基于安全间隙模型的行人动力学基本图
Fundamental Diagram of Pedestrian Dynamics by Safety Interspace Model
摘要：
NaSch模型是一种经典的高速公路交通一维元胞自动机（CA）模型。然而，由于车辆和行人之间的动力学差异，它不适合模拟行人动力学。在NaSch模型的基础上，提出了一种新的安全间距模型，用于研究单行行人流。我们对Seyfried在2006年的实验进行了定量模拟和再现，并利用实验数据对模型进行了验证。将安全空间定义为流速的线性函数，并引入正态分布的随机变量来描述空间认知的随机性。同时，将NaSch模型在空间划分上由单网格模式扩展为多网格模式，以提高空间分辨率。结果表明，通过三个模型参数的选取，新模型能够忠实地再现经验数据的基本图形的典型形态。模拟得到的速度-密度曲线可以反映出经验数据所观察到的基本图上的不连续区域。此外，我们再现了走走停停的波和相位分离到一个停车区和行人在高密度缓慢行走的区域。
英文摘要：
The NaSch model is a classical one-dimensional cellular automata (CA) model of freeway traffic. However, it is not suitable for simulating pedestrian dynamics due to the kinetic difference between vehicles and pedestrians. Based on NaSch model, we proposed a new safety interspace model to investigate the single-file pedestrian stream. We simulated and reproduced Seyfried's experiment in 2006 quantitatively and use the empirical data to validate our model. We defined the safety interspace as a linear function of current velocity and introduced a normal distributed random variable to describe the randomness of spatial cognition. Meanwhile, we extended NaSch model in space partition from single-grid mode to multi-gird mode to increase spatial resolution. It was found that through three model perimeters with appropriate values, the new model could reproduce faithfully the typical form of the fundamental diagram from empirical data. The velocity-density curve in simulation could indicate the discontinuity areas in fundamental diagram observed from empirical data. In addition, we reproduced the stop-and-go waves and phase separation into a stopping area and an area where pedestrians walk slowly at high density.
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