A Generalization of L = λ W to Moments of Queue Length and Waiting Times

Shelby L. Brumelle
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Shelby L. Brumelle: University of British Columbia, Vancouver, B.C., Canada

Operations Research, 1972, vol. 20, issue 6, 1127-1136

Abstract: The well known formula L = λ W relates the time-average number in queue to the expected wait in queue of a customer. This paper specializes a more general formula, denoted by H = λ G , in order to obtain relations between moments of L and W other than the first. The basic queue considered is G / G / k with stationary input. The special case where the arrival times form a renewal process and the more special case where they are a Poisson process are also discussed.

Date: 1972
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