Kronecker representation and decompositional analysis of closed queueing networks with phase-type service distributions and arbitrary buffer sizes

Abstract

This thesis extends two approximative fixed–point iterative methods based on decomposition for closed queueing networks (QNs) with Coxian service distributions and arbitrary buffer sizes from the literature to include phase–type service distributions. It shows how the irreducible Markov chain associated with each subnetwork in the decomposition can be represented hierarchically using Kronecker products. The proposed methods are implemented in a software tool, which is capable of computing the steady–state probability vector of each subnetwork by a multilevel method at each fixed–point iteration. The two methods are compared with others, one being the multilevel method for the closed QN itself, for accuracy and efficiency on a number of examples using the tool, and their convergence properties are discussed. Numerical results indicate that there is a niche among the problems considered which is filled by the two approximative fixed–point iterative methods.