Time characteristic analytical method of Petri nets

In order to make further research in stochastic petri Net,some concepts of time petri nets are introduced,which are close net,frequent return net,loop-net,nonloop-net.It is proved that when stochastic petri net is time characteristic net,its sufficiency and necessary condition is that its close net is frequent return net.A numerical method is gived to distinguish that a Petri net is a time charac-teristic nets or not.The time characteristics of transmit are discussed and the density formula of transmit is given.