensating for Failures with Flexible 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, Canada L8S 4L7)

Abstract

We consider the problem of maximizing capacity in a queueing network with flexible servers, where the classes and servers are subject to failure. We assume that the interarrival and service times are independent and identically distributed, that routing is probabilistic, and that the failure state of the system can be described by a Markov process that is independent of the other system dynamics. We find that the maximal capacity is tightly bounded by the solution of a linear programming problem and that the solution of this problem can be used to construct timed, generalized round-robin policies that approach the maximal capacity arbitrarily closely. We then give a series of structural results for our policies, including identifying when server flexibility can completely compensate for failures and when the implementation of our policies can be simplified. We conclude with a numerical example that illustrates some of the developed insights.

Suggested Citation

  • Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2007. "Compensating for Failures with Flexible Servers," Operations Research, INFORMS, vol. 55(4), pages 753-768, August.
    • Handle: RePEc:inm:oropre:v:55:y:2007:i:4:p:753-768
    DOI: 10.1287/opre.1070.0437
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    References listed on IDEAS

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    Cited by:

    1. Kilinc, Derya & Saghafian, Soroush & Traub, Stephen, 2016. "Dynamic Assignment of Patients to Primary and Secondary Inpatient Units: Is Patience a Virtue?," Working Paper Series rwp17-010, Harvard University, John F. Kennedy School of Government.
    2. 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.
    3. Abualkhair, Hussain & Lodree, Emmett J. & Davis, Lauren B., 2020. "Managing volunteer convergence at disaster relief centers," International Journal of Production Economics, Elsevier, vol. 220(C).
    4. Cong Shi & Yehua Wei & Yuan Zhong, 2019. "Process Flexibility for Multiperiod Production Systems," Operations Research, INFORMS, vol. 67(5), pages 1300-1320, September.
    5. Yun Fong Lim & Bingnan Lu & Rowan Wang & Wenjia Zhang, 2020. "Flexibly Serving A Finite Number of Heterogeneous Jobs in A Tandem System," Production and Operations Management, Production and Operations Management Society, vol. 29(6), pages 1431-1447, June.
    6. Peng Wang & Kai Pan & Zhenzhen Yan & Yun Fong Lim, 2022. "Managing Stochastic Bucket Brigades on Discrete Work Stations," Production and Operations Management, Production and Operations Management Society, vol. 31(1), pages 358-373, January.
    7. Schneider, Michael & Grahl, Jörn & Francas, David & Vigo, Daniele, 2013. "A problem-adjusted genetic algorithm for flexibility design," International Journal of Production Economics, Elsevier, vol. 141(1), pages 56-65.
    8. Eser Kırkızlar & Sigrún Andradóttir & Hayriye Ayhan, 2010. "Robustness of efficient server assignment policies to service time distributions in finite‐buffered lines," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 563-582, September.
    9. Paret, Kyle E. & Mayorga, Maria E. & Lodree, Emmett J., 2021. "Assigning spontaneous volunteers to relief efforts under uncertainty in task demand and volunteer availability," Omega, Elsevier, vol. 99(C).
    10. 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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