On maximally stabilizing traffic signal control with unknown turn ratios

This paper designs distributed dynamic traffic signal control policies for urban traffic networks. Vehicles at the end of an approach to an intersection queue up in separate lanes corresponding to different possible turn maneuvers at the upcoming intersection, according to fixed turn ratios. The departure rate of vehicles from the queue is governed by traffic signal control at the intersections. We consider traffic signal control architectures under which, at every intersection, only a subset of non-conflicting approaches get green light simultaneously. We propose a class of cooperative green light policies, under which traffic signal control at an intersection requires information only about the occupancy levels on the lanes incoming at that intersection. In particular, such a policy does not require information about turn ratios, external arrival rates or departure rates. We show that such minimalist policies are maximally stabilizing for acyclic network topologies under some scenarios, and, when the network is stabilizable, the network admits a globally asymptotically stable equilibrium under these policies. Simulations to illustrate the applicability of our results to cyclic network topologies are also presented.