多级速度效应模型的近似解

在速度效应模型的基础上，我们提出了多级速度效应模型．在建立该模型的过程中，我们将仅考虑本车之前第一辆车的虚拟速度推广至考虑前面多辆车的虚拟速度，因而该模型所包含的交通信息更为丰富，更能真实地反映实际道路交通状况．数值模拟得到的基本图显示： 存在交通噪声（随机减速概率p 0）时，较之NaSch模型更接近于实测数据；无交通噪声（随机减速概率p＝0）时，能诱发亚稳态和迟滞现象．进一步借助于平均场理论，获得了多级速度效应模型在有交通噪声时流量的近似解，无交通噪声时流量的精确解．

Analytical results for the multi-virtual-velocity traffic model

Based on the virtual velocity cellular automaton (CA, for short) traffic model, we propose the multi-virtual-velocity CA traffic model via considering many-neighbor interaction ahead. On the one hand, the fundamental diagrams obtained from the numerical simulation approach to the empirical data by comparing with the NaSch model under the same traffic noise. On the other hand, there exists the meta-stable state and hysteresis without traffic noise. Moreover, with the help of mean-field theory, we obtain analytical solutions of this model.