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Partitioning Customers into Service Groups

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  • Ward Whitt

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

Abstract

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
    DOI: 10.1287/mnsc.45.11.1579
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    References listed on IDEAS

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    Cited by:

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    4. Thomas J. Best & Burhaneddin Sandıkçı & Donald D. Eisenstein & David O. Meltzer, 2015. "Managing Hospital Inpatient Bed Capacity Through Partitioning Care into Focused Wings," Manufacturing & Service Operations Management, INFORMS, vol. 17(2), pages 157-176, May.
    5. 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.
    6. Lien Wang & Erik Demeulemeester & Nancy Vansteenkiste & Frank E. Rademakers, 2022. "On the use of partitioning for scheduling of surgeries in the inpatient surgical department," Health Care Management Science, Springer, vol. 25(4), pages 526-550, December.
    7. Gustavo Ramiro Rodríguez Jáuregui & Ana Karen González Pérez & Salvador Hernández González & Manuel Darío Hernández Ripalda, 2017. "Analysis of the emergency service applying the queueing theory," Contaduría y Administración, Accounting and Management, vol. 62(3), pages 733-745, Julio-Sep.
    8. Maddah, Bacel & Nasr, Walid W. & Charanek, Ali, 2017. "A multi-station system for reducing congestion in high-variability queues," European Journal of Operational Research, Elsevier, vol. 262(2), pages 602-619.
    9. Yanting Chen & Jingui Xie & Taozeng Zhu, 2023. "Overflow in systems with two servers: the negative consequences," Flexible Services and Manufacturing Journal, Springer, vol. 35(3), pages 838-863, September.
    10. Paul Joustra & Erik Sluis & Nico Dijk, 2010. "To pool or not to pool in hospitals: a theoretical and practical comparison for a radiotherapy outpatient department," Annals of Operations Research, Springer, vol. 178(1), pages 77-89, July.
    11. 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.
    12. J Ou & M Parlar & M Sharafali, 2006. "A differentiated service scheme to optimize website revenues," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(11), pages 1323-1340, November.
    13. 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.
    14. 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.
    15. 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.
    16. Jingqi Wang & Yong-Pin Zhou, 2018. "Impact of Queue Configuration on Service Time: Evidence from a Supermarket," Management Science, INFORMS, vol. 64(7), pages 3055-3075, July.
    17. 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.
    18. Gustavo Ramiro Rodríguez Jáuregui & Ana Karen González Pérez & Salvador Hernández González & Manuel Darío Hernández Ripalda, 2017. "Análisis del servicio de Urgencias aplicando teoría de líneas de espera," Contaduría y Administración, Accounting and Management, vol. 62(3), pages 719-732, Julio-Sep.
    19. Soroush Saghafian & Wallace J. Hopp & Mark P. Van Oyen & Jeffrey S. Desmond & Steven L. Kronick, 2012. "Patient Streaming as a Mechanism for Improving Responsiveness in Emergency Departments," Operations Research, INFORMS, vol. 60(5), pages 1080-1097, October.
    20. 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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