带有最优流量记忆时间差的一类新格子模型

为了分析最优流量记忆时间差对交通流稳定性的影响，本文基于考虑驾驶员估计得到的最优流量信息，同时考虑驾驶员在驾车过程中受到记忆时间的影响，给出了一类新的格子流体动力学模型.首先，基于线性稳定性理论，获得了新模型的稳定性条件；随后，通过非线性分析方法，给出该模型的mKdV方程；然后，基于求解上述方程所得到的扭结-反扭结孤立波可用于描述交通拥挤的转化和传播过程.最后，通过仿真算例验证了上述理论分析的结论，即驾驶员的记忆时间和最优流量记忆时间差能够显著影响交通流的稳定性，同时增大记忆时间步长和强度系数可以有效地增强交通流的稳定性.

A Class of New Lattice Model with Consideration of the Optimal Current Changes with Memory

Based on the effect of optimal current estimated by the driver, meanwhile, the driver is affected by the memory time during driving, in this paper, a new lattice model is presented with the consideration of the optimal current change with memory effect. The model’s linear stability condition is obtained by applying the linear stability theory, and through nonlinear analysis, a modified Korteweg-de Vries (mKdV) equation is derived to describe the propagating behavior of traffic density wave near the critical point. Numerical simulation verified that not only the sensitivity of the optimal velocity change with memory of driver but also the memory step could effectively stabilize the traffic flow. In addition, the stability of traffic flow is strengthened by increasing the memory step-size of optimal current changes and the intensity of drivers’ memory with such changes that the new model can improve the stability of traffic flow by adjusting the driver’s memory parameter, which is consistent with the theoretical analysis.