# Collaborative Trajectories Optimization for Tram and Connected Vehicles at Signalized Intersection
## 2 Literature Review
On the topic of the intersection driving strategy of CAVs, [PERSON] et al. [22; 23] conducted in-depth research on distributed trajectory optimization and stability control for CAVs. They proposed a quadratic spacing policy to improve the flexibility of speed planning and regulations. Additionally, a two-layered framework was established for optimization of the distributed trajectory. The experimental results show that these methods can effectively optimize the trajectory of a fleet. [PERSON] et al. [24] used the signal phase, time information and state prediction of the vehicle to apply the eco-approach and departure (EAD) system at intersections. Some scholars researched the technical optimization of V2V and V2I. They proved that application of these technologies can effectively improve the efficiency of intersections and reduce emissions [25; 26; 27; 28]. [PERSON] et al. [29] analyzed the driving patterns of CAVs at signalized intersections. The study utilized signal lights to communicate with vehicles and enabled CAVs to pass through intersections in a nonstop or gentle acceleration/deceleration manner. [PERSON] et al. [30] ensured the ideal speed of CAVs by optimizing the phase sequence, cycle length, duration of a green light and arrival time of vehicles. [PERSON] et al. [31] calculated the planning speed of a fleet based on [PERSON]'s minimum principle and constructed an ecological driving model based on prediction of departure time. The abovementioned documents represent some of the deep research that has been conducted on trajectory planning of CAVs at intersections. However, this past research has not considered improving the utilization ratio of intersections by combining network technology with the TSP technology of trans. Combined with the above research and the related literature, there are few studies on the positive and negative effects of the special TSP of trans, and full utilization of TSP by social vehicles was seldom considered. Another problem is that there are few studies on digital integration of trans and CAVs. Those studies of ecological driving of CAVs at intersections seldom considered integration of complex tram lines. The trajectory of a tram and CAV in different TSP schemes is shown in Figure 2. The guidance area construction method in Figure 2 is from [24; 30]. After vehicles enter the speed guide area, the tracks of vehicles are determined according to the allowed time period of the traffic signal ahead and predetermined rules. There are many options for trans and CAVs to pass through intersections. In different schemes, the tram has different running indices, and its effects on CAVs in different phases are also different. As shown in Figure 2a, when there is no signal priority, the tram and CAVs in the same phase have overall longer travel times in the running section but have no effect on vehicles in other phases. As shown in Figure 2b-d, the tram has priority to pass through the intersection by using the green extension, phase insertion and early green schemes, respectively. The same-phase CAVs follow the tram to share the benefits of signal priority. However, different signal priorities will have different impacts on the vehicles in the occupied phase, and the extent of the impact is related to the traffic flow of the occupied phase and other factors. The model of digital cooperation among trans, CAVs and traffic signals is established to solve these challenges and improve the overall performance of the signal-controlled intersection. This paper aims to solve the problem of the right-of-way conflict between trans and CAVs by developing a new cooperative control method. The new method, which combines urban rail and road traffic, aims to determine the location and duration of tram TSP more reasonably and carry out coordinated trajectory planning for trans and CAVs. The main contributions are as follows:  
1.