# Collaborative Trajectories Optimization for Tram and Connected Vehicles at Signalized Intersection
## 5 Results and Discussion
### Performance Comparison with and without Optimization  
The iteration of the fitness function is shown in Figure 5. To effectively analyze the effect of the cooperative optimization of trans and CAVs, the TransSuite traffic control method, described in [37], is compared with the target guidance method designed in this paper. When the tram is delayed and cannot move through the intersection in the corresponding phase as planned, it is necessary to control the tram to reduce its delay. When the tram still cannot pass through the intersection according to the fastest curve, the  
When the conventional method is used to solve the problem, the tram arrives at the intersection at the beginning of the second phase of the cycle, and the TSP type is the green extension scheme. When using the target guidance method in this paper, the tram arrives at the intersection at the beginning of the third phase of the cycle, and the TSP type is the phase insertion scheme. Comparing the changes in the CAV trajectories obtained by the two methods, Figure 6a-c corresponds to the three phases involved, that is, the second phase, the third phase and the first phase of the next cycle, respectively. It can be seen from Figure 6a that there are many CAVs that plan to pass in the second phase. If the TSP is set to the second phase, the green time of the second-phase CAVs is reduced, forcing the upstream vehicles to be guided into the second phase of the next cycle. If the TSP is set to the third phase, the CAVs passing through the intersection in the second phase will not be affected. As can be seen from Figure 6b, there are a few CAVs scheduled to pass through in the third phase. Although the TSP occupies part of the third phase, the CAVs of this phase can still pass in the remaining time after their arrival time delay. Therefore, the TSP did not have a significant impact on the CAVs in this phase. As can be seen from Figure 6c, if the TSP of the tram is set to the second phase, the TSP is not fully utilized as CAVs in the first phase cannot pass through the intersection with the tram. When the TSP is set to the third phase, several CAVs can pass through the intersection with the tram due to TSP, which can reduce the first-phase traffic pressure in the next cycle; thus, the overall trajectory of CAVs passing through the intersection in the first phase is optimized. The trajectory charts of a tram and CAVs obtained by using the conventional method from [37] and the target guidance method are shown in Figure 7a,b, respectively. The results are shown in Table 4. Compared with the conventional method, the transit time of the tram increased by 45.8%, but the total transit time of the tram and CAVs decreased by 17.1%. For the aspects of energy consumption and comfort, it can be observed that both the tram and CAVs run smoothly due to the guidance from this paper. The acceleration and deceleration process, which is violent in the conventional method, is avoided. The total energy consumption of the tram and CAVs is reduced by 34.7%. The discomfort value is reduced by 25.8%. The index obtained by the target guidance method is better than that obtained with the model from [37]. The scheme in this paper can effectively reduce overall transit time, running energy consumption and comfort index for different intersection users. Figure 5: Iterative process of fitness function. The passenger ratio of terms to social vehicles varies greatly between workdays and non-workdays and between peak hours and flat hours; therefore, the applicability of this model is analyzed, with the results shown in Figure 8. As can be seen from Figure 8, with the increase in the proportion of tram passengers, the value of the objective function obtained by the conventional method shows a decreasing trend. The objective function