Modeling and simulation of two-dimensional vehicle interactions at unsignalized intersections using a deep discrete grid-based framework

This paper presents a novel two-dimensional traffic simulation framework for unsignalized intersections, where traditional lane-based models fail to capture complex vehicle interactions and right-of-way competition. We develop a deep discrete grid-based approach with an integrated prediction-decision-planning behavior model that addresses these fundamental limitations. Our methodological contributions include: (1) a high-fidelity two-dimensional grid network with optimized precision parameters enabling precise spatial representation of traffic elements; (2) an interaction topology framework incorporating multinomial logistic regression and priority transitivity pruning, reducing computational complexity from O(n!) to O((n/2)!) for multi-agent interactions; and (3) a hierarchical trajectory optimization method combining improved A* algorithms with cubic polynomial interpolation to satisfy vehicle kinematic constraints in discrete environments. Validation against the inD dataset demonstrates superior performance, achieving 96.49% trajectory spatial coverage compared to VISSIM’s 13.50%, with no statistically significant differences from measured data in safety indicators (PET: p=0.068) and travel time distributions (p=0.185), both p>0.05 at 95% confidence level. The proposed method provides a high-precision analytical tool for intersection safety evaluation and traffic organization optimization.