A New Lattice Model for Traffic Flow and Its Analysis

A new lattice model of traffic is proposed to describe the motion of the dynamical traffic flow with a consideration of an arbitrary number lattice sites before the current lattice site which is different from Ge's model. The stability condition is got by using linear stability analysis and introducing a small perturbation into the uniform traffic flow. The stability of the uniform flow is strengthened by the effect of taking an arbitrary number front lattice sites into account. The modified KdV equation is derived by using the nonlinear analysis method and the kink-antikink soliton solution is obtained near the critical point. The simulation results are consistent with the analytical results and the new lattice model is valid.