The theory of a jamming transition is proposed for the homogeneous car-following model within the framework of the Lorenz scheme. We represent a jamming transition as a result of the spontaneous deviations of headway and velocity that is caused by the acceleration/braking rate to be higher than the critical value. The stationary values of headway and velocity deviations and time of acceleration/braking are derived as functions of control parameter (time needed for car to take the characteristic velocity).

• Received 21 January 2000

DOI:https://doi.org/10.1103/PhysRevE.63.036116