考虑车辆协同与时间延迟的跟驰模型的弱非线性分析

WEAK NONLINEAR ANALYSIS OF CAR-FOLLOWING MODEL CONSIDERING VEHICLE COLLABORATION AND TIME DELAY

为解决交通系统中合作驾驶引起的交通流问题,提出一种广义力跟驰模型。采用线性稳定性理论分析法推导出模型的线性稳定性条件并分析车辆协同与时滞组合对交通流稳定性的影响。通过非线性分析方法推导出考虑合作与时滞的车辆跟驰模型的Burgers方程与KdV方程,并给出它们的孤立波解及约束条件。利用解析法与数值分析法研究交通波演化过程中合作最优速度(OV)模型。实验结果表明,合作与延迟是依赖于模型的,车辆协同作用有利于抑制交通阻塞,传感器对延迟车辆的延迟检测在一定程度上有利于缓解失稳效应。

In order to solve the traffic flow problems caused by cooperative driving in traffic system,a generalized car-following model is proposed.The linear stability condition of the model was deduced by using the linear stability theory analysis method,and the influence of vehicle coordination and time delay combination on traffic flow stability was analyzed.Burgers equation and KdV equation of car-following model with cooperation and time delay were derived by means of non-linear analysis method,and their solitary wave solutions and constraints were given.The cooperative optimal velocity(OV)model in the process of traffic wave evolution was studied by analytic method and numerical analysis method.The experimental results show that cooperation and delay depend on the model.Vehicle coordination is beneficial to restrain traffic congestion.Sensor delay detection for delayed vehicles is helpful to alleviate the instability effect to a certain extent.