Numerical approximations for the steady‐state waiting times in a GI/G/1 queue

This paper focuses on easily computable numerical approximations for the distribution and moments of the steady‐state waiting times in a stable GI/G/1 queue. The approximation methodology is based on the theory of Fredholm integral equations and involves solving a linear system of equations. Numerical experimentation for various M/G/1 and GI/M/1 queues reveals that the methodology results in estimates for the mean and variance of waiting times within ±1% of the corresponding exact values. Comparisons with competing approaches establish that our methodology is not only more accurate, but also more amenable to obtaining waiting time approximations from the operational data. Approximations are also obtained for the distributions of steady‐state idle times and interdeparture times. The approximations presented in this paper are intended to be useful in rough‐cut analysis and design of manufacturing, telecommunications, and computer systems as well as in the verification of the accuracies of inequalities, bounds, and approximations.

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