IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v55y2007i4p753-768.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1070.0437
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1070.0437?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Emil Zavadlav & John O. McClain & L. Joseph Thomas, 1996. "Self-Buffering, Self-Balancing, Self-Flushing Production Lines," Management Science, INFORMS, vol. 42(8), pages 1151-1164, August.
    2. Avishai Mandelbaum & Alexander L. Stolyar, 2004. "Scheduling Flexible Servers with Convex Delay Costs: Heavy-Traffic Optimality of the Generalized cμ-Rule," Operations Research, INFORMS, vol. 52(6), pages 836-855, December.
    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. Sigrún Andradóttir & Hayriye Ayhan & Douglas G. Down, 2003. "Dynamic Server Allocation for Queueing Networks with Flexible Servers," Operations Research, INFORMS, vol. 51(6), pages 952-968, December.
    5. John J. Bartholdi & Donald D. Eisenstein, 1996. "A Production Line that Balances Itself," Operations Research, INFORMS, vol. 44(1), pages 21-34, February.
    6. Suri Gurumurthi & Saif Benjaafar, 2004. "Modeling and analysis of flexible queueing systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(5), pages 755-782, August.
    7. Wallace J. Hopp & Eylem Tekin & Mark P. Van Oyen, 2004. "Benefits of Skill Chaining in Serial Production Lines with Cross-Trained Workers," Management Science, INFORMS, vol. 50(1), pages 83-98, January.
    8. J. G. Dai & Wuqin Lin, 2005. "Maximum Pressure Policies in Stochastic Processing Networks," Operations Research, INFORMS, vol. 53(2), pages 197-218, April.
    9. William C. Jordan & Stephen C. Graves, 1995. "Principles on the Benefits of Manufacturing Process Flexibility," Management Science, INFORMS, vol. 41(4), pages 577-594, April.
    10. John J. Bartholdi & Donald D. Eisenstein & Robert D. Foley, 2001. "Performance of Bucket Brigades When Work Is Stochastic," Operations Research, INFORMS, vol. 49(5), pages 710-719, October.
    11. Sigman, Karl, 1990. "The stability of open queueing networks," Stochastic Processes and their Applications, Elsevier, vol. 35(1), pages 11-25, June.
    12. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Down, Douglas G. & Karakostas, George, 2008. "Maximizing throughput in queueing networks with limited flexibility," European Journal of Operational Research, Elsevier, vol. 187(1), pages 98-112, May.
    4. 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.
    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. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2016. "Optimal control of queueing systems with non-collaborating servers," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 79-110, October.
    7. 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.
    8. 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.
    9. Gregory Dobson & Tolga Tezcan & Vera Tilson, 2013. "Optimal Workflow Decisions for Investigators in Systems with Interruptions," Management Science, INFORMS, vol. 59(5), pages 1125-1141, May.
    10. Seyed M. Iravani & Mark P. Van Oyen & Katharine T. Sims, 2005. "Structural Flexibility: A New Perspective on the Design of Manufacturing and Service Operations," Management Science, INFORMS, vol. 51(2), pages 151-166, February.
    11. Yi‐Chun Tsai & Nilay Tanık Argon, 2008. "Dynamic server assignment policies for assembly‐type queues with flexible servers," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(3), pages 234-251, April.
    12. S.M.R. Iravani & J.A. Buzacott & M.J.M. Posner, 2005. "A robust policy for serial agile production systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 52(1), pages 58-73, February.
    13. Cong Shi & Yehua Wei & Yuan Zhong, 2019. "Process Flexibility for Multiperiod Production Systems," Operations Research, INFORMS, vol. 67(5), pages 1300-1320, September.
    14. Tuğçe Işık & Sigrún Andradóttir & Hayriye Ayhan, 2022. "Dynamic Control of Non‐Collaborative Workers When Reassignment Is Costly," Production and Operations Management, Production and Operations Management Society, vol. 31(3), pages 1332-1352, March.
    15. Nilay Tanık Argon & Sigrún Andradóttir, 2017. "Pooling in tandem queueing networks with non-collaborative servers," Queueing Systems: Theory and Applications, Springer, vol. 87(3), pages 345-377, December.
    16. 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.
    17. Achal Bassamboo & Ramandeep S. Randhawa & Jan A. Van Mieghem, 2012. "A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems," Operations Research, INFORMS, vol. 60(6), pages 1423-1435, December.
    18. 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.
    19. Wallace J. Hopp & Eylem Tekin & Mark P. Van Oyen, 2004. "Benefits of Skill Chaining in Serial Production Lines with Cross-Trained Workers," Management Science, INFORMS, vol. 50(1), pages 83-98, January.
    20. Timothy C. Y. Chan & Douglas Fearing, 2019. "Process Flexibility in Baseball: The Value of Positional Flexibility," Management Science, INFORMS, vol. 65(4), pages 1642-1666, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:oropre:v:55:y:2007:i:4:p:753-768. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.