Optimal Signal Timing for Multi-Phase Intersections

We present an optimal signal timing policy for multi-phase intersections. The policy is optimal in the sense of minimizing the increase in the number of queuing vehicles, i.e. maximizing throughput, within one signal cycle. By introducing weights in the optimality criterion, our solution also accommodates the setting of prioritized traffic, in which it is more important for certain classes of traffic to wait for a shorter time. The proposed signal timing policy is simple to compute and implement. In particular, we show that the proposed strategy can be computed as a solution to a linear programming problem. Additionally, upon parametrizing the proposed policy with respect to the vehicle queue lengths, we analyze some aspects of the multi-cycle behavior of the closed-loop system generated by the policy, most notably convergence of the queue lengths over time. Finally, we illustrate the proposed control law with two numerical examples, one of which is based on real data collected from an existing complex multi-phase intersection.