The continuous increase in traffic organization refinement requirements is prompting signal control for pedestrian friendliness to receive more attention. Under signal control, pedestrian waiting tolerance time significantly affects signal performance. This study examines the effect of pedestrian crossing on vehicle operations during passing phases and proposes a signal control optimization method considering pedestrian crossing violations. This study establishes a crossing intention model based on pedestrian waiting tolerance time, calculates the number of crossing violations, proposes a method to calculate vehicle delays caused by crossing violations, and optimizes pedestrian crossing time allocation in the passing phase. A signal timing decision model considering pedestrian violations was established. The model includes vehicle delay signal optimization (VDSO), pedestrian violation-based signal optimization (PVSO), and coordinated pedestrian and vehicle signal optimization (CPVSO), with three submodels addressing different optimization objectives. These models were solved using the enhanced Fox optimization algorithm, with simulation experiments using real data. The results show that the CPVSO strategy reduces vehicle delays by 35% and pedestrian violations by 64% compared with traditional fixed signal timing. Sensitivity analysis for parameters, including pedestrian and vehicle flow, determined the main application ranges of the CPVSO, VDSO, and PVSO. This study reduces the probability of pedestrian violations during the red light period by optimizing combined pedestrian and vehicle phases while balancing vehicle passage efficiency, thereby decreasing pedestrian–vehicle collisions caused by violations.
Hu et al. (Sat,) studied this question.