# Virtual Belt Algorithm for the Management of Isolated Autonomous Intersection  
Chetong Bian  
School of Mechanical Engineering, Southeast University, Nanjing 211189, China; [EMAIL_ADDRESS] (C.B. ); [EMAIL_ADDRESS] (L.X. ); [EMAIL_ADDRESS] (N.Z.) [PERSON]  
Correspondence: [EMAIL_ADDRESS]; Tel. : +86-025-5209-0501 (ext. 8333)  
Liwei Xu  
School of Mechanical Engineering, Southeast University, Nanjing 211189, China; [EMAIL_ADDRESS] (C.B. ); [EMAIL_ADDRESS] (L.X. ); [EMAIL_ADDRESS] (N.Z.) Xu  
there is no such an optimization problem. The permissions of CAVs to pass an intersection are determined by a predefined policy. The global-trajectory-optimization based algorithms mainly include model predictive control [9], genetic algorithm [10], mix-integer non-linear programming [11], mix-integer linear programming [12; 13], integer linear programming [14], linear programming [8], etc. Using optimization, these algorithms can plan the trajectories of the CAVs at an intersection simultaneously to improve traffic efficiency. The main advantage of these algorithms is that the optimal calculation can be used to find an optimal or a local optimal solution for intersection management. Thus, theoretically, these algorithms show better performance than the non-global-trajectory-optimization-based algorithms. The major disadvantage of these algorithms is the high requirement for calculation. Due to the coupling of vehicle trajectories, these algorithms have to simultaneously control all CAVs at an intersection (at least within a certain range including all conflict zones), which leads to a high requirement for calculation from two aspects. First, the count of decision variables of optimal calculation increases with the count of CAVs, which aggravates the calculation burden. Second, even the trajectories of all CAVs at collision zones have been planned, these trajectories have to be planned again when a new approaching CAV is found. Thus, the trajectory of a CAV may be planned again and again, which further increases the high requirement for calculation. The non-global-trajectory-optimization based algorithms mainly include cooperative adaptive cruise control [15; 16], multi-agent [1; 17], priorities and brake-safe control based algorithm [18], auction [19] (or market [20]) based algorithm, buffer-assignment mechanism algorithm [21], platoon based algorithm [22], slots preassigning [23], virtual traffic light [24], and the combination of these algorithms [25], etc. These algorithms can improve traffic efficiency by coordinating the orders of CAVs to pass intersections. The main advantage of these algorithms is the low computation burden. Thus, they can be easily applied for the intersections with a large number of CAVs. The disadvantage is that there is only one candidate trajectory for a CAV during a control circle. If there are potential collisions for a CAV, the CAV will have to slow down or stop to wait for a possible permission next control circle. Thus, there are still some potentials to improve traffic efficiency if more trajectories are designed and compared in a control circle. Aiming to enhance traffic efficiency, a VB algorithm is proposed for the management of an isolated autonomous intersection. The proposed algorithm is divided into an offline algorithm and an online algorithm. By the proposed algorithm, most of the calculation caused by the coupling of vehicle trajectories can be done offline. There is no optimization problem to calculate the trajectories of all CAVs simultaneously in the VB algorithm. Thus, the VB algorithm is a no-global-trajectory-optimization based algorithm. Compared with previous no-global-trajectory-optimization based algorithms, the main advantage of the proposed algorithm is that, there are several candidate trajectories can be chose for a CAV to pass an intersection in a control circle. Thus, there are more opportunities for an approaching CAV to get a permission to pass an intersection.