优化车流的交通流格子模型

在一维交通流格子模型的基础上，分别提出考虑最近邻车和次近邻车以及考虑前、后近邻车相互作用进行车流优化的一维交通流格子模型.应用线性稳定性理论和非线性理论进行分析，得出车流的稳定性条件，并导出了描述交通阻塞相变的mKdV方程.用数值模拟验证了mKdV方程的解，数值模拟结果表明考虑最近邻车和次近邻车的优化车流能够增强车流稳定性，而考虑前、后近邻车的优化车流将使稳定性减小. 关键词： 交通流 交通相变 稳定判据 mKdV方程

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.