  We derive a nonlinear 2-equation discrete-velocity model for traffic flow
from a continuous kinetic model. The model converges to scalar
Lighthill-Whitham type equations in the relaxation limit for all ranges of
traffic data. Moreover, the model has an invariant domain appropriate for
traffic flow modeling. It shows some similarities with the Aw-Rascle traffic
model. However, the new model is simpler and yields, in case of a concave
fundamental diagram, an example for a totally linear degenerate hyperbolic
relaxation model. We discuss the details of the hyperbolic main part and
consider boundary conditions for the limit equations derived from the
relaxation model. Moreover, we investigate the cluster dynamics of the model
for vanishing braking distance and consider a relaxation scheme build on the
kinetic discrete velocity model. Finally, numerical results for various
situations are presented, illustrating the analytical results.
