Construction and stability analysis of an evacuation model for contrary movement personnel

doi:10.16265/j.cnki.issn1003-3033.2023.09.2178

Abstract

Abstract:

To accurately depict the evolution process of individual behavior conflicts during evacuations and improve evacuation efficiency, the evolutionary game theory was applied to analyze the evolution of evacuation behaviors in two typical scenarios involving contrary movement personnel. The impact of population density, level of emergency severity, and individual psychological gains on the choice of cooperative or competitive strategies by individuals was discussed. The dynamic evolution process of game players and the influence of parameter adjustment on the strategy selection of both sides could be demonstrated with the help of Matlab. The simulation results showed that under certain constraints, there were five equilibrium points which were (1,0), (0,1), (1,1), (0,0), and a saddle point. It is found that different types of retrograde pedestrians benefit from different proportions, but the influencing parameters of their behavior evolution have the same influence trend. When the psychological benefits of regular evacuees, the risk level of the accident, and the additional time loss of counterflow individuals increase, evacuees tend to adopt a yielding strategy. Conversely, when the cost of competition for regular evacuees and the rewards of successful competition for counterflow individuals decrease, the counterflow individuals tend to adopt a yielding strategy.

Key words: retrograde behavior, evolutionary game, stable analysis, pedestrian evacuation, evacuation efficiency

DENG Qing, ZHOU Zheng, DENG Li, JIANG Huiling, ZHOU Liang, ZHOU Zhengqing. Construction and stability analysis of an evacuation model for contrary movement personnel[J]. China Safety Science Journal, 2023, 33(9): 196-203.

Figures/Tables 10

Tab.1

Tab.2

Tab.3

Local stability analysis of both sides of game

均衡点	特征值1	符号	特征值2	符号	局部稳定性
A	t+dp₂	+	t+dp₁+at₁	+	否
B	-t-dp₁-at₁	-	- $m + t - 3 d (c 2 - p 2) 5$	-	ESS
C	$2 d (c 1 - p 1) 5 - t$	+	$m - t + 3 d (c 2 - p 2) 5$	+	否
D	$t - 2 d (c 1 - p 1) 5$	-	-t-dp₂	-	ESS
E	M	+	-M	-	鞍点

Tab.3

Fig.1

Tab.4

Tab.5

Local stability analysis of both sides of game

均衡点	特征值1	符号	特征值2	符号	局部稳定性
A	t+dp₂	+	t+dp₁+at₁	+	否
B	-t-dp₁-at₁	-	$- m + t - 3 d (c 2 - p 2) 10$	-	ESS
C	$7 d (c 1 - p 1) 10 - t$	+	$m - t + 3 d (c 2 - p 2) 10$	+	否
D	$t - 7 d (c 1 - p 1) 10$	-	-t-dp₂	-	ESS
E	M₁	+	-M₁	-	鞍点

Tab.5

Fig.2

Fig.3

Fig.4

Fig.5

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疏散人员	逆行人员(抢险救灾人员)
疏散人员	避让y	争抢1-y
避让x	(-t, -t-at₁)	(m-t, dp₁)
争抢1-x	(dp₂, -t)	0.6d(p₂-c₂) 0.4d(p₁-c₁)

疏散人员	逆行人员(普通疏散人员)
疏散人员	避让	争抢
避让	(-t, -t-at₁)	(m-t, dp₁)
争抢	(dp₂, -t)	0.3d(p₂-c₂) 0.7d(p₁-c₁)

参数	偏导数	对 S₂的影响
c₁	<0	-
c₂	>0	+
m	>0	+
t	/	/
t₁	>0	+
d	/	/
p₁	>0	+
p₂	<0	-
a	>0	+