Understanding the Efficiency of Multi-Server Service Systems

Ward Whitt
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Ward Whitt: AT&T Bell Laboratories, Murray Hill, New Jersey 07974

Management Science, 1992, vol. 38, issue 5, 708-723

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.

Keywords: queues; multi-server queues; service systems; utilization; economy of scale; approximations; probability of delay; peakedness; Hayward's approximation (search for similar items in EconPapers)
Date: 1992
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