  We derive macroscopic traffic equations from specific gas-kinetic equations,
dropping some of the assumptions and approximations made in previous papers.
The resulting partial differential equations for the vehicle density and
average velocity contain a non-local interaction term which is very favorable
for a fast and robust numerical integration, so that several thousand freeway
kilometers can be simulated in real-time. The model parameters can be easily
calibrated by means of empirical data. They are directly related to the
quantities characterizing individual driver-vehicle behavior, and their optimal
values have the expected order of magnitude. Therefore, they allow to
investigate the influences of varying street and weather conditions or freeway
control measures. Simulation results for realistic model parameters are in good
agreement with the diverse non-linear dynamical phenomena observed in freeway
traffic.
