Modeling and Analysis of Metro Emergency Decision Based on Logical Game Probability Petri Net

doi:10.16182/j.issn1004731x.joss.22-0355

Abstract

Abstract:

In order to solve the problem that logical Petri net can not describe dynamic game process well, logical game probabilistic Petri net is proposed. The four elements of the game are integrated into the logical Petri net, and the players of the game are defined as an attribute of Token, for which the strategy set and utility function are defined, and the information database is introduced. Probability change and vector are introduced to represent the transformation relationship of empirical probability in the process of game, and fuzzy theory is introduced on the basis of Bayes formula to solve the problem of information loss in the early stage of decision making, and decision change is introduced to help rational people make decisions. Logical game probability Petri net was used to model the subway emergency decision-making process, and the system reachable graph was constructed to analyze the problem. Tina simulation was used to verify the model properties, the feasibility of the proposed method was also verified.

Key words: logical game probability Petri net, metro emergency decision-making, fuzzy Bayes formula, reachable graph

CLC Number:

TP391.9

Zhe Yan, Wei Liu, Yuyue Du. Modeling and Analysis of Metro Emergency Decision Based on Logical Game Probability Petri Net[J]. Journal of System Simulation, 2023, 35(7): 1602-1618.

Figures/Tables 16

Fig. 1

Fig. 2

Fig. 3

Table 1

Table 2

Table 3

Table 4

Decision group at the first stage judged that it was a level Ⅰ emergency

状态	数值
M₂	[0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₃	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅰ), (1, Ⅰ), (1, Ⅰ), (1, Ⅰ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅰ$ ), (1, $U 12 Ⅰ$ ), (1, $U 13 Ⅰ$ ), (1, $U 10 Ⅰ$ ), 0, 0, 0, 0, 0]
M₆	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₇	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₈	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₉	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

Table 4

Table 5

Decision group at the first stage judged that it was a level Ⅱ emergency

状态	数值
M₁₀	[0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₁	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅱ), (1, Ⅱ), (1, Ⅱ), (1, Ⅱ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₂	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₃	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅱ$ ), (1, $U 12 Ⅱ$ ), (1, $U 13 Ⅱ$ ), (1, $U 10 Ⅱ$ ), 0, 0, 0, 0, 0]
M₁₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₁₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₁₆	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₁₇	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

Table 5

Table 6

Decision group at the first stage judged that it was a level Ⅲ emergency

状态	数值
M₁₈	[0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₁₉	[0, 0, 1, 0, 0, 0, 0, 1, (1, Ⅲ), (1, Ⅲ), (1, Ⅲ), (1, Ⅲ), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₀	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), , (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₁	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 11 Ⅲ$ ), (1, $U 12 Ⅲ$ ), (1, $U 13 Ⅲ$ ), (1, $U 10 Ⅲ$ ), 0, 0, 0, 0, 0]
M₂₂	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₂₃	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₂₄	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₂₅	[0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

Table 6

Table 7

Decision group judged that it was a false alarm

状态	数值
M₂₆	[0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₇	[0, 0, 1, 0, 0, 0, 0, 0, (1, 0), (1, 0), (1, 0), (1, 0), (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₈	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), , (1, β₁₁, β₁₂, …, β₁_n ), (1, β₂₁, β₂₂, …, β₂_n ), (1, β₃₁, β₃₂, …, β₃_n ), (1, β₀₁, β₀₂, …, β₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
M₂₉	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, (1, $U 110$ ), (1, $U 120$ ), (1, $U 130$ ), (1, $U 100$ ), 0, 0, 0, 0, 0]
M₃₀	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0]
M₃₁	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0]
M₃₂	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
M₃₃	[0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, (1, α₁₁, α₁₂, …, α₁_n ), (1, α₂₁, α₂₂, …, α₂_n ), (1, α₃₁, α₃₂, …, α₃_n ), (1, α₀₁, α₀₂, …, α₀_n ), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0]

Table 7

Table 8

Table 9

Fig. 4

Fig. 5

Table 10

Table 11

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库所	库所含义
P₁	地铁突发事件
P₂	地铁应急决策组
P₃	地铁突发事件历史数据
P₄	决策组判断事故等级为Ⅰ级
P₅	决策组判断事故等级为Ⅱ级
P₆	决策组判断事故等级为Ⅲ级
P₇	决策组判断应急结束
P₈	计数库所
P₉	准备计算Ⅰ级概率
P₁₀	准备计算Ⅱ级概率
P₁₁	准备计算Ⅲ级概率
P₁₂	准备计算0级概率
P₁₃	事故等级Ⅰ的前验概率和条件概率
P₁₄	事故等级Ⅱ的前验概率和条件概率
P₁₅	事故等级Ⅲ的前验概率和条件概率
P₁₆	事故等级0的前验概率和条件概率
P₁₇	事故等级Ⅰ的后验概率
P₁₈	事故等级Ⅱ的后验概率
P₁₉	事故等级Ⅲ的后验概率
P₂₀	事故等级0的后验概率
P₂₁	选择应急方案1的效用
P₂₂	选择应急方案2的效用
P₂₃	选择应急方案3的效用
P₂₄	不选择应急方案的效用
P₂₅	选择应急方案1
P₂₆	选择应急方案2
P₂₇	选择应急方案3
P₂₈	不选择应急方案
P₂₉	实施所选应急方案

变迁	含义
t₁	警报
t₂	等级分类
t₃	传送专家组判断
t₄	计算在决策组判断为Ⅰ级事故时实际等级的后验概率
t₅	计算在决策组判断为Ⅱ级事故时实际等级的后验概率
t₆	计算在决策组判断为Ⅲ级事故时实际等级的后验概率
t₇	计算在决策组判断为Ⅲ级事故时实际等级的后验概率
t₈	计算在决策组判断为Ⅰ级事故时各应急方案的期望效用
t₉	计算在决策组判断为Ⅱ级事故时各应急方案的期望效用
t₁₀	计算在决策组判断为Ⅲ级事故时各应急方案的期望效用
t₁₁	计算在决策组判断为0级事故时各应急方案的期望效用
t₁₂	选择应急方案
t₁₃	实施应急方案
t₁₄	将实时信息汇总

条件概率	y₀	y₃	y₂	y₁
p(x₀\| y_k )	0.80	0.10	0.05	0.05
p(x₃\| y_k )	0.10	0.70	0.15	0.05
p(x₂\| y_k )	0.05	0.15	0.50	0.30
p(x₁\| y_k )	0.05	0.05	0.30	0.60

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