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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 nonlocal 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 one 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 nonlinear dynamical phenomena observed in freeway traffic.
Treiber et al. (1999) studied this question.