In: Systems Analysis Modelling Simulation, pages Vol 38, pages 95-128. 2000.
Abstract: In this paper, a simplification method of Controlled Stochastic Petri Nets (CSPN) is introduced. This method uses the technique of the singular perturbations and is in the field of model reduction. This contribution is related only to bounded Controlled Stochastic Petri Nets which are subjacent with Decision Markov Process. The method of simplification breaks down the initial Petri Net into two subsystems whose state probability evolutions are slow or fast. The study of the CSPN are carried out on two subsystems with reduced dimensions. This reduction facilitates the calculation of the performance of the system as well as the study of the optimal control. This method is then applied to the study of a manufacturing system, based on a repair cycle of machine tools.
Keywords: Controlled Stochastic Petri Net, Decision Markov Process, Model Reduction, Singular Perturbations.