Optimal Ramp Metering Strategy with Extended LWR Model, Analysis and Computational Methods

Authors:	Jacquet Denis, Institut National Polytechnique de Grenoble, France Canudas de Wit Carlos, Institut National Polytechnique de Grenoble, France Koenig Damien, Institut National Polytechnique de Grenoble, France
Topic:	2.4 Optimal Control
Session:	Optimal Control Applications
Keywords:	optimal control, traffic control

Abstract

This paper treats the problem of optimizing a coordinated ramp metering strategy based on a distributed macroscopic traffic model. The Lighthill, Whitham and Richards (LWR) model is extended to include on/off-ramps with on-ramp flow saturations and an optimal control formulation is proposed. Using optimization techniques in Banach spaces, a solution is shown to exist and the necessary optimality system is stated using formal adjoint calculus. An iterative descent algorithm and numerical methods for gradient evaluations are proposed to compute the optimal strategy with reasonable effort. The effectiveness of the approach is illustrated through a study case with field data.