A Lagrangian state-space representation of a macroscopic traffic flow model

We obtain a state space representation of a first order macroscopic model from a Godunov discretization of its Lagrangian reformulation. The resulting model comprises four linear regimes, each of which comes into effect for the appropriate traffic conditions using a simple switching mechanism. Unlike previous state space models of traffic flow, ours is trajectory-based as opposed to density/velocity-based, although the latter quantities are nevertheless computed during the running of the model. The Lagrangian (moving) coordinates in this scheme should provide an ideal framework for the assimilation of GPS location data from probe vehicles.