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

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  • Shelby L. Brumelle

    (University of British Columbia, Vancouver, B.C., Canada)

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.

Suggested Citation

  • Shelby L. Brumelle, 1972. "A Generalization of L = λ W to Moments of Queue Length and Waiting Times," Operations Research, INFORMS, vol. 20(6), pages 1127-1136, December.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:6:p:1127-1136
    DOI: 10.1287/opre.20.6.1127
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    Cited by:

    1. Zazanis, Michael A, 1998. "A Palm calculus approach to functional versions of Little's law," Stochastic Processes and their Applications, Elsevier, vol. 74(2), pages 195-201, June.

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