Flow-Maximizing Equilibria of the Cell Transmission Model

M. Schmitt, P. J. Goulart, A. Georghiou and J. Lygeros

in European Control Conference, Linz, Austria, pp. 2634-2639, July 2015.
BibTeX  URL 

  author = {M. Schmitt and P. J. Goulart and A. Georghiou and J. Lygeros},
  title = {Flow-Maximizing Equilibria of the Cell Transmission Model},
  booktitle = {European Control Conference},
  year = {2015},
  pages = {2634-2639},
  url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7330935},
  doi = {10.1109/ECC.2015.7330935}

We consider the freeway ramp metering problem, based on the Cell Transmission Model. This work addresses the question of how well distributed 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 distributed feedback controllers, in particular the practically successful ‘‘ALINEA’’ method, are in fact globally optimal.