Dead Transitions Analysis and Resolution in Dual-Time Petri Nets

This paper investigates the impact of static temporal parameters on the behavior of timed discrete event systems modeled using dual-time Petri nets. In such models, the firing of transitions is essential to ensure correct system evolution. However, improperly configured temporal constraints may result in dead transitions, where certain transitions are prevented from firing despite being enabled with respect to markings, thereby disrupting expected system behavior. To address this issue, we analyze the conditions under which dead transitions occur due to invalid temporal functions within the net structure. Based on this analysis, a set of adjustment options is introduced to resolve a dead transition, designed to restore an invalid firing window by modifying temporal parameters. Furthermore, we propose a cost-based adjustment strategy that iteratively derives a valid temporal function, ensuring the absence of dead transitions in the revised system. At each iteration, the strategy selects the adjustment option with the lowest associated cost to resolve a specific dead transition. To validate the effectiveness of the proposed approach, an extended state class graph is employed as a structural representation of D-TPN evolution, enabling verification of the resolution of dead transitions under each revised temporal function.