Reducing the Series-Parallel Structure of the Normal Generalized Stochastic Petri Nets

This paper adopts a novel approach to reduction techniques of serial and parallel connection models in the normal generalized stochastic Petri net (NGSPN). The equivalent theorems of reducing the NGSPN's serial connection model is deduced. An availability method for reducing the parallel connection model is proposed and emulated. We also present an asymptotic formula for reducing the two parallel transitions connection model under independent and non-identically distributed cases. The proposed theorems and methods are especially useful in modeling and analyzing complex and large scale systems with Petri net.