A Generalization ofL= λWto Moments of Queue Length and Waiting Times

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.