Keywords

1 Introduction

As an important part of the urban public transportation system, the subway shares a large number of ground passenger flow and effectively reduces the situation of urban ground traffic congestion due to its advantages of large passenger volume, fast running speed, punctuality, short departure interval and low energy consumption. The subway station is one of the main places for crowded activities in the city for pedestrians to wait, transfer and rest for a short time. With the rapid growth of the operating mileage, the working day, weekend and holiday in many cities have shown a normal large passenger flow. The vast majority of subway stations are located underground, with closed space, complex structure, few entrances and exits, and long distance walking. When emergencies come, people will inevitably be intertwined, bringing more risks and challenges to emergency evacuation.

At present, domestic and foreign scholars have carried out a lot of research on emergency evacuation in subway stations and achieved good results. Some of them study the path choice behavior of passengers from the pedestrian decision-making level. The other part of the study starts from the simulation method level, based on cellular automata, social force and agent micro-simulation models, to explore the impact of pedestrian behavior on emergency evacuation. Based on census data and questionnaire survey results, Li Feng et al. analyzed the significant influencing factors of each type of passengers through multiple logit models, and estimated the proportion of different types of passengers in subway stations [1]. Wang Heng et al. used the conditional logit model and the random parameter logit model [2] to demarcate the utility coefficients of four factors, distance, exit density, passenger flow direction and exit visibility, on emergency evacuation of subway stations, and analyzed the heterogeneity of passenger decision preference based on the results of the questionnaire survey [3]. Xu Huizhi et al. used a questionnaire combined with stated preference (SP) survey [4] and revealed preference (RP) survey [5] to investigate passengers’ choice of evacuation behavior in different situations. The results showed that: The difference in the proportion of blindly following, panicked, autonomous and impulsive passengers in subway stations has a significant impact on evacuation efficiency [6]. Lin Xiaofei et al. designed 8 evacuation methods by using orthogonal method, and analyzed the influence of 4 factors by using range method based on Pathfinder and taking evacuation time as index [7]. Guo Haixiang et al. improved the social force model [8] by considering the impact of pedestrian awareness on pedestrian's expected speed when an emergency occurred, and the results showed that pedestrian's expected speed increased with the increase of pedestrian awareness, thus reducing the evacuation time [9]. Based on the social force model, Meng et al. simulated the emergency evacuation of subway transfer stations in case of emergencies, and proposed evacuation methods to shorten the evacuation time by analyzing and comparing the evacuation time of passengers in peak periods [10]. Hu Mingwei et al. built a simulation model of subway station water invasion evacuation based on AnyLogic platform to study the impact of emergency evacuation strategies on evacuation efficiency under water invasion conditions. After optimizing evacuation strategies, the evacuation efficiency of the model increased by 11.4% overall, and the safe evacuation ratio reached 92.2%. Wang Lixiao et al. constructed a latent class model (LCM) considering pedestrian psychological heterogeneity [11] to characterize individual decision-making processes. The simulation results show that: The latent class model is a better reflection of the path choice behavior of pedestrians in reality and is more effective and reasonable than multinomial logit (MNL) model [12,13,14]. According to previous studies, most evacuation simulation models only simulate the phenomenon of crowd evacuation, and the comprehensive analysis of evacuation environment and psychological behavior is relatively scarce. The built simulation models only describe the emergency response of pedestrians from the appearance, and the models are generally studied from the perspective of group decision-making rather than individual decision-making. In addition, the pedestrian exit decision rules embedded in most simulation models are only based on the shortest path decision rules under the assumption of complete pedestrian rationality and complete information grasp, or the discrete choice model rules based on stochastic utility maximization theory, which is inconsistent with reality.

In view of this, firstly, this study adopts SP&RP survey method to investigate the influencing factors (exit distance, exit density, exit congestion, exit visibility) of pedestrian group's psychological state and behavior. Secondly, the influence of pedestrian psychological heterogeneity on path selection behavior is explored by establishing LCA model. Finally, the model of pedestrian groups with different psychological categories is used to simulate, which effectively improves the reliability of the simulation process and results. This study simulates the problem of pedestrian emergency evacuation in subway stations, considers the influence of pedestrian group's psychological behavior on route selection, and takes Nanhuomen Station in Xi ‘an City (China) as an example to conduct modeling simulation. The results have certain reference value and can provide theoretical support for emergency evacuation management in subway stations.

2 Data Source

2.1 Passenger Flow Data

Based on the AFC data of Nanhuomen Metro transfer station in Xi ‘an, the distribution characteristics of passenger flow are analyzed. The morning and evening peak traffic of working days, weekends and holidays is examined, and the flow level of large passenger flows is estimated according to the statistics. On the day of the survey, the passenger volume of Metro Line 2 was 917,000 people, the passenger flow of Nanhuamen station was 56,000 people, the maximum inbound passenger flow in 15min was 2078 people, and the outbound passenger flow was 1787 people. Nanzhaomen Station is a single transfer channel, passengers can transfer between lines 2 and 5 through the transfer channel, and the shortest time for walking to complete the conversion of the station hall is 96 s. In this study, a total of 3865 people were evacuated, including 1787 on the platform floor and 2078 on the station hall floor.

2.2 Questionnaire Survey

In the process of emergency evacuation, the psychological state of pedestrians will continue to change, and they are easy to make a series of decisions influenced by their own emotions and cognition as well as others. Under normal circumstances, the pedestrian evacuation path is composed of key nodes such as stairs or escalators between the platform and the station hall, ticket offices, security channels, gates, transfer channels, entrances and exits. However, when encountering an emergency, the psychological state of pedestrians is more fragile, and they are more susceptible to the influence of the surrounding environment and others, thus losing their rational judgment. When encountering obstacles, large crowd density and other situations, they will choose to decircuit or force crossing. Usually, waiting for service in front of a gate in the direction of an exit causes a large number of pedestrians to jam. The inconsistence of pedestrian flow velocity between stations or platforms leads to stampede events in the interweaving process. Pedestrians who lack the ability of independent judgment give up changing the evacuation path because of crowd behavior. Panic pedestrians repeatedly change the evacuation path and reverse flow of people repeatedly detour.

In order to confirm the correlation between pedestrian psychological behavior and emergency evacuation decision-making level, the influence of the above behavioral factors on pedestrian path selection was analyzed through experimental investigation, and the psychological heterogeneity of the influencing factors was quantified during pedestrian decision-making. RP survey [15], also known as behavioral survey, is a survey of actual action or completed selection behavior, and RP survey can reflect the real choice behavior of the survey object in the existing scene. SP survey [16], also known as intention survey, is a survey of choice intention to select how the subject chooses and how to consider it under hypothetical conditions. SP survey can reflect the choice behavior of the survey object for the things that have not happened in the set scene. In this study, RP&SP survey method was used to collect individual pedestrian data, so as to realize scenario selection survey based on similar scenario selection. The questionnaire is divided into three parts: the first part is about individual attributes and travel attributes of pedestrians, the second part is about psychological latent variables and preference characteristics, and the third part is about emergency evacuation choice behavior. 240 valid questionnaires were collected, and the survey results are shown in Table 1 and Table 2.

Table 1. Questionnaire on emergency evacuation of subway pedestrians
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Table 2. Questionnaire on emergency evacuation of subway pedestrians
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3 Behavioral Decision Model

Anylogic software is an effective tool for studying and simulating pedestrian behavior. Since it allows the customization of individual evacuees’ attributes and behaviors and simulates multiple evacuees at the same time, Anylogic simulation platform can explore the mechanism of pedestrian psychological behavior and emergency evacuation decision from the perspective of individual decision making. The model defines the basic attributes of individual evacuees according to the questionnaire survey results, and sets the path decision mechanism of individual evacuees based on utility theory and latent category model, so as to simulate the path choice behavior of evacuees.

3.1 Establishment of Utility Function

Utility theory is a decision-making theory used by individuals to choose decision schemes. Decision-makers are often affected by subjective consciousness. In decision-making problems, the consideration of individual benefits and losses is called utility. The Utility theory is based on the Random Utility Maximization model (RUM) which is completely rational for decision makers. In this study, it is assumed that individuals choose the maximum utility path for evacuation according to their personal attributes, travel attributes (variables \(a_i ,i = 1,2,...,10\)), emergency evacuation behaviors and preference characteristics (variables \(b_i ,i = 1,2,...,18\)). The utility function formula consists of directly observable (\(V_{ij}\)) and unobservable (\(\varepsilon_{ij}\)) items. The utility (\(U_{ij}\)) of the decision maker's choice scheme is shown in formulas (1) and (2).

$$ U_{ij} = V_{ij} + \varepsilon_{ij} $$
(1)
$$ V_{ij} = \alpha_i S_{ij} + \beta_i M_{ij} + r_i $$
(2)

where: \(S_{ij}\) is the personal attribute and travel attribute vector that influence decision maker's choice of path, and \(M_{ij}\) is the emergency evacuation behavior and preference feature vector (i.e., psychological latent variable vector) that influence decision maker's choice of path; \(\alpha_i\) and \(\beta_i\) is the parameter to be estimated of the corresponding attribute vector, reflecting the sensitivity of the attribute vector to the path. The regression analysis is performed based on the SP&RP questionnaire survey data and subsequent latent category analysis results. If its value is positive, it has a positive impact on the path selection; if its value is negative, it has a negative impact on the path selection; \(r_i\) is a constant term. The basic form of the decision model is derived based on the assumption that it has independent and identical distribution characteristics and follows Gumbel distribution. The expression of the probability density function of the random error term is shown in Eq. (3), and the probability of the decision maker choosing the path is shown in Eq. (4).

$$ f\left( {\varepsilon_{ij} } \right) = e^{ - \varepsilon_{ij} - e^{ - \varepsilon_{ij} } } $$
(3)
$$ P_{ij} = \frac{{{\text{e}}^{\left( {V_{ij} } \right)} }}{{\sum_{k = 1}^I {{\text{e}}^{\left( {V_{kj} } \right)} } }} = \frac{{e^{\alpha_i S_{ij} + \beta_i M_{ij} + r_i } }}{{\sum_{k = 1}^I {e^{\alpha_k S_{kj} + \beta_k M_{kj} + r_k } } }} $$
(4)

where: \(I\) is the set of other paths, \(V_{kj}\) is the utility observable item of the decision maker's choice of path, \(S_{kj}\) is the personal attribute and travel attribute vector that influence the decision maker's choice of path, \(M_{kj}\) is the emergency evacuation behavior and preference feature vector that influence the decision maker's choice of path; \(\alpha_k\) and \(\beta_k\) is the parameter to be estimated of the corresponding attribute vector; \(r_k\) is a constant term.

3.2 Latent Category Model

LCA [17, 18] is a statistical method for estimating parameters based on individuals’ response patterns on explicit indicators, i.e. different joint probabilities, clustering into different latent classes based on posterior probabilities. In this study, emergency evacuation behavior and preference characteristics (variables \(b_i ,i = 1,2,...,18\)) are used as observable explicit variables for potential category analysis. The potential category model includes two model parameters, potential category probability and conditional probability. When there are multiple explicit variables (survey data), the number of options for each variable is \(i_i\). At the same time, there is also latent variable \(X\) with \(T\) latent categories after the explicit variable, and each explicit variable in each category of \(X\) has local independence, then the basic equation of the LCA model can be obtained, as shown in Eq. (5).

$$ \pi_{i_1 i_2 ,...,i_{18} }^{b_1 b_2 ,...,b_{18} } = \sum_{t = 1}^T {\pi_t^X } \pi_{i_1 t}^{\overline{b_1 }X} \pi_{i_2 t}^{\overline{b_2 }X} \cdot \cdot \cdot \pi_{i_{18} t}^{\overline{{b_{18} }}X} $$
(5)

where: \(\pi_{i_1 i_2 ,...,i_{18} }^{b_1 b_2 ,...,b_{18} }\) represents the joint distribution probability of the explicit variables estimated by the latent class model, and \(\pi_t^X\) represents the conditional probability that the observed data belongs to a certain latent class of \(i_i\).

3.3 Parameter Calibration

Mplus 7.4 software was used to carry out LCA on pedestrian's emergency evacuation behavior and preference characteristics (variable \(b_i ,i = 1,2,...,18\)) attributes. The indicators [19] used in this study include: Log-L, Akaike Information Criterion (AIC), Bayesian information criterion (BIC), Adjusted Bayesian information Criterion (aBIC), Entropy, likelihood ratio test (LMR), Bootstrap-based likelihood ratio test (BLRT). The results show that the smaller the values of Log-L, AIC, BIC and aBIC, the better the fitting effect is. The higher the Entropy value, the higher the classification accuracy, LMR and BLRT values were significant (p-value&lt, 0.05), indicating that the model of C categories is better than that of C-1 categories. By comparing the relevant fitting indicators of each category, the best model is selected, and the fitting results are shown in Table 3.

Table 3. Goodness of fit of LCA model and model selection
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According to the data of various models in Table 3, when the number of categories is 4, all indicators are optimal, so the category 4 model is selected to divide the population. Further, the posterior conditional probability and class probability of the four-class model are analyzed to determine the mental activity characteristics of various other groups. In the part of psychological latent variables and preference characteristics of this RP&SP questionnaire, option 1 means sensitive to the problem, option 2 means normal, option 3 means insensitive to the problem, and the conditional probability of option 1 is shown in Fig. 1.

Fig. 1.
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Conditional probability that the 4-category model option is 1

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For people in category 1, the category probability is 18.3%, showing that they are more sensitive to “following the command of staff”, “knowing the location of entrances and escalators” and “knowing the transfer route”, indicating that they have clear spatial cognition ability and follow the suggestions of others, so they can be named “calm” people. Among the people in category 2 (31.3%), “they can find their own location on the map”, “they are used to withdrawing from familiar channels” and “choosing less crowded channels” are sensitive, which can be called “autonomous” people. Among the people in category 3 (29.6%), the characteristics of “strong sense of direction”, “following the command of staff”, “I will patiently queue up when encountering crowds” and “I will choose the passageway with fewer people” are more sensitive, belonging to the “mass” crowd. Category 4 group (20.8%) is the only group that “walks with the majority of people” and shows sensitivity and other behaviors are more general, so it can be regarded as a “conformity” group.

The group category is taken as variable \(b\), option 1 is the calm group, option 2 is the autonomous group, option 3 is the mass group, option 4 is the conformity group, and the personal attributes and travel attributes variables \(a_i ,i = 1,...,10\) are combined into independent variables, and the distance of pedestrians’ choice of entrance and exit in SP survey is taken as the dependent variable \(c\), option 1 is the shortest path, option 2 is the longer path. Option 3 is the longest path, and Option 3 is used as a utility reference to perform ordered multivariate logictic regression analysis [20, 21] on the data and solve the regression parameters of the respective variables. The results are shown in Table 4.

Table 4. Results of multivariate Logictic regression model parameter estimation
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4 Simulation and Result Analysis

4.1 Evacuation Environment Construction

Nanhuomen Station is the transfer station of Xi ‘an Metro Line 2 and Line 5, Line 2 station is north-south, Line 5 station is east-west, Nanhuomen station has six entrances: Line 2 has four entrances A, B, C, D, and Line 5 has two entrances F and G. The layout of pedestrian passages and facilities inside the subway station was investigated on the spot, and the plane and three-dimensional diagram of the station were combined to clarify the plane and spatial relationship of each part of the subway station, and the emergency evacuation simulation environment was established, as shown in Fig. 2.

Fig. 2.
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Emergency evacuation simulation environment construction

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4.2 Analysis of LCA Model Results

In this study, passengers who later enter the train and the entrance are not considered in the simulation process, and emergency evacuees are loaded to the station floor and platform floor at the beginning of the simulation. By using the evacuation simulation model established above, the LCA model considering the influence of psychological behavior is compared and analyzed with the results of the actual SP survey. To verify the impact of psychological heterogeneity on route selection and evacuation efficiency, the simulation results are shown in Fig. 3 and Fig. 4.

Fig. 3.
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The evacuation time varies with the number of evacuees

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Fig. 4.
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Comparison of the number of evacuees at each entrance and exit

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By observing Fig. 3, it can be found that the evacuation time curve based on the LCA model is smooth. With the increase of the number of evacuees, the overall evacuation time increases, which is approximately linear. The fitting line is shown in Eq. (6).

$$ y = 0.0857x - 0.634, \, R^2 = 0.995 $$
(6)

where: \(y\) is the evacuation time and \(x\) is the number of evacuees. This is because in the evacuation process, pedestrians based on the distance and queuing time of the two optimal conditions in the gate and the result of the selection of the entrance and exit, therefore, the entire evacuation process is relatively smooth, there is no large crowded period, in the evacuation time curve is no obvious “bump” and “depression”. In addition, through the comparison of the number of evacuees at each entrance and exit in Fig. 4, it can be found that the simulation results are roughly consistent with the results of SP survey, with a maximum error of 1.1%. The number of evacuees at entrance C and entrance D is relatively small, accounting for no more than 14.6%, and the number of evacuees at entrance F is the largest, accounting for the largest 22.0%.

4.3 Comparison of Evacuation Efficiency of Different Proportions of People

The crowd is divided into calm type, autonomous type, mass type and conformity type. In order to explore the differences in the path selection behavior of each latent group, the influence of different groups of people on evacuation efficiency under different proportions is studied. The proportion of conformity type is taken as a variable, and the proportion of autonomous and mass type people is kept unchanged. In order to observe the influence of coolness on evacuation efficiency, the proportion of coolness on evacuation efficiency should be increased while the number of conformity groups should be reduced. The research methods used to observe other groups of people are similar. Evacuation efficiency is expressed by the average number of evacuees, and the results are shown in Fig. 5.

Fig. 5.
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The relationship between different proportion of people and evacuation efficiency

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Figure 5(a) shows that in the case of calm crowd with different proportions, the evacuation efficiency increases with the proportion of calm crowd. In the first 5.2% of the increase of crowd proportion, the evacuation efficiency curve changes greatly, and then the change trend gradually slows down with the increase of the proportion. When the proportion reaches the maximum, the maximum evacuation efficiency is 12.0 person/s, and the evacuation efficiency is increased by 10.1%, indicating that the proportion of calm crowd can effectively improve the evacuation efficiency, while the other proportion is not conducive to crowd evacuation.

The initial proportion of autonomous people is relatively large, which is consistent with the actual situation. As can be seen from Fig. 5(b), evacuation efficiency increases steadily as the proportion of autonomous people increases. However, when the proportion of autonomous people increases to the third 5.2%, evacuation efficiency no longer changes, and the maximum evacuation efficiency is 11.8 person/s, which increases by 7.3%. It shows that the proportion of autonomous population can improve the evacuation efficiency to a certain extent, but there is a threshold for the improvement effect.

The mass crowd is similar to the autonomous crowd. Figure 5(c) shows that in the case of the mass crowd with different proportions, the evacuation efficiency changes with the proportion of the crowd. The evacuation efficiency curve changes greatly only in the first 5.2% when the proportion of the crowd increases. Compared with the initial 10.9 person/s, the evacuation efficiency only increased by 0.3, and the evacuation efficiency only increased by 2.8%, indicating that the proportion of autonomous people had a general impact on the evacuation efficiency.

5 Conclusion

This study models the crowd based on LCA, and verifies the necessity of considering the impact of pedestrian psychological behavior in the emergency evacuation process by comparing the simulation results with the SP survey results. Based on this, the impact of different psychological characteristics on the evacuation efficiency is further analyzed. The main research results are as follows:

  1. (1)

    LCA model can accurately classify people in emergency evacuation. In this study, four categories of model are used, and the classification accuracy rate is as high as 84.7%, which better reflects the path decision-making behavior of pedestrians in the actual scene. The simulation results show that the LCA model is in good agreement with the real observed values in the SP questionnaire scenario setting, and the maximum error is less than 1.1%.

  2. (2)

    The influence of people with different psychological characteristics on evacuation efficiency exists objectively, and the degree of influence is different. The simulation results show that the calm crowd has the greatest impact on the evacuation efficiency, with the evacuation efficiency increased by 10.1%, the independent crowd has a moderate impact on the evacuation efficiency, with the evacuation efficiency increased by 7.3%, the mass crowd has a little impact on the evacuation efficiency, with the evacuation efficiency only changing by 2.8%, which is basically negligible.

  3. (3)

    The research results show that the psychological behavior of pedestrians in the process of emergency evacuation has an important impact on route selection, and the more calm crowd and autonomous crowd occupy, the more conducive to emergency evacuation. Therefore, it is necessary for pedestrians to improve their spatial cognition ability, ability to identify signs and maps, and emergency evacuation safety education. The evacuation guidance of the staff also plays an important role in the emergency evacuation process.

Finally, all the data in this study come from the field investigation, but the modeling and simulation method of subway station emergency evacuation for people with different psychological characteristics has a certain universality, which can provide reference for further research on the combined decision model of emergency evacuation.