On the Use of Kronecker Operators for the Solution of Generalized Stochastic Petri Nets

We discuss how to describe the Markov chain underlying a generalized stochastic Petri net using Kronecker operators on smaller matrices. We extend previous approaches by allowing both an extensive type of marking-dependent behavior for the transitions and the presence of immediate synchronizations. The derivation of the results is thoroughly formalized, including the use of Kronecker operators in the treatment of the vanishing markings and the computation of impulse-based reward measures. We use our techniques to analyze a model whose solution using conventional methods would fail because of the state-space explosion. In the conclusion, we point out ideas to parallelize our approach. "This research was partially supported by the National Aeronautics and Spare Administration under NASA Contract No. NAS1-19480. tThis research was initiated during a visiting stay at the College of William and Mary. It was supported by the Japanese Ministry of Education, Science and Culture and the DAAD.