## 7 Conclusions  
This study first introduces a subjective risk-perception-based driving behavior model built under the unified framework of \"risk prediction-motion planning\" and further refines it using fuzzy decision-making theory. The improved model is then embedded into a simulation environment for isolated signalized intersections, where the functions of each module and the associated input-output parameters are explicitly defined. Subsequently, simulations are conducted to analyze the efficiency and safety performance of isolated signalized intersections under varying yellow durations. The findings reveal that, assuming that vehicles strictly adhere to the designed speed, an increase in yellow light duration from 3 s to 5 s leads to greater traffic volume under high traffic density. Meanwhile, real-time fluctuations in traffic speed stabilize and the occurrence of unsafe driving behaviors is mitigated. Finally, the study explains these phenomena through the lens of risk-perception theory, recommending that traffic managers consider appropriately extending yellow phase durations within the range of 3-5 s during periods of high traffic volume. A comparative discussion with other research findings also supports the feasibility of the proposed model in simulating the impact of yellow phase duration on traffic flow performance. Furthermore, the study emphasizes the importance of accounting for both short-term behavioral responses and long-term system-level impacts when optimizing signal timing strategies.  
This study provides a simulation environment to evaluate traffic performance at isolated intersections under various signal timing schemes. By analyzing traffic phenomena from the perspective of risk perception and driving behavior mechanisms, the study explores the application of risk-based driving behavior models in improving overall in tersection efficiency and safety. It offers a theoretical foundation for describing driving behaviors at signalized intersections in greater detail and for explaining the underlying logic behind intersection performance. Additionally, it serves as a decision-making tool for the design of signal timing schemes. For traffic simulation, the approach also facilitates the development of more refined driving behavior models and reduces the complexity of switching between different models across diverse road spaces and traffic scenarios.  
However, this study has several limitations. First, the simulation results are inherently stochastic, necessitating an increased number of iterations to support more reliable conclusions. Meanwhile, comparing the proposed model with simplified driver behavior models and other existing models is necessary to further demonstrate its validity and reliability, as well as to examine the sensitivity of yellow phase duration to traffic flow performance. Second, only isolated intersections were considered, without accounting for the influence of upstream intersections. Third, the simulation process involves stepwise computation of risk fields, making it time-consuming and computationally intensive, which poses challenges for conducting larger-scale or more extensive simulations. Finally, future research could further explore the impact of yellow phase duration on mixed traffic with both human-driven vehicles and autonomous vehicles.  
Conceptualization, J.H., B.L.; methodology, J.H.; software, J.H., P.L. and W.Z.; validation, J.H. and W.Z.; formal analysis, J.H.; writing--original draft preparation, J.H.; writing--review and editing, B.L.; visualization, P.L.; supervision, B.L.; funding acquisition, Z.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the State Key Lab of Intelligent Transportation System under Project No. 2024-Z001.  
The data presented in this study is available on request from the corresponding author. The data is not publicly available due to the requirements of the data provider.  
The authors declare no conflicts of interest.