## 6 Discussion  
### Traffic Volume  
The observed finding that traffic volume increases as yellow light duration extends from 3 s to 5 s under high departure rates can be attributed to the following reasons: When departure rate is low, the signal state encountered by vehicles near the intersection is highly influenced by the randomness of vehicle departure time sequences [(66)]. As a result, the probability of vehicles arriving at the intersection during the yellow phase is relatively low, and thus the impact of yellow light duration on traffic volume is minimal. However, under higher departure rates, more vehicles are required to make stop/go decisions during the yellow phase. From the perspective of driver risk perception, the decision-making process during the yellow phase involves assessing the trade-off between perceived risk and the potential benefit of crossing the intersection. With an extended yellow phase duration, drivers are more likely to perceive a lower signal risk at the onset of a yellow light (assuming equal vehicle speed and distance to the stop line). This perceived risk may also fall below their desired threshold, increasing the likelihood of vehicles crossing the stop line during the yellow phase.  
Furthermore, a longer yellow duration not only reduces perceived risk but also creates a psychological buffer that allows drivers to anticipate their movements more confidently. This aligns with risk homeostasis theory, which suggests that drivers continuously adjust their behavior to maintain an acceptable risk level based on real-time traffic conditions. The extended yellow phase helps drivers recalibrate their risk perception dynamically, thereby facilitating smoother traffic flow and reducing abrupt stopping decisions.  
Studies support the idea that an extended yellow phase duration provides traffic with additional passing and buffer time, enhancing intersection performance during high traffic volumes [(67; 68; 37)]. However, this must be balanced against safety concerns, as excessively long yellow light durations could encourage aggressive driving behavior or undermine the predictability of traffic signals. Therefore, within the context of design speed and  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\(t_{y}\) **(s)**} & \multirow{2}{*}{\(V_{\text{max}}\) **(km/h)**} & \multicolumn{2}{c}{**Yellow-Running Vehicles (veh)**} & \multicolumn{2}{c}{**Red-Running Vehicles (veh)**} & \multicolumn{2}{c}{**Unsafe Driving Vehicles (veh)**} \\ \cline{3-8}  & & \multicolumn{2}{c}{**Left-Turn Lane**} & **Straight Lane** & **Left-Turn Lane** & **Straight Lane** & **Left-Turn Lane** & **Straight Lane** \\ \hline \multirow{3}{*}{3} & 50 & 3 & 4 & 1 & 6 & 4 & 10 \\  & 60 & 6 & 2 & 1 & 3 & 7 & 5 \\  & 70 & 3 & 2 & 3 & 6 & 6 & 8 \\ \hline \multirow{3}{*}{4} & 50 & 3 & 2 & 1 & 1 & 4 & 3 \\  & 60 & 0 & 2 & 1 & 2 & 1 & 4 \\  & 70 & 4 & 4 & 7 & 7 & 11 & 11 \\ \hline \multirow{3}{*}{5} & 50 & 1 & 0 & 0 & 0 & 1 & 0 \\  & 60 & 2 & 0 & 4 & 2 & 6 & 2 \\ \cline{1-1}  & 70 & 4 & 3 & 3 & 1 & 7 & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Number of yellow- and red-running vehicles on left-turn and straight lanes under different \(t_{y}\) (\(\lambda\) = 0.3 veh/s).  
intersection geometry, it is recommended to moderately extend the yellow phase duration within the range of 3-5 s during high traffic volumes.