Integrating survival analysis and machine learning for modeling overtaking duration on rural two-lane highways

Overtaking duration is closely associated with overtaking safety because longer maneuvers increase exposure in the opposing traffic lane. However, evidence on overtaking duration on rural mountainous two-lane highways remains limited, particularly under mixed-traffic conditions. This study investigates the determinants of overtaking duration on rural mountainous two-lane highways using an explainable survival machine-learning framework. Unmanned aerial vehicle videos were collected, and vehicle trajectories were extracted to obtain detailed overtaking maneuver data, including complete and right-censored observations. To model censored duration data and capture nonlinear relationships between overtaking duration and its influencing factors, a random survival forest (RSF) model was developed and compared with a conventional log-logistic accelerated failure time (AFT) model. The results show the average values of overtaking duration and overtaking distance were 10.2 seconds and 201.2 meters, respectively. The RSF model achieved a higher C-index than the log-logistic AFT model, indicating better discrimination of overtaking completion times. SHAP results identified the initial speed of the overtaking vehicle, lateral distance, initial speed difference, and overtaking vehicle type as the most influential factors, with pronounced nonlinear effects observed for overtaking-vehicle speed and speed difference. These findings highlight the potential of interpretable survival machine learning for analyzing overtaking-duration data and provide insights into overtaking behavior and safety on rural mountainous two-lane highways.