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

Abstract

The well known formula L = λW 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 = λG, 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.