Performance evaluation of colored Petri net models using simulation and moment generating functions

This paper formulates a methodology to evaluate the performance of various stochastic Petri net models including colored stochastic Petri net models. The results include an example of the performance evaluation of a stochastic Petri net. This formulation utilizes simulation to generate an approximation of the reachability graph of a Petri net, then applies moment generating function analysis to this approximate reachability graph. The approximation of the reachability graph is constructed from paths taken by a simulator as it executes the Petri net. This partial reachability graph is then combined with the firing rates of the original Petri net to form a state machine Petri net which can then be analyzed via moment generating functions. This analysis involves computing a system transfer function for the time elapsed between two specified markings of the state machine. This paper demonstrates by a small example the ability to identify a transfer function that approximates the behavior of a system represented by a Petri net.