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Understanding the Efficiency of Multi-Server Service Systems


  • Ward Whitt

    (AT&T Bell Laboratories, Murray Hill, New Jersey 07974)


In the design and operation of service systems, it is important to determine an appropriate level of server utilization (the proportion of time each server should be working). In a multi-server queue with unlimited waiting space, the appropriate server utilization typically increases as the number of servers (and the arrival rate) increases. We explain this economy of scale and give a rough quantitative characterization. We also show how increased variability in the arrival and service processes tends to reduce server utilization with a given grade of service. As part of this analysis, we develop simple approximations for the mean steady-state waiting time and the full steady-state waiting-time distribution. These approximations exploit an infinite-server approximation for the probability of delay and a single-server approximation for the conditional waiting-time distribution given that waiting occurs. The emphasis is on simple formulas that directly convey understanding.

Suggested Citation

  • Ward Whitt, 1992. "Understanding the Efficiency of Multi-Server Service Systems," Management Science, INFORMS, vol. 38(5), pages 708-723, May.
  • Handle: RePEc:inm:ormnsc:v:38:y:1992:i:5:p:708-723

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    References listed on IDEAS

    1. Leech, Dennis, 1985. "Ownership Concentration and the Theory of the Firm : A Simple-Game-Theoretic Approach to Applied US Corporations in the 1930's," The Warwick Economics Research Paper Series (TWERPS) 262, University of Warwick, Department of Economics.
    2. Guillermo Owen, 1972. "Multilinear Extensions of Games," Management Science, INFORMS, vol. 18(5-Part-2), pages 64-79, January.
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    Cited by:

    1. 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.
    2. Venkateshan, Prahalad & Mathur, Kamlesh & Ballou, Ronald H., 2010. "Locating and staffing service centers under service level constraints," European Journal of Operational Research, Elsevier, vol. 201(1), pages 55-70, February.
    3. Zohar Feldman & Avishai Mandelbaum & William A. Massey & Ward Whitt, 2008. "Staffing of Time-Varying Queues to Achieve Time-Stable Performance," Management Science, INFORMS, vol. 54(2), pages 324-338, February.
    4. Izady, Navid & Worthington, Dave, 2012. "Setting staffing requirements for time dependent queueing networks: The case of accident and emergency departments," European Journal of Operational Research, Elsevier, vol. 219(3), pages 531-540.
    5. Josh Reed & Bo Zhang, 0. "Managing capacity and inventory jointly for multi-server make-to-stock queues," Queueing Systems: Theory and Applications, Springer, vol. 0, pages 1-34.
    6. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    7. Marcos Singer & Patricio Donoso & Natalia Jadue, 2004. "Evaluacion De Las Oportunidades De Mejoramiento De La Logistica Directa De Emergencia," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 7(2), pages 179-209.
    8. Defraeye, Mieke & Van Nieuwenhuyse, Inneke, 2016. "Staffing and scheduling under nonstationary demand for service: A literature review," Omega, Elsevier, vol. 58(C), pages 4-25.
    9. O. Garnet & A. Mandelbaum & M. Reiman, 2002. "Designing a Call Center with Impatient Customers," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 208-227, October.
    10. repec:kap:hcarem:v:20:y:2017:i:4:d:10.1007_s10729-016-9364-4 is not listed on IDEAS
    11. Guodong Pang & Ward Whitt, 2009. "Service Interruptions in Large-Scale Service Systems," Management Science, INFORMS, vol. 55(9), pages 1499-1512, September.
    12. Constantinos Maglaras & Assaf Zeevi, 2003. "Pricing and Capacity Sizing for Systems with Shared Resources: Approximate Solutions and Scaling Relations," Management Science, INFORMS, vol. 49(8), pages 1018-1038, August.
    13. Morton, Alec & Bevan, Gwyn, 2008. "What's in a wait: Contrasting management science and economic perspectives on waiting for emergency care," Health Policy, Elsevier, vol. 85(2), pages 207-217, February.
    14. Müller-Clostermann, Bruno, 2007. "Using G/G/m-models for multi-server and mainframe capacity planning," ICB Research Reports 16, University Duisburg-Essen, Institute for Computer Science and Business Information Systems (ICB).
    15. Benjaafar, Saifallah, 1995. "Performance bounds for the effectiveness of pooling in multi-processing systems," European Journal of Operational Research, Elsevier, vol. 87(2), pages 375-388, December.
    16. Ward Whitt, 1999. "Partitioning Customers into Service Groups," Management Science, INFORMS, vol. 45(11), pages 1579-1592, November.
    17. repec:spr:queues:v:86:y:2017:i:1:d:10.1007_s11134-017-9519-0 is not listed on IDEAS
    18. Marcos Singer & Patricio Donoso & Alan Scheller-Wolf, 2008. "Una Introducción A La Teoría De Colas Aplicada A La Gestión De Servicios," Abante, Escuela de Administracion. Pontificia Universidad Católica de Chile., vol. 11(2), pages 93-120.
    19. René Bekker & Paulien Koeleman, 2011. "Scheduling admissions and reducing variability in bed demand," Health Care Management Science, Springer, vol. 14(3), pages 237-249, September.
    20. Karin Eeden & Dennis Moeke & René Bekker, 2016. "Care on demand in nursing homes: a queueing theoretic approach," Health Care Management Science, Springer, vol. 19(3), pages 227-240, September.
    21. Rodney B. Wallace & Ward Whitt, 2005. "A Staffing Algorithm for Call Centers with Skill-Based Routing," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 276-294, August.
    22. Komonen, Kari, 2002. "A cost model of industrial maintenance for profitability analysis and benchmarking," International Journal of Production Economics, Elsevier, vol. 79(1), pages 15-31, September.


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