Integrating synchronization with priority into a Kronecker representation

The compositional representation of a Markov chain using Kronecker algebra, according to a compositional model representation as a superposed generalized stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a Kronecker expression and associated data structures, that allows to handle nets with synchronization over activities of different levels of priority. New algorithms for these structures are provided to perform an iterative solution method of Jacobi or Gauss–Seidel type. These algorithms are implemented in the APNN Toolbox. We use this implementation in combination with GreatSPN and exercise an example that illustrates characteristics of the presented algorithms.