# An Optimal Scheduling Model for Connected Automated Vehicles at an Unsignalized Intersection
### Literature Review  
Traditional methods to avoid vehicle conflicts at intersections generally include two approaches. The first involves setting up traffic signals, which use signal control to separate vehicles in both time and space, thereby preventing conflicts [16; 17; 18; 19; 20]. Huang et al. [16] proposed a reservation-based traffic signal control method for mixed traffic flow at intersections. The simulation results showed that the proposed method is superior to the actuated traffic signal control. Yao et al. [17] developed a dynamic predictive traffic signal control framework in a cross-sectional vehicle infrastructure integration environment. The results showed that, compared with the traditional full-actuated control, the proposed method can reduce the average delay and queue length by up to 33% and 35%, respectively. Yao et al. [18] proposed a cell transmission model (CTM)-based traffic signal timing of mixed traffic flow with connected automated vehicles. The results show that the proposed model can effectively reduce the range and dissipation time of traffic congestion. Mirchandani et al. [19] developed a real-time traffic signal control system. Moreover, Feng et al. [20] proposed a real-time adaptive traffic signal control in a connected vehicle environment. The simulation results showed that the proposed algorithm outperforms actuated control by reducing the total delay by as much as 16.33% in a high-penetration rate case and by a similar amount in a low-penetration rate case.  
The second approach involves placing stop signs at the entrance to intersections and requiring vehicles entering the intersection to stop and yield when their path conflicts with vehicles already within the intersection [21; 22; 23; 24]. Brilon and Wu [21] developed a new simplified theoretical approach for the determination of capacities at unsignalized intersections. Heidemann and Wegmann [22] proposed a general queueing theory model for traffic flow at unsignalized intersections. The numerical results showed that the proposed model can capture the traffic flow at unsignalized intersections. Krbalek et al. [23] developed statistical aspects of gap acceptance theory for investigating unsignalized intersection capacity. Moreover, this paper estimated an implicit acceptance rule, with the help of a situation in which a minor street driver is deciding on the acceptance/rejection of an offered priority clearance. Li et al. [24] investigated the phase diagrams of traffic states induced by the bottleneck of an unsignalized intersection, which consists of two perpendicular one-lane roads. The results of the theoretical analysis are in good agreement with the computer simulation.  
Consequently, the first method is suitable for any scenario, while the second only applies to situations with low intersection traffic flow. With the advancement of vehicle-infrastructure cooperated autonomous driving, some scholars have attempted to optimize the sequence of vehicles passing through intersections to avoid conflicts [25; 26; 27; 28; 29]. These methods can also be divided into two categories. The first is based on traffic signal optimization, emphasizing collaborative optimization between vehicles and traffic signals [30; 31; 32]. The second assumes all vehicles are CAVs, eliminating the need for traffic signals at intersections. Instead, it only requires assigning a reasonable sequence for vehicles to arrive at the intersection, thereby preventing conflicts between vehicles [33; 34; 35]. For the second control method, the main issues in existing research are as follows: (1) when the optimization time window is long, the algorithm takes a considerable amount of time to solve, resulting in low efficiency; (2) the connection between different optimization time windows is not considered, making the algorithm theoretical and difficult to apply in practice; and (3) the influence mechanism of the key model parameters on the results is not analyzed.