Fokker-Planck equation approach to vehicle statistics

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This contribution presents a derivation of the steady-state distribution of velocities and distances of vehicles in freeway traffic which has been suggested for the evaluation of interaction potentials among vehicles (see preprint cond-mat/0301484). Despite the forwardly directed interactions and the additional driving terms in vehicle traffic, the steady-state velocity and distance distributions agree with the equilibrium distributions of classical many-particle systems with symmetrical interactions, if the system is large enough. Finally, this analytical result is confirmed by computer simulations.