ABSTRACT
The need for including timing variables in the models of various types of dynamic systems is apparent since these systems are real-time in nature. Petri nets that contain timing variables are called timed Petri nets. A timed Petri net takes the same topological structure as its underlying Petri net model. In a place-timed Petri net, when a place gets a token, the token will not be available for its outgoing transitions until the time defined on the place has elapsed. In a regular Petri net, markings are the states of the system of interest, because from a marking one can decide the future behavior of the Petri net. A stochastic process is a collection of random variables indexed on some mathematical set. The index is often interpreted as time. The simplest class of stochastic timed Petri nets is stochastic Petri nets, in which every transition is associated with exponentially distributed firing time.
