A continuum theory for the flow of pedestrians
A continuum theory for the flow of pedestrians
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DOI：
10.1016/s0191-2615(01)00015-7
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发表时间：
2002-07-01
影响因子：
6.8
通讯作者：
Hughes, RL
中科院分区：
文献类型：
--
作者：
Hughes, RL
运动方程的二维流动的行人推导出单一和多个行人类型的流量。两种流动状态，高密度（亚临界）和低密度（超临界）流动状态是可能的。而不是针对每种类型的行人的两种流态。亚临界流总是充满可用空间。然而，根据边界位置，超临界流可以填充可用的空间，或者对于每种类型的行人是自限制的。虽然，这些流动的方程是同时的，时间相关的，非线性的，偏微分方程，显着他们可以共形映射。这些方程的解在许多情况下变得微不足道。自由流线计算，利用这一属性，揭示了上游和下游分离的行人流周围的障碍。这样的分析告诉了很多关于行人流量的各种模型中使用的假设的性质。目前的理论是为发展一般技术，以了解运动的大型人群。然而，它也是一种有用的预测工具。这些方程的运动预测的行为进行比较，沙特阿拉伯麦加附近的Jamarat桥的空中观测。它表明，在这个重要的情况下，行人，也就是朝圣者，旨在实现每个最小的什一税，而不是在整体上最小的时间内实现所有目标的直接目标。在许多典型的例子中，这个案例说明了路径对所涉及的行人的心理状态的强烈依赖。建议通过适当的障碍物放置来改善Jamarat桥上的行人流量，这迫使人们有效地看待目标。(C)2002爱思唯尔科技有限公司版权所有。
The equations of motion governing the two-dimensional flow of pedestrians are derived for flows of both single and multiple pedestrian types. Two regimes of flow, a high-density (subcritical) and a low-density (supercritical) flow regimes, are possible. rather than two flow regimes for each type of pedestrian. A subcritical flow, always fills the space available. However, a supercritical flow may either fill the space available or be self-confining for each type of pedestrian, depending on the boundary location. Although, the equations governing these flows are simultaneous, time-dependent, non-linear, partial differential equations, remarkably they may be made conformally mappable. The solution of these equations becomes trivial in many situations. Free streamline calculations, utilizing this property, reveal both upstream and downstream separation of the flow of pedestrians around an obstacle. Such analysis tells much about the nature of the assumptions used in various models for the flow of pedestrians. The present theory is designed for the development of general techniques to understand the motion of large crowds. However, it is also useful as a predictive tool. The behavior predicted by these equations of motion is compared with aerial observations for the Jamarat Bridge near Mecca, Saudi Arabia. It is shown that, for this important case, pedestrians, that is pilgrims, aim at achieving each immediate goal in minimum tithe rather than achieving all goals in overall minimum time. Typical of many examples, this case illustrated the strong dependence of path on the psychological state of the pedestrians involved. It is proposed that the flow of pedestrians over the Jamarat Bridge be improved by appropriate barrier placement, that force an effective global view of the goals. (C) 2002 Elsevier Science Ltd. All rights reserved.