Investigating Lane Departure Warning Utility with Survival Analysis Considering Driver Characteristics  
[PERSON]  
1 Beijing Key Laboratory of Urban Road Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China; [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (Z.W. ); [EMAIL_ADDRESS] (T.Z.) [PERSON]  
1 Beijing Key Laboratory of Urban Road Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China; [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (Z.W. ); [EMAIL_ADDRESS] (T.Z.) [PERSON]  
1 Beijing Key Laboratory of Urban Road Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China; [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (Z.W. ); [EMAIL_ADDRESS] (T.Z.) [PERSON]  
1 Beijing Key Laboratory of Urban Road Intelligent Traffic Control Technology, North China University of Technology, Beijing 100144, China; [EMAIL_ADDRESS] (X.Z. ); [EMAIL_ADDRESS] (Z.W. ); [EMAIL_ADDRESS] (T.  
et al. found that about one third of drivers thought that the warning thresholds from LDW systems based on the time of crossing the lane line were too conservative and that frequent false alarms seriously affected the driving mood, thus many drivers were inclined to disuse LDW systems [10]. [PERSON] et al. designed an LDW system with immediate and delayed warning functions to improve driving behavior [11]. The actual utility of LDW systems was also affected by the driver's distraction state. In highway environments, small-amplitude lane departure may occur for drivers who are concentrating on driving, and premature line-crossing warnings may lead to excessive alerting messages that cause disturbance to drivers [12]. During the normal driving process, warning messages issued by the LDW system in situations without collision risk are perceived as nuisance alerts. Nuisance alerts are very likely to reduce the driver's willingness to use the LDW system, and the drivers may ignore the potential positive impact of this system for driving safety [13; 14]. Undeniably, LDW systems can promptly warn the driver when a vehicle is departing the lane and the distracted or sleepy driver did not detect the potential driving hazard. [PERSON] et al. investigated the effect of LDW systems on distracted driving behaviors with naturalistic driving data and found that LDW systems based on real-time distraction monitoring could reduce the occurrence rate of aggressive driving behaviors, including rapid acceleration and harsh braking [15]. In addition to the distraction state, driving style also impact on warning utility. [PERSON] et al. designed an LDW system based on driving style to improve the effectiveness of lane departure warnings, but the acceptance of this system from drivers needs to be further verified [16]. [PERSON] et al. proposed a lane departure warning algorithm based on the probabilistic statistics of driving habits, and the warning mechanism was adaptively adjusted with driving habits [17]. However, a comprehensive analysis from the perspectives of driver state characteristics and subjective cognition has not been adequately investigated for the applicability of lane departure warning modes. To address these research gaps, this study identified two key variables, distraction state and driving style, to further explore their potential influence on the actual utility of LDW systems. The warning effectiveness was defined by its ability to reduce lane departure duration. Both the actual warning utility analysis and a subjective acceptance evaluation were integrated to match warning timing with various distraction levels and driving styles. A simulation driving experiment was conducted to observe real behavioral reactions of participants without exposing them to the risk of physical harm. This study analyzed the dimensions of departure duration and driver state, aiming to answer the following two primary research questions:  
* Which warning timing is more suitable for drivers when lane departure occurs?