## 4 Simulation Framework
### Setting Simulation Parameters  
Setting the yellow light at the signalized intersection serves as a buffer and warning for passing vehicles [61]. If a driver decides to decelerate and stop upon seeing the yellow light, he/she needs to stop in front of the stop line before the red light is activated. Therefore, the design method for the yellow light duration (\(t_{y}\)) at an isolated signalized intersection typically follows Equation (13):  
\[t_{y}=t_{0}+\frac{v}{2b} \tag{13}\]  
where \(t_{0}\) represents the reaction time (s) for a driver to make a decision after seeing the yellow light; \(v\) denotes the vehicle speed (m/s); and \(b\) indicates the vehicle braking deceleration (m/s\({}^{2}\)). Figure 7: Simulation environment architecture. Vehicle speed is a key variable in determining yellow phase duration and is generally taken as the speed limit at the intersection. According to the European agreement on road traffic signs and signals, [PERSON] [62] provides recommended yellow light durations for different speed limits, as shown in Table 2. Additionally, [PERSON] et al. [63] have suggested minimum yellow phase durations based on a comprehensive comparison of yellow phase duration calculation methods in Germany, the United States, and Japan, in conjunction with actual conditions in China. Therefore, this paper considers yellow phase durations of 3 s, 4 s, and 5 s in the simulation, which represent commonly adopted values in international practice. Specifically, 3 s is typical for low-speed urban roads (\(\leq\)40 km/h), 4 s is widely used for medium-speed roads (40-70 km/h), and 5 s accounts for higher-speed or safety-enhanced settings. These values ensure the simulation reflects representative traffic control standards. Variability in driving behavior is one of the main reasons for poor stability and safety in traffic flow [64]. To analyze the impact of differences in driver behavior under varying yellow phase durations on traffic efficiency and safety at signalized intersections, a scenario for a specific approach direction at an isolated signalized intersection was set up in the constructed simulation environment, with specific simulation parameters as follows:  
* The total length of the upstream segment of the signalized intersection is 2000 m.
* To intuitively analyze the traffic volume for each direction and specifically observe the impact of yellow phase duration, the approach direction was individually configured with three lanes, with vehicle departure proportions for left-turn, straight, and right-turn lanes set at 30%, 30%, and 40%, respectively, without considering lane-changing behavior on the upstream segment. * It is assumed that vehicle departures follow a Poisson curve, with the number of departing vehicles per unit time (\(\lambda\)) set at 0.2 veh/s, 0.3 veh/s, and 0.4 veh/s. For all vehicles, the departure speed was set as equal to the intersection design speed. * The simulation duration is 3600 s. The signal cycle length is 123 s, with a constant green duration, and three signal timing schemes are set:
* Green light lasts for 60 s, yellow light lasts for 3 s, and red light lasts for 60 s.
* Green light lasts for 60 s, yellow light lasts for 4 s, and red light lasts for 59 s.
* Green light lasts for 60 s, yellow light lasts for 5 s, and red light lasts for 58 s.
* It is assumed that vehicles strictly adhere to the intersection design speed, meaning they always travel at the speed limit in a free-flowing state. Since the observed maximum acceleration rate is nearly 4 m/s\({}^{2}\) and the maximum deceleration rate is about 8 m/s\({}^{2}\), the range of vehicle acceleration is from \(-\)8 to 4 m/s\({}^{2}\), and overtaking is not allowed during travel. Additionally, the effects of signal timing at upstream consecutive intersections on vehicle departures and the impacts of other conflicting vehicles at the intersection are not considered, as well as non-motorized vehicles and pedestrians. The specific parameter settings for different simulation experimental groups are shown in Table 3.