考虑多前车位置及分位数速度差跟驰模型稳定性分析

Stability analysis of car-following model considering multiple ahead vehicle positions and quantile velocity difference

为探究交通流特性对车辆跟驰行为的影响,基于分位数回归方法对跟驰模型进行改进,通过稳定性分析方法利用车头间距描述交通拥堵情况。根据分位数回归方法对模型中的优化速度函数进行改进,并将其应用于考虑多前车位置及速度差跟驰模型,使模型可以通过分位点的变换,在仿真过程中模拟不同驾驶风格的车辆。运用傅里叶变换理论推导出该模型的线性稳定性条件,并通过摄动法求得其修正Korteweg-de Vries(mKdV)方程的解,根据车头间距的扭结-反扭结解描述交通拥堵的变化情况。分析对比考虑不同因素的跟驰模型的稳定性临界曲线,为评估改进模型的有效性,搭建环形车道仿真平台并对改进模型进行数值实验。结果表明:在仿真实验中,随着分位点的增加,改进模型达到稳定状态的平均速度逐渐增加,车速分别为9.57、12.58、14.76 m/s;相比原模型,改进模型能够实现更少的位移波动,位移差最小为1.05 m;在混合模型实验中,随着激进驾驶风格车辆数量的增加,改进模型与多速度差模型相比,车队整体的平均速度达到12.42 m/s,位移波动能够达到稳定状态。

To investigate the influence of traffic flow characteristics on vehicle following behavior,this paper improves the car following model based on quantile regression method and describes the traffic congestion by the distance between the space headway through the stability analysis method.The optimized speed function in the model is improved based on the quantile regression method and it is applied to the car following model considering the position and velocity difference of multiple ahead vehicles,ensuring it can simulate vehicles with different driving styles in the simulation process by changing the quantile points.The linear stability conditions of the model are derived using Fourier transform theory,and the solution to the modified Korteweg-de Vries(mKdV)equation is obtained by using perturbation method,and the knot-anti-knot solution of the headway is obtained to describe the evolution of traffic congestion.The stability critical curves of the car-following models considering different factors are analyzed and compared.To evaluate the effectiveness of the improved model,a simulation platform for a circular roadway is built to perform numerical experiments on the improved model.Our results show the average speed of the improved model to reach the stable state gradually increases with the rises of the quantile points,and the vehicle speeds are 9.57 m/s,12.58 m/s and 14.76 m/s respectively.Compared with the original model,the improved model achieves less displacement fluctuation and its minimum displacement difference is 1.05 m.In the mixed model experiment,with the growing number of vehicles with aggressive driving style,the average speed of the whole fleet reaches 12.42 m/s,and the displacement fluctuation reaches a stable state.