Aggregation of stochastic automata networks with replicas

AbstractWe present techniques for computing the solution of large Markov chain models whose generators can be represented in the form of a generalized tensor algebra, such as Stochastic Automata Networks (SAN). Many large systems include a number of replications of identical components. This paper exploits replication by aggregating similar components. This leads to a state space reduction, based on lumpability. We define SAN with replicas, and we show how such SAN models can be strongly aggregated, taking functional rates into account. A tensor representation of the matrix of the aggregated Markov chain is proposed, allowing to store this chain in a compact manner and to handle larger models with replicas more efficiently. Examples and numerical results are presented to illustrate the reduction in state space and, consequently, the memory and processing time gains