## 6 Discussion
### Average Speed  
The fluctuations in average speed can reflect the stability of traffic flow on a road segment [70]. One finding is that as traffic flow increases but does not reach saturation, the amplitude of average speed fluctuations within each signal cycle gradually decreases. This is consistent with the conclusions drawn in the study of [PERSON] et al. [65]. However, a unique perspective may be to explain this phenomenon from the viewpoint of risk perception. Specifically, this may be because, at lower traffic volumes, there are more vehicles traveling freely, and when these vehicles are constrained by dynamic signal risks, they are more likely to experience sudden risk changes, leading to abrupt acceleration or deceleration. This results in unstable vehicle speeds [71; 72]. In contrast, at higher traffic volumes, the traffic flow tends to stabilize into steady following behavior during each signal cycle, which reduces the amplitude of average speed fluctuations.  
Another finding is that as the road speed limit increases, the amplitude of average speed fluctuations within each signal cycle also increases. This could be due to the higher vehicle speeds associated with higher speed limits. When vehicles approach the intersection during the yellow phase (assuming the distance to the stop line remains the same), the perceived signal risk increases. As a result, greater deceleration and longer deceleration time are required to either safely pass through the intersection or stop before the red light turns on [73]. This leads to greater speed variations in the vehicles following, which in turn affects the overall average speed of the vehicle queue [74].  
A further observation is that, under the same departure rate, shorter yellow phase durations (e.g., 3 s) result in slightly larger average speed fluctuations compared to longer durations (4 s or 5 s). This could be explained by the fact that with a shorter yellow phase duration, drivers perceive a higher risk at the onset of the yellow light (assuming equal vehicle speed and distance to the stop line). The larger gap between the perceived and desired risks compels drivers to decelerate more aggressively, causing abrupt changes in individual vehicle speeds. These sudden adjustments ripple through the traffic flow, increasing real-time speed fluctuations and reducing overall stability. Therefore, when traffic volume has not reached saturation, appropriately increasing the yellow duration within the range of 3-5 s can stabilize the fluctuations in real-time vehicle speeds, thereby reducing the potential risks associated with sudden acceleration or deceleration [57].  
The interplay between traffic volume, speed limits, and yellow phase duration underscores the importance of understanding driver risk perception in optimizing signal control strategies. Moderate increases in yellow phase duration can contribute to smoother traffic flow by reducing abrupt speed fluctuations and enhancing stability. However, the impact of these adjustments should be carefully balanced against operational constraints and intersection characteristics to ensure that stability gains do not compromise traffic efficiency.