# Analyzing Delay and CO Emissions: A Simulation Study of the Median U-Turn Method at Intersections
## 3 Results
### Congested Intersection  
Through simulating the schemes with through traffic volume \(\mathrm{Q_{s}}\geq 500\) veh/h, shown in Figure 5, the relationships between the average delay and CO emissions at the intersection and the left-turn ratio under each through traffic volume are shown in Figure 10.  
Figure 8: The delay reduction rate of using a U\(-\)turn method at the intersection. Figure 9: The critical left-turn ratio boundary curves \(\mathrm{R_{dcri(1)}}\), \(\mathrm{R_{dcri(2)}}\), \(\mathrm{R_{dcri(3)}}\), and \(\mathrm{R_{COri}}\). average delay at the intersection using the direct left-turn method decreases firstly and then increases, and the average delay at the intersection using the median U-turn method also decreases slightly and then increases rapidly. The intersection point of the two average delay curves at the intersection using the median U-turn method and the direct left-turn method is near the left-turn ratio of 0.5. From Figure 10b, it can be observed that when the through traffic volume is 500 veh/h and the left-turn ratio is between 2.6 and 3.0, the CO emissions curve of the intersection using the median U-turn method is lower than that of the intersection using a direct left-turn method. When the through traffic volume \(\mathrm{Q_{s}}\geq 1000\) veh/h, with the increase in the left-turn ratio, the CO emissions at the intersection using both the U-turn method and the direct left-turn method increase first and then decrease on the whole. With the increase in the left-turn ratio, the CO emissions of the intersection using a median U-turn method change from larger than to less than those of the intersection using a direct left-turn method. When the through traffic volume is 1000 veh/h, there is an intersection point with left-turn ratio of about 0.3 between the CO emission curves at the intersection using the U-turn method and the direct left-turn method. When the through traffic volume \(\mathrm{Q_{s}}>1000\) veh/h, there is a single intersection point between the CO emission curves of the intersection using a direct left-turn method and the median U-turn method. When the real left-turn ratio is larger than that of the intersection point, the CO emissions at the intersection using the median U-turn method are smaller. In order to more intuitively show the applicability of the intersection using a median U-turn method with the through traffic volume \(\mathrm{Q_{s}}\geq 500\) veh/h, similar to the condition of through traffic volume \(\mathrm{Q_{s}}\leq 500\) veh/h shown in Figure 8, the delay reduction rate and CO emission reduction rate under different through traffic volumes can be obtained through Formulas (2) and (3), as shown in Figure 11.  
\[\mathrm{R_{Er}}=(\mathrm{E_{dlt}}-\mathrm{E_{ut}})/\mathrm{E_{dlt}}\times 100\% \tag{3}\]  
where \(\mathrm{R_{Er}}\) is the CO emission reduction rate, \(\mathrm{E_{dlt}}\) is the CO emissions of the intersection using a direct left-turn method, and \(\mathrm{E_{ut}}\) is the CO emissions of the intersection using a median U-turn method. From Figure 11, it can be observed that under each through traffic volume, every average delay reduction rate curve has an intersection point with the \(X\)-axis, and the fitting line for the left-turn ratios corresponding to these intersection points can be named as delay-based critical left-turn ratio boundary curve \(\mathrm{R_{dcri(3)}}\) under large through traffic volumes. As shown in Figure 9, it can be seen that \(\mathrm{R_{dcri(3)}}\) decreases rapidly and then stabilizes. When the left-turn ratio is lower than the left-turn ratio corresponding to the intersection point under each through traffic volume, the average delay reduction rate of the intersection is positive, which means that the average delay at the intersection using the median U-turn method is smaller. From Figure 11, it can be seen that the reduction rate of CO emissions increases with the increase in left-turn ratio on the whole.