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