# Collaborative Trajectories Optimization for Tram and Connected Vehicles at Signalized Intersection
## 1 Introduction  
Green and intelligent urban transportation systems have become the main focus in the development of the transportation industry. A series of products of the information era, such as modern trams, the car network, car-road coordination, road network monitoring and automatic driving, have been increasingly applied in modern transportation systems. As a kind of urban transportation mode with a large transportation capacity, good energy conservation, short construction period and good investment return, modern trams are developing rapidly in many cities across the world [1]. In China, for example, 21 cities or regions nationwide had opened tram lines by the end of June 2022, totaling a length of 532.97 km.  
Trams in a semi-exclusive right-of-way mode have an exclusive lane in the running section and share right-of-way with other line users at intersections. Semi-exclusive right-of-way systems can make full use of the advantages of modern trams [2, 3]. Currently, it has become the most widely used form of right-of-way.  
In operation of modern trams in a semi-exclusive right-of-way mode, allocation of right-of-way between trams and social vehicles at intersections is one of the most important contradictions and core problems. When trams running at top speed cannot pass through an intersection during a green light, the signal priority strategy is usually given to tramsbased on their arrival time. This easily leads to an increase in the delay of other users at intersections, which reduces the service level and other indicators of the intersections.  
In recent years, connected and automated vehicle (CAV) technologies have become a research hotspot in the transportation industry. However, there are few studies on the digital information exchange between urban rail and road. If we study the digital integrated traffic control in the network environment according to the characteristics of the tram and CAVs, the indices of the intersections of tram lines will be further improved.  
As shown in Figure 1, this article will research the optimization scheme of the intersections of tram lines in a network environment. In the networked environment built in this article, terms, CAVs and intersection signals can interact with the central computing equipment. Before passing through the intersection, the initial information, such as the timing information from the approaching signal machine, the running status and the number of passengers of the tram and the CAVs, etc., is sent to the central computing equipment. According to the basic information it receives, the computing equipment returns the scheme of adjustment (including adjustment of signal timing and vehicle speed).  
The structure of the paper is as follows: in the literature review, studies of transit signal priority, optimal control of urban rail and intersection driving strategy of CAVs are summarized. Section 3 introduces the mathematical model of the tram and CAVs, as well as the objective function and constraints. The methodology to solve the proposed model is developed and outlined in Section 4. Case studies and the results are discussed in Section 5. Finally, the research conclusions and future research directions are put forward in Section 6.