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