ANNALS OF OPERATIONS RESEARCH, VOL.164, PP.193-210, 2008.

TITLE: Kronecker representation and decompositional analysis of 
closed queueing networks

AUTHORS: Tugrul Dayar and Akin Meric

ABSTRACT: Two approximative fixed-point iterative methods based on 
decomposition for closed queueing networks with Coxian service 
distributions and arbitrary buffer sizes are extended to include 
phase-type service distributions. The irreducible Markov chain 
associated with each subnetwork in the respective decompositions is
represented hierarchically using Kronecker products. The two methods 
are implemented in a software tool capable of computing the 
steady-state probability vector of each subnetwork by a multilevel 
method at each fixed-point iteration and are compared with other 
methods for accuracy and efficiency. Numerical results indicate that 
there is a niche filled by the two approximative methods.

KEY WORDS: Closed queueing network; phase-type service distribution; 
Kronecker representation; network decomposition; fixed-point 
iteration; multilevel method