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双出口房间人群疏散的实验研究和数学建模
Exp erimental features and mathematical mo del of p edestrian evacuation from a ro om with two exits
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摘要: 本文设计了一个双出口房间内人群疏散的实验方案，通过不同条件下疏散过程的实况录像及视频检测，得到不同人数疏散时间的许多定量结果。提出了双出口房间吸引区间的概念，证明了较小出口吸引区间的边界总是一段圆弧，可以解释行人流出口处的圆形成拱现象。通过类比地铁候车厅内人群疏散过程，建立了双出口房间内疏散时间的二次函数模型，成功拟合不同条件下的实测数据。疏散人数较少时，疏散时间随着人数增加而线性增长；人数较多，在出口附近出现待行区域时，疏散时间则呈二次函数增长。与一些已知疏散时间数学模型相比，本文模型对出口宽度变化的反应更敏感。Abstract: A set of experimental schemes of pedestrian evacuation from a room having two exits is proposed and applied to experiments. Some quantitative results of evacuation time varying with the number of pedestrians in different circum-stances are obtained from the video recordings. The concept of attraction domain of a two-exit room is established. It is proved that the boundary curve of attraction domain of the smaller exit is always a circular arch, by which the mechanism of arch formation near an exit can be illustrated. Compared with the passenger evacuation procedure in a subway waiting hall, we have established a quadratic function model of evacuation time which can fit the measured data well for various cases. The evacuation time increases linearly with the number of people without waiting, and increases as a quadratic function of the number of people after the formation of a waiting region. It is also found that the expression is affected by the width of exit more sensitively than in other well-known models.
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