Piecewise Approximation of Densities Applying the Principle of Maximum Entropy: Waiting Times in G/G/1-Systems

Abstract

Two methods are proposed for the calculation of the densities of the waiting times in G/G/1 queues. The densities are approximated by distributions with maximum entropy or minimum cross-entropy. Begining with a given distribution for the first job, the distributions for the succeeding jobs are computed until equilibrium is reached, thus not only obtaining a solution in case of equilibrium. Both methods determine the necessary moments by themselves, no other approximations are needed. Comparing sample results to exact values and other approximations, the accuracy of the methods is demonstrated. The first method is suited for systems with medium or high utilization. In the second method the real axis is partitioned suitably, and densities over the subsets are considered. This allows to control the accuracy.