地铁候车厅客流运动的数学模型

Mathematical model for the passenger flow in subway station waiting rooms

通过对上海地铁一号线车站候车厅内的客流运动进行实地观测和统计分析,借助流体力学比拟思想,将地铁站台内的客流运动比拟为一维和二维空间流体的运动,从而建立了定量描述地铁站台客流运动的数学模型。选取的观测对象为上海地铁一号线人民广场站和陕西南路站,在观测中发现同一列车在同一站点不同车门上下车人数呈空间不均匀分布,在此基础上建立了地铁候车厅近车门处客流速度-密度的一维和二维数学模型。根据模型计算了上车时间,将其与实测数据比较,两者吻合较好,表明该模型具有合理性。通过应用该模型,显示了其工程意义。

This article is based on the observation and statistics analysis of the movement of people in subway station waiting rooms. We choose two important subway stations of No.1 subway line in Shanghai which are People Square Station and South Shanxi Road Station for our experiment. It is found that the space distribution unevenness of the people's flow exits in different train doors of the same station at one time. Two velocity-density mathematical models are put forward. One is 1-d model about the movement of people near train door region in the waiting room and the other is 2-d model for getting on train people of the whole room. The time of people getting on train is formulated, and it accords with the observe data. It is also predicted by the new model that the time of people getting on train under the influence of safety separate wall.