Double DQN for Optimizing Safety by Minimizing Driver Uncertainty at Highway-Rail Crossings: A Dilemma Field Theory

Abstract

This article addresses the stop-go dilemma at four-quadrant gate (4QG) highway-rail crossings (HRCs) by introducing a novel reinforcement learning (RL) and Dilemma Field (DF) framework to minimize driver uncertainty. Conventional Type I and Type II dilemma-zone definitions rely on rigid spatial boundaries, risking over-protection or under-protection when driver behaviors deviate from assumed norms. In contrast, the proposed DF theory represents uncertainty as a continuous probability distribution, capturing the reality that vehicles beyond a nominal zone may remain partially confused while some within a zone might be decisive. A Markov chain stability theorem based on the Foster–Lyapunov criterion demonstrates that reducing the aggregate probability of uncertainty drives near-exponential convergence to safer, more stable traffic flow. To leverage these insights in real time, a Double Deep Q-Network (Double DQN) agent integrates the DF metric into its state and reward functions to adaptively optimize the warning signal activation at 4QG HRCs. Simulation results demonstrate that the proposed method raises minimum time-to-collision margins by 61% and reduces late-amber passing rates by 62% compared to constant-warning-time systems. These findings confirm that a probabilistic treatment of uncertainty, coupled with a learning-based control policy, yields substantially improved safety outcomes.