Decentralized control of traffic networks

An arbitrary interconnected network of intersecting streets with one-way traffic flow is considered in which some or all intersections are assumed to be operating at maximum capacity. In this case, it is desired to find a robust decentralized controller at each traffic intersection, so that for all perturbed external traffic flow sources/sinks, the resulting perturbed queues at each intersection are asymptotically "balanced". The only local knowledge required of the controllers at each intersection is that re the queue lengths of the intersection. It is shown that the necessary and sufficient conditions for a solution to the problem to exist depend solely on the topology of the network and the percentage of vehicles turning at each intersection, and are identical to the conditions required for a solution to exist for the centralized controller case. In particular, it is shown that if turns always occur at an intersection, then a solution to the problem always exists. A characterization of controllers which solve the problem are then given. In particular, it is shown that the local controllers which solve the problem are identical to each other, which implies that if the network is expanded (assuming a solution exists) then one can use the same local controllers to solve the problem. It is also shown that the local controllers can, in principle, give "perfect control" to the problem. Some examples are included to illustrate the results.