Interpolation Approximations of Sojourn Time Distributions

Abstract

We present a method for approximating sojourn time distributions in open queueing systems based on light and heavy traffic limits. The method is consistent with and generalizes the interpolation approximations for moments previously presented by M. I. Reiman and B. Simon. The method is applicable to the class of systems for which both light and heavy traffic limits can be computed, which currently includes Markovian networks of priority queues with a unique bottleneck node. We illustrate the method of generating closed-form analytic approximations for the sojourn time distribution of the M/M/1 queue with Bernoulli feedback, the M/M/1 processor sharing queue, a priority queue with feedback and the M/Ek/1 queue. Empirical evidence suggests that the method works well on a large and identifiable class of priority queueing models.

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