## 6 Discussion
### Safety  
The finding that the number of yellow-running vehicles gradually decreases as traffic volume increases (without reaching saturation) under certain speed limits and longer yellow phase durations can be explained by the interaction between driver risk perception and following behavior. In dense traffic conditions, most vehicles upstream are in a following state, with their movement significantly influenced by the one ahead [75; 76]. According to [PERSON]'s \"Mitschlepp\" effect [77], this following state diminishes individual drivers' autonomy, as risk perception is partly transferred from the leading driver to the followers. If the lead driver during the yellow phase opts to stop, downstream vehicles, regardless of their own risk preferences, are often compelled to do the same, reducing the likelihood of yellow-running behavior. In contrast, under sparse traffic conditions, vehicles operate more freely, and drivers' decisions are dominated by their individual risk thresholds. Drivers who perceive a higher risk may stop, while those who find the risk acceptable are more likely to continue through the yellow light. This disparity in behavior results in higher yellow-running frequencies, as fewer vehicles are constrained by the actions of others. Furthermore, due to situations where vehicles decelerate during the yellow phase but fail to stop completely before the stop line, leading to red-running behavior, when yellow-running behavior decreases, the associated red-running behavior also decreases for the reason mentioned above. Therefore, under longer yellow phase durations, the number of red-running vehicles also decreases as traffic volume increases. This conclusion has also been confirmed in past research [78; 79]. For instance, [PERSON] and [PERSON] [78] made a finding that an increase of 1 s in yellow phase duration (such that it does not exceed 5.5 s) would decrease the red-running frequency by at least 50%. Another important finding is that at lower speed limits (e.g., 50 km/h), increasing the yellow duration from 3 s to 5 s significantly reduces both the number of yellow- and red-running vehicles. This could be explained by the fact that under longer yellow light durations, drivers perceive a lower risk at the onset of the yellow light or as the green light is about to end, and the perceived risk is more likely to be smaller than their desired risk. In this case, if the vehicle speed is relatively high when the yellow light turns on (assuming the distance to the stop line is the same), the vehicle may maintain a high speed as it approaches the intersection, making it more likely to cross the stop line during the yellow phase. The following vehicles, also moving at higher speeds, may be unable to stop in time before the yellow or red light turns on, thus increasing the likelihood of yellow- or red-running behavior. A study that reached a finding that 71% of those who passed an intersection after yellow light onset were platoon leaders and 23% were first followers can support this conclusion [80]. On the other hand, if a vehicle's approaching speed is lower, the occurrence of this behavior may decrease. The number of yellow- and red-running vehicles was also observed to decrease as the yellow light duration extended from 3 s to 5 s under higher traffic volume. This finding is consistent with the conclusions in the study of [PERSON] et al. [60]. However, the study of [PERSON] et al. [81] found that when the yellow light duration is longer (e.g., 5 s), a smaller following distance makes it more likely for the first yellow-running vehicle in a queue to lead the following vehicles to do the same, thus increasing the number of yellow- and red-running vehicles. This phenomenon is closely related to factors such as traffic volume, following distance, and vehicle speed [82; 83; 84].