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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)


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.

Suggested Citation

  • Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
  • Handle: RePEc:inm:ormnsc:v:45:y:1999:i:11:p:1579-1592

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    References listed on IDEAS

    1. 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.
    2. Ward Whitt, 1985. "The Best Order for Queues in Series," Management Science, INFORMS, vol. 31(4), pages 475-487, April.
    3. 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.
    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. 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.
    6. Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
    7. John A. Buzacott, 1996. "Commonalities in Reengineered Business Processes: Models and Issues," Management Science, INFORMS, vol. 42(5), pages 768-782, May.
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    Cited by:

    1. Jeff Hong, L. & Xu, Xiaowei & Zhang, Sheng Hao, 2015. "Capacity reservation for time-sensitive service providers: An application in seaport management," European Journal of Operational Research, Elsevier, vol. 245(2), pages 470-479.
    2. Bin Hu & Saif Benjaafar, 2009. "Partitioning of Servers in Queueing Systems During Rush Hour," Manufacturing & Service Operations Management, INFORMS, vol. 11(3), pages 416-428, October.
    3. Noah Gans & Yong-Pin Zhou, 2007. "Call-Routing Schemes for Call-Center Outsourcing," Manufacturing & Service Operations Management, INFORMS, vol. 9(1), pages 33-50, May.
    4. van Dijk, Nico & van der Sluis, Erik, 2009. "Pooling is not the answer," European Journal of Operational Research, Elsevier, vol. 197(1), pages 415-421, August.
    5. repec:nax:conyad:v:62:y:2017:i:3:p:733-745 is not listed on IDEAS
    6. repec:eee:ejores:v:262:y:2017:i:2:p:602-619 is not listed on IDEAS
    7. Ananth V. Iyer & Apurva Jain, 2004. "Modeling the Impact of Merging Capacity in Production-Inventory Systems," Management Science, INFORMS, vol. 50(8), pages 1082-1094, August.
    8. repec:pal:jorsoc:v:57:y:2006:i:11:d:10.1057_palgrave.jors.2602100 is not listed on IDEAS
    9. Oualid Jouini & Yves Dallery & Rabie Nait-Abdallah, 2008. "Analysis of the Impact of Team-Based Organizations in Call Center Management," Management Science, INFORMS, vol. 54(2), pages 400-414, February.
    10. repec:nax:conyad:v:62:y:2017:i:3:p:719-732 is not listed on IDEAS
    11. Muhammad El-Taha & Bacel Maddah, 2006. "Allocation of Service Time in a Multiserver System," Management Science, INFORMS, vol. 52(4), pages 623-637, April.


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