Modeling, forecasting and game control of road traffic systems

The Grenoble Traffic Lab (GTL http://necs.inrialpes.fr/pages/reseach/gtl.php) initiative is a real-time traffic data center (platform) intended to collect traffic road infrastructure information in real-time with minimum latency and fast sampling periods. This lecture includes several aspects on modeling, forecasting and control of traffic systems, which are applied to the GTL. In this presentation, we first review main flow-conservation models which are used as a basis to design physical-oriented forecasting & control algorithms. In particular we underline fundamental properties like downstream/upstream controllability and observability of such models, and present a new network set-up for analysis. Then we present advances in traffic forecasting using graph-constrained macroscopic models which substantially reduce the number of possible affine dynamics of the system and preserve the number of vehicles in the network. This model is used to recover the state of the traffic network and precisely localize the eventual congestion front. The last part of the talk we discuss issues on optimal density balancing control based on game theory, where the objective is to design the homogeneous distribution of density on the freeway using the input flows as decision variables. The problem is formulated by using Nash game theory and a suitable controllability partition of the system.