基于非对称作用的二维优化速度改进模型

摘要

【目的】通过分析行人流非对称作用的二维优化速度改进模型的稳定性,探讨行人交通流拥堵的临界行为。【方法】在二维优化速度模型基础上,用非对称作用力函数形式代替原来的对称力函数,并考虑后方行人的作用强度,提出一个改进的二维优化速度模型。【结果】通过线性稳定性分析得出沿ψ=0,π/6,π/3,π/2方向传播的横波模式和纵波模式的稳定性条件,以及改进后的模型相图。在扰动波沿 x 轴传播的情况下,行人流的稳定性与敏感性系数 a 、行人间的距离 r 以及后方行人的作用强度λ同时相关；在其它情况下,稳定性条件都只与行人间的距离 r 有关。改进的模型中沿着 x 轴方向传播的纵波模式的临界曲线沿着 r 轴向左移动,且临界曲线下方的区域变得更小；而沿着 x 轴方向传播的横波模式的临界曲线沿着 r 轴向右移动,且临界曲线下方的区域变大。【结论】后方行人的作用强度对行人交通拥堵有较大的影响。%[Objective]The critical behavior of congestion of pedestrian traffic is explored by ana-lyzing the stability of two-dimensional optimal velocity model with the asymmetrical force.[Methods]Based on the two-dimensional optimal velocity model,an improved optimal velocity model is proposed by applying the asymmetrical force in the place of the symmetrical force and introducing the interaction with following pedestrians.[Results]The stability conditions of the transverse mode and longitudinal mode along the direction ofψ =0,π/6,π/3,π/2 are obtained by linear stability analysis,and the related phase diagrams are given.When the perturbation travels along the x axis,the stability condition of pedestrian flow is influenced by the sensitivity a , the distance r among pedestrians and the intensi-tyλ of interaction with the following pedestri-ans.But in the other cases,the stability condi-tions are only influenced by the distance r .The critical curve of longitudinal mode which travels along the x axis moves leftward along the r-axis and the regions below the critical curve becomes small.But the critical curve of transverse mode which travels along the x axis moves rightward along the r-axis and the regions below the criti-cal curve becomes large.[Conclusion]It is found that the intensityλof interaction with the fol-lowing pedestrians has great effect on congestion of pedestrian traffic.