Automating Mason´s rule and its application to analysis of stochastic Petri nets

A symbolic performance analysis approach for discrete-event systems can be formulated based on the integration of Petri nets and moment generating function concepts. The key steps in the method include modeling a system with stochastic Petri nets, generation of state machine Petri nets with transfer functions, derivation of equivalent transfer functions, and symbolic derivation of transfer functions to obtain the performance measures. To automate the above procedure, computer implementation of Mason´s rule becomes very important for a symbolic solution. This paper proposes and implements the algorithms to evaluate the Mason´s rule and describes their applications to deriving transfer functions of a state machine Petri net for system performance. The complexity of the algorithms is analyzed. Finally, future research toward construction of a CAD tool for design of discrete-event systems is discussed