Traffic control and queues management for a single intersection

It is by now well known that, the traffic signal control is the most effective measure for reducing traffic congestion in an intersection. Traffic congestion arises when arrival rate exceeds capacity in the intersection. The most undesirable symptom of this kind of instability is an unbounded accumulation of vehicles in the system. Our contribution in this paper is to show that, for a single intersection, congestion can be prevented by using a state feedback controller having an appropriate positive structure. It is shown that two main objectives are achieved with the proposed controller: firstly, when traffic flow is not in excess, the queuing of automobiles cannot exceed intersection capacity. Secondly, in order to fit physically reasonable signalization, the controller respects the boundary conditions. Example is worked out to illustrate the results.