Rational Automata Networks: A Non‐Markovian Modeling Approach

A new class of non‐Markovian models is introduced that results from the combination of stochastic automata networks and a very general class of stochastic processes, namely, rational arrival processes, which are derived from matrix exponential distributions. It is shown that the modeling formalism allows a compact representation of complex models with large state spaces. The resulting stochastic process is non‐Markovian, but it can be analyzed with numerical techniques like a Markov chain, and the results at the level of the automata are stochastic distributions that can be used to compute standard performance and dependability results. The model class includes stochastic automata networks with phase‐type distributed and correlated event times and also includes models that have a finite state space but cannot be represented by finite Markov chains. The paper introduces the model class, shows how the descriptor matrix can be represented in compact form, presents some example models, and outlines methods to analyze the new models.