Accuracy of the Diffusion Approximation for Some Queuing Systems

Abstract

This paper presents the results of a rather extensive study of the accuracy of the diffusion approximation technique as applied to queuing models. The motive for using the diffusion process approximation here is to develop realistic analytical models of computing systems by considering service time distributions of a general form. We first review the theory of the diffusion approximation for a single server and then develop a new and simplified treatment of a queuing network system. The accuracy of this approximation method is then considered for a wide class of distributional forms of service and interarrival times and for various queuing models. The approximate solutions and exact (or simulation) solutions are compared numerically in terms of the means and variances of queue sizes, server utilizations, the asymptotic decrements of the distributions, and the queue size distributions themselves. The accuracy of the diffusion approximation is found to be quite adequate in most cases and is considerably higher than that obtained by an exponential server model that is prevalent in computer system modeling.

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