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Partitioning Customers into Service Groups

  • Ward Whitt

    (Room A117, AT&T Labs, Shannon Laboratory, 180 Park Avenue, Florham Park, New Jersey 07932-0971)

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    We explore the issues of when and how to partition arriving customers into service groups that will be served separately, in a first-come first-served manner, by multiserver service systems having a provision for waiting, and how to assign an appropriate number of servers to each group. We assume that customers can be classified upon arrival, so that different service groups can have different service-time distributions. We provide methodology for quantifying the tradeoff between economies of scale associated with larger systems and the benefit of having customers with shorter service times separated from other customers with longer service times, as is done in service systems with express lines. To properly quantify this tradeoff, it is important to characterize service-time distributions beyond their means. In particular, it is important to also determine the variance of the service-time distribution of each service group. Assuming Poisson arrival processes, we then can model the congestion experienced by each server group as an M/G/squeue with unlimited waiting room. We use previously developed approximations for M/G/sperformance measures to quickly evaluate alternative partitions.

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    File URL: http://dx.doi.org/10.1287/mnsc.45.11.1579
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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 45 (1999)
    Issue (Month): 11 (November)
    Pages: 1579-1592

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    Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1579-1592
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    1. Jimmie L. Davis & William A. Massey & Ward Whitt, 1995. "Sensitivity to the Service-Time Distribution in the Nonstationary Erlang Loss Model," Management Science, INFORMS, vol. 41(6), pages 1107-1116, June.
    2. Linda V. Green & Debashis Guha, 1995. "Note: On the Efficiency of Imbalance in Multi-Facility Multi-Server Service Systems," Management Science, INFORMS, vol. 41(1), pages 179-187, January.
    3. Ward Whitt, 1985. "The Best Order for Queues in Series," Management Science, INFORMS, vol. 31(4), pages 475-487, April.
    4. Seelen, L. P., 1986. "An algorithm for Ph/Ph/c queues," European Journal of Operational Research, Elsevier, vol. 23(1), pages 118-127, January.
    5. Otis B. Jennings & Avishai Mandelbaum & William A. Massey & Ward Whitt, 1996. "Server Staffing to Meet Time-Varying Demand," Management Science, INFORMS, vol. 42(10), pages 1383-1394, October.
    6. John A. Buzacott, 1996. "Commonalities in Reengineered Business Processes: Models and Issues," Management Science, INFORMS, vol. 42(5), pages 768-782, May.
    7. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
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