Analysis of Stochastic Automata Networks using copula functions

In this paper we develop a copula based approximation framework for scalable analysis of Stochastic Automata Networks (SAN) arising in reliability analysis, and can be described by CTMCs. Copulas provide a general approach to model joint distributions in terms of their marginals. Using copulas functions, the dependencies between the interacting automata in the SAN can be captured in terms of local state probabilities associated with the automata involved, avoiding the need of reachability analysis, which is cursed with state space explosion.We prove results related to invariance of copula with system parameters, and consistency of the approximation. We also outline an empirical procedure for determining copulas that can best represent the underlying dependence in a given SAN. We illustrate this approach through various examples of increasing complexity.