  Macroscopic traffic models have recently been severely criticized to base on
lax analogies only and to have a number of deficiencies. Therefore, this paper
shows how to construct a logically consistent fluid-dynamic traffic model from
basic laws for the acceleration and interaction of vehicles. These
considerations lead to the gas-kinetic traffic equation of Paveri-Fontana. Its
stationary and spatially homogeneous solution implies equilibrium relations for
the `fundamental diagram', the variance-density relation, and other quantities
which are partly difficult to determine empirically.
  Paveri-Fontana's traffic equation allows the derivation of macroscopic moment
equations which build a system of non-closed equations. This system can be
closed by the well proved method of Chapman and Enskog which leads to
Euler-like traffic equations in zeroth-order approximation and to
Navier-Stokes-like traffic equations in first-order approximation. The latter
are finally corrected for the finite space requirements of vehicles. It is
shown that the resulting model is able to withstand the above mentioned
criticism.

Statistical Mechanics