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