1. Shanghai Institute of Applied Mathematics and Mechanics,
Shanghai University, Shanghai 200072, China
;2. Department of Physics, Guangxi University, Nanning 530003,
China
Abstract:
The optimal velocity model of traffic is extended to take
the relative velocity into account. The traffic behavior is investigated
numerically and analytically with this model. It is shown that the car
interaction with the relative velocity can effect the stability of the
traffic flow and raise critical density. The jamming transition between
the freely moving and jamming phases is investigated with the linear
stability analysis and nonlinear perturbation methods. The traffic jam is
described by the kink solution of the modified Korteweg--de Vries equation.
The theoretical result is in good agreement with the simulation.