Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model

We derive macroscopic traffic equations from specific gas-kinetic equations , dropping some of the assumptions and approximations made in previous pape rs. The resulting partial differential equations for the vehicle density an d average velocity contain a nonlocal interaction term which is very favora ble for a fast and robust numerical integration, so that several thousand f reeway kilometers can be simulated in real time. The model parameters can b e easily calibrated by means of empirical data. They are directly related t o the quantities characterizing individual driver-vehicle behavior, and the ir optimal values have the expected order of magnitude. Therefore, they all ow one to investigate the influences of varying street and weather conditio ns or freeway control measures. Simulation results for realistic model para meters are in good agreement with the diverse nonlinear dynamical phenomena observed in freeway traffic. [S1063-651X(99)10501-4].