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 mode
l 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.
Modeling of headway/spacing between two consecutive vehicles has many applications in traffic flow theory and transport practice. Most known approaches only study the vehicles running on freeways. In this paper, we propose a model to explain the spac
ing distribution of queuing vehicles in front of a signalized junction based on random-matrix theory. We show that the recently measured spacing distribution data well fit the spacing distribution of a Gaussian symplectic ensemble (GSE). These results are also compared with the spacing distribution observed for car parking problem. Why vehicle-stationary-queuing and vehicle-parking have different spacing distributions (GSE vs GUE) seems to lie in the difference of driving patterns.
