A Route Planning and Traffic Control Model for Autonomous Intersections by Minimizing Conflict Zones

Most existing studies on autonomous intersection management (AIM) primarily focus on modeling and resolving conflicts between vehicles within an intersection, assuming predetermined routes of the autonomous vehicles (AVs) as exogenous inputs. Additionally, these studies presume scenarios in which AVs traverse the intersection at a constant speed without stopping. However, such scenarios are difficult to realize under heavy traffic demand. To address this issue, this study first discretized the intersection into numerous grids and proposed formulations to calculate the time at which the vehicles enter and exit a given grid at different speeds and accelerations based on the outer-boundary-projection dimension-reduction method. Thereafter, a bi-level programming model was established to optimize the route choices and traffic control schemes. The upper-level model aimed to minimize the conflicts within the intersection zones, considering the lane options for vehicles entering and exiting the intersection as the decision variable to optimize the AV routes. In addition, the lower-level model strived to minimize the delay for all upcoming vehicles. The time when a vehicle enters an intersection and whether it stops are utilized as decision variables. Based on the sliding time-window technique, the proposed model was transformed into a mixed-integer linear programming (MILP) problem, which is compiled by a mathematical programming language (AMPL) and solved by CPLEX. The numerical analysis shows that the proposed models significantly reduced the conflicts between the vehicles, and consequently, improved the space utilization of the intersection, reduced vehicle delays, and saved a significant amount of energy.