A Generalized Influence Model for Networked Stochastic Automata

The joint dynamics of a collection or network of interacting discrete-time automata can often be described by a single Markov chain. In general, however, analyzing such a chain is computationally intractable for even moderately sized networks because of the explosion in the size of the state space. Asavathiratham introduced the influence model (IM) as a framework for overcoming such limitations. The IM imposes constraints on the update behavior of a network of automata, allowing efficient analysis while still permitting interesting global behavior. However, some of the constraints of the IM are unnecessarily restrictive. The generalized IM (GIM) presented here relaxes some restrictions of the IM, thereby permitting more complex behavior without losing many of the attractive properties of the IM and actually enabling simpler proofs of several results. The GIM is explained and illustrated in relation to the IM from a variety of different perspectives, including geometric. Several examples of GIMs are presented.