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 generali zed stochastic Petri net or a stochastic automata network, has been studied for a while. In this paper we describe a Kronecker expression and associat ed data structures, that allows to handle nets with synchronization over ac tivities of different levels of priority. New algorithms for these structur es are provided to perform an iterative solution method of Jacobi or Gauss- Seidel type. These algorithms are implemented in the APNN Toolbox. We use t his implementation in combination with GreatSPN and exercise an example tha t illustrates characteristics of the presented algorithms. (C) 2001 Elsevie r Science B.V. All rights reserved.