Lattice models of the optimal traffic current

Based on the lattice model of traffic flow, the lattice models which consider the next-nearest-neighbour flow on traffic and pay attention to the following vehicle as well as the preceding vehicle are presented, respectively. The stability criterion is derived by the linear stability analysis. The evolution of density wave has been investigated analytically with the perturbation method. The results show that the occurrence of traffic jamming transitions is described by the kink solution of the modified KdV equation. The theoretical results are in good agreement with the simulation. Moreover, the simulation indicates that the lattice models considering the next-nearest-neighbour interaction can stabilize the traffic flow, but the other model is just in opposition to the former model.