Gas kinetics of traffic jam

The kinetics of one-dimensional traffic flow is descibed in terms of Boltzmann-like gas kinetic equation. Paveri-Fontana's gas kinetic equation is modified to take into account the desired velocity depending on the car density. A discrete version of the gas kinetic equation is derived to numerically solve the equation. The velocity distributions are calculated by a numerical method. It is found that the traffic jam is formed in the congested traffic flow when the car density is higher than the critical value. The traffic jam propagates backward, its propagation velocity increases with the accerelation and the density within the jam decreases with increasing accerelation. It is shown that the velocity distributions change significantly before and after the traffic jam.