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Understanding the Efficiency of Multi-Server Service Systems

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  • Ward Whitt

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

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    Abstract

    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.

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    File URL: http://dx.doi.org/10.1287/mnsc.38.5.708
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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 38 (1992)
    Issue (Month): 5 (May)
    Pages: 708-723

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    Handle: RePEc:inm:ormnsc:v:38:y:1992:i:5:p:708-723

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    Related research

    Keywords: queues; multi-server queues; service systems; utilization; economy of scale; approximations; probability of delay; peakedness; Hayward's approximation;

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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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).

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