# Collaborative Trajectories Optimization for Tram and Connected Vehicles at Signalized Intersection
## 2 Literature Review  
Transit signal priority (TSP) is a key technology in operation of terms that can learn from mature research results of conventional buses. Based on these studies, the characteristics of the running process of terms can be considered. [PERSON] et al. [4] conducted a preliminary study on a signalized intersection in Athens and ranked priority according to bus carrying capacity. [PERSON] et al. [5] proposed an optimization model to optimize bus signal priority and took bus delay as the basis for TSP. Some scholars considered the effects of the TSP characteristics and the additional delay of the queue on the nonpriority route. These studies estimated the impact of TSP on the service levels at each approach point. They also observed that the signal priority decreased the level of intersection service by several levels under the condition of heavy traffic [6; 7]. [PERSON] et al. [8] designed a simulated annealing algorithm to verify the efficiency and security of the generated optimal signal. [PERSON] et al. [9] took real-time vehicle information and facility information as the basic information for the input system and used the efficient dynamic programming algorithm to configure this system. [PERSON] et al. [10] provided a new way to optimize signal priority. They proposed  
Figure 1: Schematic diagram of a tram line’s network environment. a combined model of predictive control and a deep reinforcement learning solution to minimize stopping of trans at intersections while reducing delay of general vehicles. In recent years, some scholars have discussed the negative impact of trans on social vehicles at controlled intersections, but the description of social vehicles was rough, and the negative impact of TSP was simply calculated based on historical traffic flow [11; 12; 13]. Most of the studies of TSP were focused on bus signal priority. A tram is different from a conventional bus in that it has a long body and large capacity; thus, the timing, duration and impact of the priority signal need to be reconsidered. At present, there is little research on TSP of trans as most studies have focused on basic calculations and qualitative analyses. The positive effects of TSP on trans have seldom been considered. For the aspect of optimal control of the trajectory of urban rail, [PERSON] et al. [14] analyzed the energy consumption characteristics of trains under different working conditions. However, they simplified the traction force, braking force and resistance of trains to a constant. The model increased the difficulty of solving practical problems. [PERSON] et al. [15] used the control subsection method to analyze the travel time and energy consumption of a subway system. [PERSON] and [PERSON] [16] proposed a network energy-saving schedule design method, which considered the requirements of passengers and operators, and constructed a multiobjective optimization model to solve the problem of balance between train running times and energy consumption. [PERSON] et al. [17] analyzed the energy required for railway operation and took different speed limit sections as the research background. The study designed a particle swarm algorithm to obtain the interstation operation curve. [PERSON] et al. [18] optimized the train speed curve based on the genetic algorithm and ant colony optimization algorithm. The model planned the curve according to the classical four-stage method of train operation. [PERSON] and [PERSON] [19; 20; 21] designed an optimal speed controller to reduce energy consumption of heavy-duty trains. The objective was to reduce energy wasted when braking. These studies mainly focused on energy-saving operation of subways. These scholars took the line between two adjacent stations as a whole section. Although trans usually operate in a similar mode to a subway, the influences of signal timing and speed limits at intersections should be taken into account; therefore, it is difficult to directly apply these past results to tram systems.