Different from previous models based on scatter theory and random matrix theory, a new interpretation of the observed log-normal type time-headway distribution of vehicles is presented in this paper. Inspired by the well known Galton Board, this model views drivers velocity adjusting process similar to the dynamics of a particle falling down a board and being deviated at decision points. A new car-following model based on this idea is proposed to reproduce the observed traffic flow phenomena. The agreement between the empirical observations and the simulation results suggests the soundness of this new approach.
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