Iterative Block Methods for Solving Stochastic Automata Network Models of a Computer Network Switch

this paper we compare different iterations methods to solve the underlying Markov chain based on Stochastic Automata Network. This comparison is based on a model of an ATM switch : the Leaky Bucket. We propose here an adaptation of the Gauss-Seidel iterative method on Stochastic Automata Networks (SAN). This methods is given with a threshold value that determines the diagonal block size. This method particularly suits to SAN since the tensor algebra used to construct the Markov chain of a SAN, gives naturally blocks. Thus, we can show the efficiency of modelisation using SAN combined with an appropriate iterative method, the Gauss-Seidel method may in our study divide by more than three the number of iteration compared with simple iteration method. In section 2 we give a short introduction on SAN. Section 3 presents the different iterative methods we use in sequel. In section 4, we present the Leaky Bucket modelisation using SAN. Finally, in section 5, we present the implementation and the results. 2 A notion of the stochastic automata networ