Traffic Control in a Mixed Autonomy Scenario at Urban Intersections: An Optimal Control Approach

We consider an intersection zone where autonomous vehicles (AVs) and human-driven vehicles (HDVs) can be simulteneously present. As a new vehicle arrives, the traffic controller needs to decide and suggest an optimal sequence of the vehicles which will exit the intersection zone. The traffic controller can inform the time at which an AV can cross the intersection; however, the traffic controller can not communicate with the HDVs, rather the HDVs can only be controlled using the traffic lights. We formulate the problem as an integer constrained nonlinear optimization problem. Since the number of possible combinations increases exponentially with the number of vehicles in the traffic system, we relax the original problem and proposes an algorithm which gives the optimal solution of the relaxed problem and yet only scales linearly with the number of vehicles in the system. The numerical validation shows that our algorithm outperforms the First-In-First-Out (FIFO) algorithm.