存在逆行人员的疏散模型构建及稳定性分析

doi:10.16265/j.cnki.issn1003-3033.2023.09.2178

中国安全科学学报 ›› 2023, Vol. 33 ›› Issue (9): 196-203.doi: 10.16265/j.cnki.issn1003-3033.2023.09.2178

存在逆行人员的疏散模型构建及稳定性分析

邓青¹^,²(), 周郑¹^,², 邓立³, 蒋慧灵¹^,⁴^,^**(), 周亮¹^,², 周正青¹^,²

¹ 北京科技大学大安全科学研究院,北京 100083
² 北京科技大学土木与资源工程学院,北京 100083
³ 中南建筑设计院股份有限公司,武汉湖北 430071
⁴ 北京科技大学金属冶炼重大事故防控技术支撑基地,北京 100083

收稿日期:2023-03-01 修回日期:2023-06-13 出版日期:2023-09-28
通讯作者:
**蒋慧灵(1975—),女,湖南祁阳人,硕士,教授,主要从事电气防火及火灾监控、智慧消防方面的研究。E-mail:87398930@qq.com。
作者简介:
邓青 (1990—),女,湖北孝感人,博士,副教授,主要从事智能疏散、大数据分析、公共安全等方面的研究。E-mail:dengqing0415@126.com。
邓立工程师
周亮副教授
周正青副教授
基金资助:
国家自然科学基金资助(72174099); 国家自然科学基金资助(72004113); 国家重点研发计划项目(2021YFC1523504); 国家应急管理部科技计划项目(2021XFCX25); 国家应急管理部科技计划项目(2022XFZD05); 河北省重点研发项目(22375419D)

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

DENG Qing¹^,²(), ZHOU Zheng¹^,², DENG Li³, JIANG Huiling¹^,⁴^,^**(), ZHOU Liang¹^,², ZHOU Zhengqing¹^,²

¹ Research Institute of Macro-Safety Science, University of Science and Technology Beijing, Beijing 100083, China
² School of Civil and Resource Engineering, University of Science and Technology Beijing, Beijing 100083, China
³ Central South Architectural Design Institute Co., Wuhan Hubei 430071, China
⁴ Technical Support Center for Prevention and Control of Disastrous Accidents in Metal Smelting, University of Science and Technology Beijing, Beijing 100083, China

Received:2023-03-01 Revised:2023-06-13 Published:2023-09-28

摘要/Abstract

摘要：

为探究疏散过程中人员行为冲突的演化过程,提高疏散效率,运用演化博弈理论,分析 2种典型存在逆行人员场景下的人员疏散行为演化过程,讨论人员密度、事件紧急程度以及个体心理收益对人员合作或竞争策略选择的影响;借助Matlab仿真工具,展示博弈参与者的动态演化过程及参数调整对于双方策略选择的影响。结果表明:在一定约束条件下,存在5个均衡点,分别为(1,0)、(0,1)、(1,1)、(0,0)和一个鞍点。针对不同类型的逆行人员,获得的收益比例不同,但参数对其行为演化的影响趋势是一致的。当正常疏散人员的心理收益、事故的危险程度、逆行人员的额外时间损失增大时,正常疏散人员倾向礼让的策略;当正常疏散人员争抢的成本和逆行人员争抢成功的收益减小时,逆行人员倾向于礼让的策略。

关键词: 逆行人员, 演化博弈, 稳定性分析, 疏散过程, 疏散效率

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

邓青, 周郑, 邓立, 蒋慧灵, 周亮, 周正青. 存在逆行人员的疏散模型构建及稳定性分析[J]. 中国安全科学学报, 2023, 33(9): 196-203.

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.

图/表 10

表1

表2

表3

博弈双方的局部稳定性分析

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

表3

图1

表4

表5

博弈双方的局部稳定性分析

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

表5

图2

图3

图4

图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	+

存在逆行人员的疏散模型构建及稳定性分析

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

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