Timed State Graphs for Scheduling a Class of Place-Timed Petri Nets

In this paper, to solve the scheduling problem of discrete event systems modeled by Place-timed Petri nets, a timed state graph with time information is designed to abstract the state space of Place-timed Petri nets. The feasible firing transitions sequence with the minimal duration is kept in the timed state graph. Furthermore, a modified timed state space is further designed with smaller size than the timed state graph, and it also keeps the feasible firing transitions sequence with the minimal duration. By searching these timed state graphs, we can find the optimal solution, i.e., the feasible firing transitions sequence with minimal duration directly.