Understanding overtaking risk evolution patterns and their influencing factors based on trajectory data

Understanding the dynamic risk of overtaking behaviors is essential for improving highway safety and guiding adaptive driving strategies. This study develops a stage-based overtaking risk framework, capturing longitudinal and lateral risks across Lane-change, Overtaking, and Back-to-lane stages. A comprehensive risk indicator is constructed by weighting risk metrics at specific stages, and overtaking trajectories are aligned via Dynamic Time Warping for time-series clustering. Three typical risk evolution patterns are identified: hesitant, aggressive, and robust, accounting for 42.45%, 10.07%, and 47.48%, respectively. These risk evolution patterns reveal distinct temporal peaks of risk: hesitant drivers exhibit dual peaks at both lane changes; aggressive drivers face the highest risk during Overtaking stage; while robust drivers complete the overtaking task with the lowest overall risk. To explain the formation of these patterns, random parameters multinomial logit models with heterogeneity in means are estimated using macroscopic traffic-flow indicators. Results show that truck presence significantly increases the likelihood of hesitant trajectories, while higher standard deviation of upstream speed exhibits a significant positive association with aggressive behaviors. Furthermore, heterogeneity analysis reveals that under higher upstream speeds, drivers become more sensitive to downstream disturbances, amplifying failed overtaking. Compared with conventional multinomial logit model, the counter model with random parameters with heterogeneity in means shows a substantially better fit, highlighting the necessity of accounting for unobserved heterogeneity in traffic flow. This study contributes a data-driven paradigm that integrates interpretable risk metrics, time-series clustering, and discrete choice modeling, offering practical insights for adaptive risk management in automated driving.