Iterative methods based on splittings for stochastic automata networks

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. With 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 could be solved by explicitly storing the global generator in the core of a target architecture especially if the generator is reasonably dense.