| 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。 |
| 关键词: 行人流 优化速度模型 行人交通拥堵 |
| DOI： |
| 投稿时间：2015-05-27修订日期：2015-06-18 |
| 基金项目:国家重点基础研究发展计划(973计划)项目(2012CB725404),国家自然科学基金项目(11162019,11262003),广西自然科学基金青年项目(2014GXNSFBA118019,2013GXNSFBA019014)和玉林师范学院科研项目(2013YJZD01)资助。 |
|
| Improved Two-Dimensional Optimal Velocity Model Based on Asymmetric Interaction |
|
TIAN Huan-huan1,2, DONG Li-yun2, XUE Yu2,3
|
| (1.College of Physical Science and Engineering, Yulin Normal University, Yulin, Guangxi, 537000, China;2.Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai, 200072, China;3.College of Physical Science and Engineering, Guangxi University, Nanning, Guangxi, 530004, China) |
| Abstract: |
| [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 of φ=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 intensity λ of 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 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 critical curve becomes large.[Conclusion] It is found that the intensity λ of interaction with the following pedestrians has great effect on congestion of pedestrian traffic. |
| Key words: pedestrian flow optimal velocity model congestion of pedestrian traffic |
