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Understanding the Efficiency of Multi-Server Service Systems

  • Ward Whitt

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

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    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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    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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