  In this work, a family of finite volume discretization schemes for LWR-type
first order traffic flow models (with possible on- and off-ramps) is proposed:
the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are
formally equivalent to the kinetic systems used to model chemical reaction
networks. An in-depth numerical analysis of the TRM is performed. On the one
hand, the analytical properties of the scheme (nonnegative, conservative,
capacity-preserving, monotone) and its relation to more traditional schemes for
traffic flow models (Godunov, CTM) are presented. Finally, the link between the
TRM and kinetic systems is exploited to offer a novel compartmental
interpretation of traffic models. In particular, kinetic theory is used to
derive dynamical properties (namely persistence and Lyapunov stability) of the
TRM for a specific road configuration. Two extensions of the proposed model, to
networks and changing driving conditions, are also described.
