Derivation and empirical validation of a refined traffic flow model

The gas-kinetic foundation of fluid-dynamic traffic equations suggested in previous papers (D. Helbing, Physica A 219 (1995) 375 and 391) is further refined by applying the theory of dense gases and granular materials to the Boltzmann-like traffic model by Paveri-Fontana. It is shown that, despite the phenomenologically similar behavior of ordinary and granular fluids, the relations for these cannot directly be transferred to vehicular traffic. The dissipative and anisotropic interactions of vehicles as well as their velocity-dependent space requirements lead to a considerably different structure of the macroscopic traffic equations, also in comparison with the previously suggested traffic flow models. As a consequence, the instability mechanisms of emergent density waves are different. Crucial assumptions are validated by empirical traffic data and essential results are illustrated by figures.