# Analyzing Delay and CO Emissions: A Simulation Study of the Median U-Turn Method at Intersections
## 3 Results  
### Unobstructed Intersection  
Through simulating the above schemes with through traffic volume Q\({}_{s}\leq\) 500 veh/h in Figure 5, the relationship between the average delay, CO emissions at the intersection, and the left-turn ratio with each through traffic volume is shown in Figure 6.  
Figure 5: The simulation schemes. From Figure 6a, it can be observed that when the through traffic volume is constant, with an increase in the left-turn ratio, the average delay of the intersection using the direct left-turn method experiences an accelerated increase, and the average delay of the intersection using the median U-turn method shows a steady increase. The accelerated increase in the average delay at the intersection using the direct left-turn method is related to the stop times at the intersection. When more and more vehicles cannot pass through the intersection in a signal cycle, it will lead to a sharp increase in the average delay at the intersection. The relationship between the average stop times and the left-turn ratio is shown in Figure 7, from which it can been seen that the stop time is larger than 1 when the through traffic volume is 350, 400, 450, and 500 veh/h, respectively, with the left-turn ratio approaching 1. Correspondingly, in Figure 6a, the above four through traffic volumes all show an accelerated increase in the average delay at the intersection. In Figure 7, the  
Figure 6: The relationship between the average delay, CO emissions at the intersection, and the left-turn ratio. (**a**) Average delay; (**b**) CO emissions. average stop times of the intersection using a U-turn method do not appear to be larger than 1, and accordingly, there is no accelerated increase in the average delay at the intersection in Figure 6a. From Figure 6b, it can be observed that when the through traffic volume is constant, both the U-turn and direct left-turn methods show an increasing trend in CO emissions at the intersection with an increase in the left-turn ratio. When the through traffic volume \(\rm Q_{s}\geq 500\) veh/h, the CO emission curve of using a median U-turn method is lower than that of the intersection using a direct left-turn method. Therefore, from the point of view of the emission index, the median U-turn method is more suitable when the through traffic volume \(\rm Q_{s}\leq 500\) veh/h. In terms of the average delay index at the intersection, with the increase in left-turn ratio, the accelerated increasing average delay curve of the intersection using a direct left-turn method may intersect with the continually increasing average delay curve of the intersection using a median U-turn method. In order to quantify the effect of the intersection using a median U-turn method on the average delay reduction at the intersection under different through traffic volumes, the relationship between the reduction rate of the average delay at the intersection using a median U-turn method and using a left-turn ratio method is given, as shown in Figure 8. In Figure 8, when the delay reduction rate is positive, it indicates that it is better to use a median U-turn method. \[\rm R_{dr}=(d_{dt}-d_{dt})/d_{dt}\times 100\% \tag{2}\]  
where \(\rm R_{dr}\) is the delay reduction rate, \(\rm d_{dt}\) is the delay of the intersection using a direct left-turn method, and \(\rm d_{dt}\) is the delay of the intersection using the median U-turn method. From Figure 8, it can be observed that the delay reduction rate at the intersection using a median U-turn method initially decreases and then increases with the increase in left-turn ratio. When the through traffic volume \(\rm Q_{s}\leq 450\) veh/h, the delay reduction rate curve of the intersection using a median U-turn method intersects with the \(X\)-axis. When the through traffic volume is 450 veh/h, the distribution of the left-turn ratio of the two intersection points is more discrete than that of the other intersection points, which are no longer considered here.