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The WKB Approximation to the G/M/m Queue

Charles Knessl
SIAM Journal on Applied Mathematics
Vol. 51, No. 4 (Aug., 1991), pp. 1119-1133
Stable URL: http://www.jstor.org/stable/2101836
Page Count: 15
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The WKB Approximation to the G/M/m Queue
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Abstract

G/M/m queues with a large number of servers (m ≫ 1) and an interarrival time density that is sharply peaked near the origin, i.e., typical interarrival times are short, of the order O(1/m), are considered. Using the WKB method, asymptotic approximations to the stationary queue length distribution for m ≫ 1 are constructed. Some numerical comparisons illustrate the quality of the approximations.

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