EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, VOL.110, NO.1, PP.166-186, 1998.

TITLE: Iterative Methods Based on Splittings for Stochastic Automata 
Networks

AUTHORS: Ertugrul Uysal and Tugrul Dayar

ABSTRACT: This paper presents iterative methods based on splittings 
(Jacobi, Gauss-Seidel, Successive Over Relaxation) and their block versions 
for Stochastic Automata Networks (SANs). These methods prove to be better 
than the power method that has been used to solve SANs until recently. 
Through the help of three examples we show that the time it takes to solve 
a system modeled as a SAN is still substantial and it does not seem to be 
possible to solve systems with tens of millions of states on standard 
desktop workstations with the current state of technology. However, the 
SAN methodology enables one to solve much larger models than those could be 
solved by explicitly storing the global generator in the core of a target 
architecture especially if the generator is reasonably dense.

KEY WORDS: Markov processes; Stochastic automata networks; Tensor algebra;
Splittings; Block methods