车–车互联下多前车速度差的跟驰模型  

A Car-Following Model of the Velocity Difference of Multiple Front Vehicles Considering Vehicle-Vehicle Internet

作　　者：李良鹏 化存才[1] 

机构地区：[1]云南师范大学数学学院,云南 昆明

出　　处：《应用数学进展》2021年第7期2292-2304,共13页Advances in Applied Mathematics

摘　　要：基于多前车速度差跟驰模型(MCF),考虑在车联网环境下,车辆安装V2V设备后可提前时间获得多前车的速度信息,提出了一种改进的多前车速度差模型(MCF-CT)。首先,通过线性稳定性分析得到该模型的稳定性条件,发现随着多前车数量m和提前时间t0的增大,交通流的稳定区域面积明显扩大,其占比增加至89.03% (m = 3, t0 = 0.75 s)。其次,通过约化摄动方法导出了密度波方程——Burgers方程、mKdv方程,并给出Burgers的孤波解,mKdv方程的扭结—反扭结波解;最后,通过对MCF-CT模型和全速度差模型(FVD)在车间距减少5 m的紧急情况下的数值模拟,发现当MCF-CT模型中的m = 3,t0 = 0.3 s时,可以避免车辆碰撞的发生。Based on the multiple front vehicle velocity difference car-following model (MCF), and by considering that the velocity information of multi front vehicles can be obtained t0 time in advance after the vehicle is installed with V2V equipment under the environment of Internet of vehicles, an improved multiple front vehicle velocity difference model (named MCF-CT) is proposed. Firstly, the stability condition of the model is obtained by linear stability analysis. It is found that the area of the stable region enlarges obviously as number m of vehicles and the advanced time t0 increase. The ratio of the area of the stable region from attains to 89.03% (m = 3, t0 = 0.75 s). Secondly, the density wave equations—Burgers, mKdv, are derived, by using the reduced perturbation method. The solitary wave solutions of Burgers and the kink anti kink wave solutions of mKdv are given. Finally, numerical simulation results are given for the MCF-CT model and the full velocity difference model (FVD) in the case of an emergency in which the distance between vehicles is reduced by 5 m. It is found that collision can be avoided for the MCF-CT model as m = 3, t0 = 0.3 s.

关 键 词：跟驰模型 BURGERS方程 MKDV方程 数值模拟 

分 类 号：O17[理学—数学]