Enforcement of Time-Constrained GMECs on Time-Colored Petri Nets

This paper addresses the enforcement of a class of generalized mutual exclusion constraints (GMECs) within time constraints on time-colored Petri nets by adjusting the time restrictions of transitions with soft time intervals. Colored GMECs are defined to represent a set of markings that are determined by a subset of colors. Then, time constraints are imposed on the proposed colored GMECs to further refine the representation of state specifications in real-time systems. To enhance the modeling accuracy of real-world systems, we formally define time-colored Petri nets, based on which the extended GMECs are enforced. In this research, two types of time-constrained colored GMECs are proposed, with the main idea being to adjust the time boundaries of soft transitions, such that the system's specifications represented by time-constrained colored GMECs are satisfied. A structure called a parameterized modified state class graph is designed to describe the possible behaviors of the time-colored Petri net, where the time intervals of soft transitions are parameterized by variables. Based on the proposed graph, the enforcement of time-constrained colored GMECs is achieved by solving a linear programming problem.