基于非对称作用的二维优化速度改进模型

Improved Two-Dimensional Optimal Velocity Model Based on Asymmetric Interaction

【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φ=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 analyzing 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 ofφ =0,π/6,π/3,π/2are obtainedby linear stability analysis,and the related phase diagrams are given.When the perturbation travels along the xaxis,the stability condition of pedestrian flow is influenced by the sensitivity a,the distance ramong pedestrians and the intensityλof interaction with the following pedestrians.But in the other cases,the stability conditions are only influenced by the distance r.The critical curve of longitudinal mode which travels along the xaxis moves leftward along the r-axisand the regions below the critical curve becomes small.But the critical curve of transverse mode which travels along the xaxis moves rightward along the r-axis and the regions below the critical curve becomes large.【Conclusion】It is found that the intensityλof interaction with the following pedestrians has great effect on congestion of pedestrian traffic.