A new iterative numerical solution algorithm for a class of stochastic Petri Nets

Abstract

In the area of the numerical analysis of stochastic Petri Nets we present an algorithm which enables the reduction of storage requirements for generator matrices of the underlying Markov chain. We show that neither the generator matrix nor “parts” of them need be generated and stored. The solvable model class contains the superposed stochastic automatas defined by Donatelli [2] as a special case. The state spaces of the underlying Markov chains in the examples range from about 107 up to 108 states with up to 109 matrix entries and we show that for such models a solution is possible. Further, this algorithm can be easily integrated in tools which contain iterative numerical solution techniques.KeywordsGenerator MatrixMatrix EntryProcedure CallColumn IndexInput PlaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.