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

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Author Info

  • Colin E. Bell

    (University of Iowa)

  • Shaler Stidham, Jr.

    (North Carolina State University)

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    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.29.7.831
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 29 (1983)
    Issue (Month): 7 (July)
    Pages: 831-839

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    Handle: RePEc:inm:ormnsc:v:29:y:1983:i:7:p:831-839

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    Related research

    Keywords: queueing; individual vs social optimization; joining behavior;

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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Parlakturk, Ali & Kumar, Sunil, 2004. "Self-Interested Routing in Queueing Networks," Research Papers 1782r, Stanford University, Graduate School of Business.
    8. Elahi, Ehsan, 2013. "Outsourcing through competition: What is the best competition parameter?," International Journal of Production Economics, Elsevier, vol. 144(1), pages 370-382.
    9. Ehud Kalai, 1990. "Optimal Service Speeds in a Competitive Environment," Discussion Papers 901, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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