Numerical Issues for Stochastic Automata Networks

In this paper we consider some numerical issues in computing solutions to networks of stochastic automata (SAN). In particular our concern is with keeping the amount of computation per iteration to a minimum, since iterative methods appear to be the most effective in determining numerical solutions. In a previous paper we presented complexity results concerning the vector-descriptor multiplication phase of the analysis. In this paper our concern is with implementation details. We experiment with the size and sparsity of individual automata; with the ordering of the automata; with the percentage and location of functional elements; with the occurrence of different types of synchronizing events and with the occurrence of cyclic dependencies within terms of the descriptor. We also consider the possible benefits of grouping many small automata in a SAN with many small automata to create an equivalent SAN having a smaller number of larger automata