Flow-maximizing equilibria of the Cell Transmission Model

We consider the freeway ramp metering problem, based on the Cell Transmission Model and address the question of how well decentralized control strategies, e.g. local feedback controllers at every onramp, can maximize the traffic flow asymptotically under time-invariant boundary conditions. We extend previous results on the structure of steady-state solutions of the Cell Transmission Model and use them to optimize over the set of equilibria. By using duality arguments, we derive optimality conditions and show that closed-loop equilibria of certain decentralized feedback controllers, in particular the practically successful “ALINEA” method, are in fact globally optimal.