Analysis of stochastic Petri nets by the method of supplementary variables

Abstract

This paper presents a unified numerical solution framework for stochastic Petri nets in which transition firing is immediate, exponentially distributed, or generally distributed. The proposed solution approach is based on the method of supplementary variables and extends the class of nets for which a numerical analysis is possible. Deterministic and Stochastic Petri Nets (DSPN) are taken as the basic modeling formalism which is extended by other non-exponential firing times and concurrently enabled deterministic transition firings. Under the assumption that the non-exponential distributions belong to the class of polynomial distributions, computational formulas for numerically solving the state equations are given. In case of concurrently enabled deterministic transitions the solution approach yields a system of partial differential equations which we propose to solve numerically by discretization.