## 1 Introduction  
In recent years, to improve the problem of urban traffic congestion, China has been vigorously developing public transportation. Since the public transport priority became the trend in public transport development, the Ministry of Transport released the \"Thirteenth Five-Year Plan\" for the development of urban public transport in 2017, which clearly put forward the in-depth implementation of public transport priority development strategy. At present, the main bus priority strategy includes right-of-way priority and signal priority, of which right-of-way priority is developing rapidly [1], bringing a total of 16,551.6 km of bus lanes set up nationwide in 2020, an increase of 51.65% since 2017. In contrast, China's bus signal priority control technology is relatively lagging behind and needs to be studied in depth. The existing bus signal priority research mainly includes passive priority and active priority, among which active priority has been studied more and applied in some cities, with Nanjing first conducting a pilot project in the Jianye District in 2014 and gradually promoting active bus signal priority in the city. In 2021, Changsha opened three bus priority routes based on vehicle-road cooperation technology in areas with high traffic flow within the city center. However, active bus priority requires a comprehensive intelligent transformation of buses, signal control equipment, roadside equipment, etc., which is costly and prone to cause traffic congestion in nonpriority phase time, leading to detrimental problems to traffic safety and management. Therefore, the study of passive bus signal priority is still of great significance. China's arterial road coordination control technology is becoming increasingly mature and has been widely used in many cities, achieving good application effects. By 2021, coordinated control of two-way green waves has been implemented on 50 road sections in Beijing, including 289 signalized intersections, and the overall road traffic efficiency has been improved by over 40% after optimization [2]; 574 green wave road sections have been set up in Shenzhen, involving 1742 signalized intersections. The cumulative green wave road length spans 520 km, and the vehicle traffic condition of arterial roads has been greatly improved after optimization. Take Heping Road as an example, its two-way travel time reduced by 31% and 46%, respectively [3]. Arterial coordination control methods mainly include the maximum green wave band method and the minimum delay method [4]. The minimum delay method takes the operating conditions of vehicles into account, which is more consistent with the actual situation so that it can improve the traffic efficiency to a greater extent. For the mixed traffic flow of buses and cars in arterial coordination control, the existing delay calculation method with a single conversion standard converts buses into cars and calculates the delays of all vehicles first, and then receives the delays of buses and cars, without considering the differences in the operating characteristics of different vehicle types. Because the speed and stop of buses and cars are quite different [5], and the stopping time and passenger capacity of different bus routes are different, the average vehicle delay and per capita delay obtained are subject to large errors. On the basis of the research on vehicle delay, some scholars have proposed a method of minimizing the total delay of the trunk lines [6; 7]; some scholars have optimized the intersection characteristics of bus vehicles through the combination of speed guidance [8], active priority, and signal adjustment based on the coordination of social vehicle trunk lines [9; 10]; some scholars have also proposed an analysis method of the impact of bus signal priority on vehicle delay [11] and an evaluation method of the effect of bus priority [12]. Additionally, some scholars proposed a signal control method for bus priority considering the delay of non-priority vehicles in a connected-vehicle environment [13].