Numerical study of traffic flow considering the probability density distribution of the traffic density

The probability density distribution of the traffic density is analyzed based on the empirical data. It is found that the beta distribution can fit the result obtained from the measured traffic density perfectly. Then a modified traffic model is proposed to simulate the microscopic traffic flow, in which the probability density distribution of the traffic density is taken into account. The model also contains the behavior of drivers’ speed adaptation by taking into account the driving behavior difference and the dynamic headway. Accompanied by presenting the flux-density diagrams, the velocity evolution diagrams and the spatial-temporal profiles of vehicles are also given. The synchronized flow phase and the wide moving jam phase are indicated, which is the challenge for the cellular automata traffic model. Furthermore the phenomenon of the high speed car-following is exhibited, which has been observed in the measured data previously. The results set demonstrate the effectiveness of the proposed model in detecting the complicated dynamic phenomena of the traffic flow.