Hybrid state analysis method in stochastic Petri nets

The authors consider the analysis of stochastic Petri net models with generally distributed transition firing times. A so-called hybrid state analysis method is developed. The basic idea is to make the extended state, i.e., the hybrid state, which is composed of a marking and the enabling times of enabled transitions under the marking, propagate as a Markov process by the inclusion of supplementary variables. The recursive equation of hybrid state density functions is given