An Approximation for the Moments of Waiting Times

Abstract

Methods are available for computing properties of the waiting time associated with a variety of single-server queuing models in the equilibrium state. Since these calculations are more difficult in the time-dependent case, this paper develops an approximation procedure applicable to a wide class of single-server queues. Specifically, it considers the moments of the waiting time W n of the n th arriving customer of the system GI / G /1 and (given certain conditions) uses an expansion related to the central limit theorem to derive approximations to these moments. The expectation EW n is treated in some detail, particularly for the Erlang system E k / E m /1, and numerical illustrations are given. The same arguments apply to higher moments, but the calculations become tedious and details are not given.