Optimization of Differentiated Pricing Strategies for Freeways Considering Vehicle Collision Probability

In response to the limitations of the conventional fixed-rate pricing model for freeways in addressing spatiotemporal imbalances in traffic flow distribution and low road network resource utilization, as well as the neglect of Vehicle Collision probability in existing differentiated pricing frameworks, this study analyzes the underlying relationship between road traffic saturation and collision probability. On this basis, a bi-level programming model for differentiated freeway pricing that explicitly accounts for Vehicle Collision probability is developed. The upper-level model maximizes the economic benefit of freeway operations while incorporating vehicle-collision-probability-related costs, whereas the lower-level model minimizes vehicle travel impedance, including both travel cost and time delays induced by collisions. A hybrid algorithm combining particle swarm optimization (PSO) and pattern search (PS) is employed to solve the optimal pricing scheme across different vehicle types (passenger cars and trucks), road segments, and time periods. A nested Logit model is introduced to characterize travelers’ route choice behavior between alternative routes, thereby capturing the traffic redistribution effect induced by pricing rate adjustments. Empirical data from a section of the Shenyang–Haikou Freeway corridor in China for the year 2024 are used for model calibration and validation. The results indicate that following the optimized pricing scheme, the freeway’s monthly net revenue increased by 9.44%, truck and passenger car traffic volumes rose by 8.59% and 6.12%, respectively, and total segment traffic volume increased by 7.18%. The saturation of the freeway increased from approximately 0.18 to about 0.32, while that of the parallel arterial decreased from approximately 0.9 to about 0.67, indicating a more balanced traffic flow distribution across the network and a substantial reduction in Vehicle Collision probability. These findings demonstrate that the proposed method can effectively balance the trade-offs among operational revenue, traffic efficiency, and driving safety, providing both theoretical support and a quantitative tool for the scientific formulation of differentiated freeway pricing schemes.