  We study the derivation of macroscopic traffic models from car-following
vehicle dynamics by means of hydrodynamic limits of an Enskog-type kinetic
description. We consider the superposition of Follow-the-Leader (FTL)
interactions and relaxation towards a traffic-dependent Optimal Velocity (OV)
and we show that the resulting macroscopic models depend on the relative
frequency between these two microscopic processes. If FTL interactions dominate
then one gets an inhomogeneous Aw-Rascle-Zhang model, whose (pseudo) pressure
and stability of the uniform flow are precisely defined by some features of the
microscopic FTL and OV dynamics. Conversely, if the rate of OV relaxation is
comparable to that of FTL interactions then one gets a
Lighthill-Whitham-Richards model ruled only by the OV function. We further
confirm these findings by means of numerical simulations of the particle system
and the macroscopic models. Unlike other formally analogous results, our
approach builds the macroscopic models as physical limits of particle dynamics
rather than assessing the convergence of microscopic to macroscopic solutions
under suitable numerical discretisations.
