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The Stochastic Automata Network (SAN in the following) methodology is in general associated to exact numerical analysis taking into account the tensor decomposition of the chain to improve matrix vector product. Here, we advocate a completely different approach: use the automata, their properties and the definition of tensor operations to derive structural properties of the chain and stochastic bounds to simplify the SAN. We focus on lumpability and stochastic bounds. Rather than a complete theory which remains to establish, we present a real example: the computation of the loss rate for a multistage ATM switch.

Discrete time stochastic automata networks: using structural properties and stochastic bounds to simplify the SAN