## 5 Results
### Safety  
Under the conditions where \(\lambda\) is 0.2 veh/s, 0.3 veh/s, and 0.4 veh/s and \(V_{\text{max}}\) is 60 km/h, the numbers of yellow- and red-running vehicles on left-turn and straight lanes for \(t_{y}\) of 3 s, 4 s, and 5 s are presented in Table 6. Similarly, under the conditions where \(V_{\text{max}}\) is 50 km/h, 60 km/h, and 70 km/h and \(\lambda\) is 0.3 veh/s, the corresponding numbers for \(t_{y}\) of 3 s, 4 s, and 5 s are shown in Table 7. In the simulations, vehicles that decelerated upon encountering a yellow light but failed to stop before the stop line during the yellow phase were also considered as engaging in red running. In reality, however, vehicles that have crossed the stop line may still choose to wait. This discrepancy causes the simulated number of red-running vehicles to be higher than the real-world situation. Nonetheless, the focus is to compare the impact of different yellow durations to vehicles crossing the stop line during the red phase, so the statistical bias in red-running vehicle counts is disregarded.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{\(t_{y}\) (s)} & \multirow{2}{*}{\(\lambda\) (veh/s)} & \multicolumn{2}{c}{**Yellow-Running Vehicles (veh)**} & \multicolumn{2}{c}{**Red-Running Vehicles (veh)**} & \multicolumn{2}{c}{**Unsafe Driving Vehicles (veh)**} \\ \cline{3-8}  & & **Left-Turn Lane** & **St straight Lane** & **Left-Turn Lane** & **St straight Lane** & **Left-Turn Lane** & **St straight Lane** \\ \hline \multirow{3}{*}{3} & 0.2 & 2 & 2 & 4 & 2 & 6 & 4 \\  & 0.3 & 6 & 2 & 1 & 3 & 7 & 5 \\  & 0.4 & 5 & 7 & 5 & 3 & 10 & 10 \\ \hline \multirow{3}{*}{4} & 0.2 & 2 & 1 & 1 & 1 & 3 & 2 \\  & 0.3 & 0 & 2 & 1 & 2 & 1 & 4 \\  & 0.4 & 2 & 2 & 3 & 2 & 5 & 4 \\ \hline \multirow{3}{*}{5} & 0.2 & 1 & 1 & 4 & 6 & 5 & 7 \\  & 0.3 & 2 & 0 & 4 & 2 & 6 & 2 \\ \cline{1-1}  & 0.4 & 0 & 1 & 1 & 2 & 1 & 3 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Number of yellow- and red- running vehicles on left-turn and straight lanes under different \(t_{y}\) (\(V_{\text{max}}=60\) km/h).  
Figure 10: Average vehicle speed under different \(t_{y}\) (\(\lambda\) = 0.3 veh/s): (**a**) left-turning vehicles, \(V_{\text{max}}=50\) km/h; (**b**) left-turning vehicles, \(V_{\text{max}}=60\) km/h; (**c**) left-turning vehicles, \(V_{\text{max}}=70\) km/h; (**d**) straight-going vehicles, \(V_{\text{max}}=50\) km/h; (**e**) straight-going vehicles, \(V_{\text{max}}=60\) km/h; and (**f**) straight-going vehicles, \(V_{\text{max}}=70\) km/h.  
From Table 6, it can be observed that under a given speed limit and a longer yellow duration (\(t_{y}\) = 5 s), the number of yellow-running vehicles gradually decreases as traffic flow increases (without reaching saturation). For higher traffic volumes (\(\lambda\) = 0.4 veh/s), increasing \(t_{y}\) from 3 s to 5 s results in fewer yellow- and red-running vehicles, consistent with the conclusions in the study of [PERSON] et al. (2016). As shown in Table 7, under a fixed departure rate, a lower speed limit (\(V_{\text{max}}\) = 50 km/h) and an increase in \(t_{y}\) from 3 s to 5 s significantly reduce the numbers of both yellow- and red-running vehicles.