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 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.

DATE: 24 May, 2007, Thursday@ 10:00
PLACE: EA 502