# 特殊人群疏散特性的元胞自动机模拟Cellular Automata Simulation of Evacuation Characteristics of Special Pedestrian

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Based on cellular automata theory, the cellular automata model describing the normal pedestrian evacuation is extended to study the evacuation scenario including special pedestrians. Through analyzing the psychological characteristics of special pedestrians (This article mainly refers to the pedestrian who are unable to move freely), a cellular automaton model is established. The numerical simulations are performed to investigate the influence of the proportion and location distribution of special pedestrian on the evacuation process in the hall. The spatio-temporal dynamic characteristic of pedestrian evacuation process is also discussed. The results show that the effect of the special crowd on the whole evacuation efficiency is related to the total pedestrian density. At low density, this effect on the evacuation efficiency is not obvious, but with the increase of density, the proportion of special pedestrians will lead to a significant decrease in the evacuation efficiency. In addition, the location distribution of the special pedestrians will also affect the evacuation efficiency. Especially at high density, compared with the random distribution of the special pedestrians, to put them in a certain position and separate them from the normal pedestrians will reduce the overall evacuation time remarkably.

1. 引言

2. 模型

${p}_{i,j}=0\text{\hspace{0.17em}}\left(x,y\right)\notin {{S}^{\prime }}_{i,j}$ ；(行人下一步移动位置不为空，则停在原位置)

${p}_{i,j}=1/|{{S}^{\prime }}_{i,j}|\left(x,y\right)\in {{S}^{\prime }}_{i,j}$ ；(行人下一步移动位置为空，则等概率选择方向移动)

${p}_{i,j}=1\left(i,j\right)=\left({i}_{0},{j}_{0}\right)$ 。(行人在出口位置，则下一步一定移出系统)， $|{{S}^{\prime }}_{i,j}|$ 表示 ${{S}^{\prime }}_{i,j}$ 中元素个数。

3. 模拟结果与讨论

Figure 1. Sketch of model

(a)(b)

Figure 2. The selectable movement directions. (a) Normal pedestrians; (b) Pedestrians who are unable to move freely

Figure 3. Relationship between evacuation time T and density ρ under n = 0, 0.2, 0.4, 0.5, 0.8, 1

Figure 4. The typical spatial-temporal patterns as ρ = 0.7. n = 0: (a) T = 40 s, (b) T = 100 s, (c) T = 190 s; n = 0.2: (d) T = 40 s, (e) T = 100 s, (f) T = 190 s; n = 1: (g) T = 40 s, (h) T = 100 s, (i) T = 190 s

(a)(b)

Figure 5. The typical spatial-temporal patterns as ρ = 0.7. (a) T = 10 s; (b) T = 40 s

Figure 6. The distribution of pedestrians who are unable to move freely

Figure 7. Relationship between evacuation time T and case under n = 0.2, ρ = 0.1, 0.4, 0.7

4. 结论

1) 人群中加入行动不便行人将会影响行人总体的疏散时间。

2) 低密度下，行人不便行人对人群疏散效率影响不明显，随着密度的增加，行动不便行人所占比例的增大则会导致混合人群的疏散效率显著下降。

3) 高密度下，将行动不便行人和正常行人分开，会大幅提高疏散效率，且将行动不便行人置于出口附近或房间中央位置，对人群疏散最有利。

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