  We present a new fluid-dynamical model of traffic flow. This model
generalizes the model of Aw and Rascle [SIAM J. Appl. Math. 60 916-938] and
Greenberg [SIAM J. Appl. Math 62 729-745] by prescribing a more general source
term to the velocity equation. This source term can be physically motivated by
experimental data, when taking into account relaxation and reaction time. In
particular, the new model has a (linearly) unstable regime as observed in
traffic dynamics. We develop a numerical code, which solves the corresponding
system of balance laws. Applying our code to a wide variety of initial data, we
find the observed inverse-$\lambda$ shape of the fundamental diagram of traffic
flow.
