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Individual versus Social Optimization in the Allocation of Customers to Alternative Servers

Author

Listed:
  • Colin E. Bell

    (University of Iowa)

  • Shaler Stidham, Jr.

    (North Carolina State University)

Abstract

Customers arrive at a service area according to a Poisson process. An arriving customer must choose one of K servers without observing present congestion levels. The only available information about the kth server is the service time distribution (with expected duration \mu k -1 ) and the cost per unit time of waiting at the kth server (h k ). Although service distributions may differ from server to server and need not be exponential, it is assumed that they share the same coefficient of variation. Individuals acting in self-interest induce an arrival rate pattern (\lambda \^ 1 , \lambda \^ 2 , ..., \lambda \^ k ). In contrast, the social optimum is the arrival rate pattern (\lambda 1 *, \lambda 2 *, ..., \lambda k *) which minimizes long-run average cost per unit time for the entire system. The main result is that \lambda \^ k 's and \lambda \^ k *'s differ systematically. Individuals overload the servers with the smallest h k /\mu k values. For an exponential service case with pre-emptive LIFO service an alternative charging scheme is presented which confirms that differences between individual and social optima occur precisely because individuals fail to consider the inconvenience that they cause to others.

Suggested Citation

  • Colin E. Bell & Shaler Stidham, Jr., 1983. "Individual versus Social Optimization in the Allocation of Customers to Alternative Servers," Management Science, INFORMS, vol. 29(7), pages 831-839, July.
  • Handle: RePEc:inm:ormnsc:v:29:y:1983:i:7:p:831-839
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    File URL: http://dx.doi.org/10.1287/mnsc.29.7.831
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    References listed on IDEAS

    as
    1. Ian I. Mitroff, 1972. "The Myth of Objectivity OR Why Science Needs a New Psychology of Science," Management Science, INFORMS, vol. 18(10), pages 613-618, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Michael Rubinovitch, 1983. "The Slow Server Problem," Discussion Papers 571, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. Mei Xue & Patrick T. Harker, 2003. "Service Co-Production, Customer Efficiency and Market Competition," Center for Financial Institutions Working Papers 03-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
    3. Gérard P. Cachon & Fuqiang Zhang, 2007. "Obtaining Fast Service in a Queueing System via Performance-Based Allocation of Demand," Management Science, INFORMS, pages 408-420.
    4. Knight, Vincent A. & Harper, Paul R., 2013. "Selfish routing in public services," European Journal of Operational Research, Elsevier, vol. 230(1), pages 122-132.
    5. Saif Benjaafar & Yanzhi Li & Dongsheng Xu & Samir Elhedhli, 2008. "Demand Allocation in Systems with Multiple Inventory Locations and Multiple Demand Sources," Manufacturing & Service Operations Management, INFORMS, pages 43-60.
    6. Brooks, James D. & Kar, Koushik & Mendonça, David J., 2016. "Allocation of flows in closed bipartite queueing networks," European Journal of Operational Research, Elsevier, vol. 255(2), pages 333-344.
    7. Ali K. Parlaktürk & Sunil Kumar, 2004. "Self-Interested Routing in Queueing Networks," Management Science, INFORMS, pages 949-966.
    8. Weng, Z. Kevin, 1996. "Manufacturing lead times, system utilization rates and lead-time-related demand," European Journal of Operational Research, Elsevier, vol. 89(2), pages 259-268, March.
    9. Xuanming Su & Stefanos Zenios, 2004. "Patient Choice in Kidney Allocation: The Role of the Queueing Discipline," Manufacturing & Service Operations Management, INFORMS, pages 280-301.
    10. Gérard P. Cachon & Martin A. Lariviere, 1999. "Capacity Choice and Allocation: Strategic Behavior and Supply Chain Performance," Management Science, INFORMS, pages 1091-1108.
    11. Grossman, Thomas A. & Brandeau, Margaret L., 2002. "Optimal pricing for service facilities with self-optimizing customers," European Journal of Operational Research, Elsevier, vol. 141(1), pages 39-57, August.
    12. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, pages 1314-1333.
    13. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
    14. George L. Vairaktarakis, 2013. "Noncooperative Games for Subcontracting Operations," Manufacturing & Service Operations Management, INFORMS, pages 148-158.
    15. Albert Y. Ha, 2001. "Optimal Pricing That Coordinates Queues with Customer-Chosen Service Requirements," Management Science, INFORMS, pages 915-930.
    16. repec:spr:queues:v:87:y:2017:i:3:d:10.1007_s11134-017-9547-9 is not listed on IDEAS
    17. Zhang, Zhongju & Daigle, John, 2012. "Analysis of job assignment with batch arrivals among heterogeneous servers," European Journal of Operational Research, Elsevier, vol. 217(1), pages 149-161.
    18. repec:pal:jorsoc:v:58:y:2007:i:9:d:10.1057_palgrave.jors.2602290 is not listed on IDEAS
    19. Ehud Kalai, 1990. "Optimal Service Speeds in a Competitive Environment," Discussion Papers 901, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    20. Elahi, Ehsan, 2013. "Outsourcing through competition: What is the best competition parameter?," International Journal of Production Economics, Elsevier, vol. 144(1), pages 370-382.
    21. Shone, Rob & Knight, Vincent A. & Williams, Janet E., 2013. "Comparisons between observable and unobservable M/M/1 queues with respect to optimal customer behavior," European Journal of Operational Research, Elsevier, vol. 227(1), pages 133-141.

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