  We consider an intersection zone where autonomous vehicles (AVs) and
human-driven vehicles (HDVs) can be present. As a new vehicle arrives, the
traffic controller needs to decide and impose an optimal sequence of the
vehicles that will exit the intersection zone. The traffic controller can send
information regarding 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 non-linear optimization problem where the
traffic-intersection controller only communicates with a subset of the AVs.
Since the number of possible combinations increases exponentially with the
number of vehicles in the system, we relax the original problem and proposes an
algorithm that gives the optimal solution of the relaxed problem and yet only
scales linearly with the number of vehicles in the system. The numerical
evaluation shows that our algorithm outperforms the First-In-First-Out (FIFO)
algorithm.
