## 7 Results and Analysis
### Validity Analysis  
With 178 sets of examples as input, the optimal phase difference and the corresponding per capita delay, average delay, average delay of bus, and average delay of cars were calculated for all examples according to this model and the model without considering the bus priority. Compared with the optimization result of the model without considering the bus priority, the average change in each delay after the optimization of this model was calculated as an evaluation index to analyze the effectiveness of this model. The optimization target of the model without considering bus priority was the average vehicle delay \(d_{v}\), and the calculation formula of \(d_{v}\), as follows:  
\[d_{v}=\frac{N_{c}{}^{down}\times d_{c}{}^{down}+N_{c}{}^{up}\times d_{c}{}^{ up}+\sum_{l=1}^{n1}N_{bi}{}^{down}\times d_{bi}{}^{down}+\sum_{l=1}^{n2}N_{bi}{}^{ up}\times d_{bi}{}^{up}}{N_{c}{}^{down}+N_{c}{}^{up}+\sum_{l=1}^{n1}N_{bi}{}^{ down}+\sum_{l=1}^{n2}N_{bi}{}^{up}} \tag{26}\]  
As shown in Figure 12, compared with the model without considering bus priority, the per capita delay and bus average delay after optimization of the model in this paper decreased by 1.88 s and 3.85 s, respectively, with a reduction ratio of 13% and 24.85%; the average vehicle delay and car average delay increased by 0.9 s and 1.59 s, respectively, with an increase ratio of 6.63% and 11.9%. Comparing the changes of each type of delay, it can be seen that the increase in average vehicle delay and average car delay is small compared with the decrease in per capita delay and average bus delay. This indicates that the model in this paper can effectively reduce bus delay and per capita delay and has a small negative impact on car traffic and the overall vehicle traffic at the intersection. The following are the results of average bus delay, per capita delay, average car delay, and average vehicle delay after optimizing 178 sets of examples for both models. (1) Average bus delay  
As can be seen from Figure 13, compared with the average bus delay after optimization of the model without considering the bus priority, 3% of the optimized results of the model in this paper were larger, 10% were equal, and 87% were smaller, indicating that the average bus delay was lower in most of the examples optimized by this model. Moreover, the average bus delay was reduced by 3.85 s on average and 12.49 s maximum. A total of 45% of the reduction value was higher than the average, indicating that the optimization effect of bus delay in nearly half of the examples was higher than the average level. (2) Per capita delay  
As can be seen from Figure 14, compared with the per capita delay after optimization of the model without considering the bus priority, 10% of the optimized results of the model in this paper were equal to it, and 90% were smaller, which meant that the per capita delay of most of the examples optimized by this model was lower. Moreover, the per capita delay was reduced by 1.88 s on average and 6.84 s maximum. A total of 44% of the reduction value was higher than the average, indicating that the optimization effect of per capita delay in nearly half of the examples was higher than the average level. Figure 12: Comparison of the variations in each delay. Figure 13: Comparison of the average bus delay after the optimization of the two models. (3) Average car delay  
As can be seen from Figure 15, compared with the average delay of cars after optimization of the model without considering the bus priority, 1% of the optimization results of the model in this paper are smaller, 10% are equal to it, and 89% are larger, which means that the average delay of cars is higher in most of the examples optimized by this model. Moreover, the average delay of cars increased by 1.59 s on average and 5.14 s maximum. A total of 56% of the increase value was lower than the average, indicating that the optimization effect of the average delay of cars in more than half of the examples was higher than the average level.