Decomposition methods for finite queue networks with a non-renewal arrival process in discrete time

Abstract

The purpose of this thesis is to develop a decomposition method for obtaining the queue length distributions of open, tandem and split queue networks with Markovian arrival processes, and finite intermediate queues. Equivalent geometric systems are also studied to determine if maintaining the relationship between the decomposed queues improves the results over existing methods. This thesis contains an introduction, conclusion and three main sections: a literature review; a section outlining the exact and decomposition procedures for the tandem networks; and a section outlining the exact and decomposition procedures for the split networks. Neuts' (46) Matrix Geometric Method is adopted to provide exact results which are used to validate the approximate results. It can be concluded that for tandem and split systems with Markovian arrival processes the decomposition method developed in this thesis is superior to existing methods which fail to represent the dependence between the isolated queues. The opposite is true for both configurations of the geometric systems. That is, existing methods which do not maintain the dependence in their decomposition approach produce equal or superior results. Therefore, it can be concluded that utilizing the approximation method which captures the relationship between the queues is not worth the extra effort for geometric systems.