A study of evacuation model based on personnel vision change

Abstract

This paper proposes a new model for characterizing the emergency evacuation process of people during a disaster. This model considers the change of visual field based on a cellular automata model combined with a behavioral heuristic model. Using the behavioral heuristic model, the dynamic field parameters related to the change of visual field are first established. Then, new judgment rules are developed for personnel encountering obstacles by combining the characteristics of the new field of view. Finally, an analytical comparison is made between the proposed model and the traditional evacuation model in terms of the changes in the fields of view and the number of evacuees. The results show that the level of path service determines the efficiency of evacuation. It is also seen that herd mentality acts as a hindrance in cases where the personnel are dependent while otherwise acting as a facilitator. It is also shown that the evacuation time increases by the number of evacuees up to a certain threshold. Beyond that threshold the evacuation time fluctuates within a certain range by increasing the number of evacuees is not affected by changes in the field of view. The new model is also faster than the social force model, easier to calculate on a large scale, and more realistic than the traditional cellular model.

Keywords

Cellular automata Pedestrian dynamics view pedestrian evacuation

1 Introduction

With the development of society, the principle of human-centered design becomes deeply rooted in urban design. The focus of this research is to improve evacuation efficiency and reduce casualties in the event of disasters [1]. There exist several studies on people’s behavior during evacuation [2 –5]. In the process of evacuation, there are often complications due to poor vision resulting in casualties. Therefore, it is essential to investigate the impact of the change in personnel’s visual field on the evacuation process.

In recent years, different topics were investigated related to the changes in the visual field during evacuation operations. For instance, in 2013, Lu Wei et al. [6]. developed a 2D continuum model of the visual field. In their approach, they incorporated typical phenomena using experimental data to obtain kinematic equations. They then combined these equations with the distribution of visual impairment. Tsurushima Akira [7] also proposed a new model of evacuation for tunnel vision. This model shows that the evacuation of personnel from their functional visual field (FFV) is influenced by their observational cognitive biases. Li Shiwei [8] also constructed a dynamic evolutionary game model based on visual field directional ambiguity. Using this model they then effectively demonstrate the self-organization phenomenon in the pedestrian flow.

The cellular automaton model has been widely adopted and well-received as a tool for pedestrian flow simulation due to its simple design and fast operation [B]. Nevertheless, such a model is not capable of effectively solving the interactions between individual cells. Others improved the cellular automaton algorithms to characterize the interactions between cells [10 –12]. Furthermore, adding a social force model allows the model to calculate the interactions between individual cells in a more refined way, see, e.g., [13] which results in improved realism of the model.

In this paper, we consider the visual field as one of the important factors affecting evacuation and investigate the effect of changes in the field of view on evacuation. Here, we combine a cellular automaton model with a behavioral heuristic model derived from a social mechanics model. We argue that this combination results in a more accurate characterization of reality and improves the authenticity of the model. Therefore, on this basis, this paper establishes an evacuation model that considers the change of vision. This paper hopes that this model can provide more accurate help for the study of evacuation in the field of vision, and through the model, some simple and effective experiments are carried out to explore the impact of psychology and part of the evacuation environment on people during the evacuation process.

The paper is organized as follows. Section 2 provides a review of the relevant research literature. Section 3 describes our proposed model for evacuating people considering visual field change. Section 4 presents the simulation results and the corresponding discussion. Finally, in the last section, conclusions are provided.

2 Literature review

Currently, the studies on the evacuation processes are mainly based on computer simulations. The existing evacuation models can be broadly divided into discrete and continuous categories. Discrete models include social force models, cellular automata models, and lattice gas models. In 2001, Burstedde et al. [14] introduced the field concept and developed a cellular automata automaton namely the “ground field model". In this model, a combination of “dynamic field strength” and “static field strength” determines the movement of people. Kirchner et al. [15 –17] also proposed a method to modify the field model by optimizing the algorithms for “dynamic field strength” and “static field strength” based on the field concept. The optimization of the “dynamic field strength” and “static field strength” algorithms provides part of the theoretical basis for the subsequent research on metric automata.

The “field” cellular automata were used in various research areas resulting in remarkable results. The view field of trapped people is an essential factor in the evacuation process. Therefore, the development of a cellular automata model for the field of view is widely discussed by scholars. For example, Yue Hao et al. [18] proposed the first cellular automata model considering the influence of the visual field. In this model, they further added the direction and the square lattice parameters and further concluded that the evacuation time is related to the radius of the visual field and the size of the exit. ZhiHongLi et al. [19] also considered other factors such as the differences in individual characteristics of pedestrians, the size of the exit, the operation door, evacuation efficiency, the bottleneck area density, and the escape route characteristics to adapt the model for the human visual field.

Furthermore, JiaYangLi et al. [20] established a fuzzy visual model based on cellular automata. This model effectively characterized the phenomena of the evacuation of people based on domain selection and distance rules. They then concluded the efficiency of the evacuation can be improved if people can maintain a visual field within a certain radius. Also, BaoBaoZhou et al. [21] introduced a local density field with the hesitation time cost and investigated the impact of the visual field direction, and the number of collaborators and defectors on the evacuation process. They further obtained the optimal visual field radius and the optimal pedestrian speed during the evacuation process.

XingLiLi et al. [22] proposed an extended cost-potential field cellular automaton model to explore the effects of factors such as mental tension, visual radius, and pedestrian density on pedestrian evacuation through numerical simulations. WangWeili et al. [23] investigated pedestrian exit selection mechanisms by integrating game theory into a cellular automaton simulation framework. They further systematically studied the impact of factors such as visual radius, selection firmness of the pedestrians, initial crowd distribution in the room, exit layout, and exit width.

The above-mentioned research work has not considered the impact of human-human and human-obstacle forces on the metamorphic automata. Further research on the cellular automata model incorporated the forces between people. I.G. Georgoudas et al. [24] used a hardware implementation of FPGA logic by combining a cellular automaton with an electrostatically induced potential field. This enabled a low-cost, high-running model that facilitates the simulation of large-scale people. Chen ChangKun et al. [25] also introduced an analogous formulation for the magnetic forces describing the repulsive effects among people, and between people and obstacles. Their formulation led to the development of a force-driven cellular automaton model for simulating the evacuation behavior of pedestrians for different pedestrian densities, distributions, and corridor widths. This model was further used for analyzing evacuation times. Yameng Chen et al. [26] also created a cellular automaton model of social forces interacting in building evacuation, modeling and analyzing the positive and negative effects of social forces on evacuation time. Song WeiGuo et al. [27] also adapted the cellular automaton through the social forces model. The advantages of the new model were verified by making comparisons with the social forces model proposed by Helbing.

As was seen, the above works considered the behavioral and psychological effects on people in studying social force models. Nevertheless, these works are not sufficient for realizing behavioral and psychological changes. Ioakeim G. Georgoudas et al. [28] proposed a cellular automaton-based model for evacuating people, which is based on generating virtual fields along obstacles used to overcome obstacles.

Although the existing works take into account human-to-human and human-to-obstacle forces, they are deficient in terms of improving the computational efficiency of cellular automata when combined with social force models.

In 2000, Helbing [29] proposed a social force model inspired by Newtonian mechanics which provided a strong research direction for studying the forces between the people and between people and obstacles in the evacuation processes. Lakeba et al. [30] also pointed out that there exist some parameters in the social force model that may produce counter-intuitive results when applied to the movement of isolated pedestrians or a small number of pedestrians.

In addition to the above, Johansson et al. [31] applied an evolutionary optimization algorithm to determine the optimal parameters for the social force model. Hou et al. [32] further investigated the effect of evacuation leaders on evacuation dynamics with a limited range of visibility. Their results showed that having only one or two leaders could achieve significant results in a single exit configuration. Yuan Zhilu et al. also proposed an improved social force model based on the field of view and pedestrian movement states to investigate the effects of tracking behavior on the lane formation process, conflicts, number of lanes formed, and traffic efficiency [33]. Later, using an improved social mechanics model, Yuan Zhilu et al. compared the impact of wall signs versus ground signs and exits on evacuation where the field of view was restricted [34]. Zhou Min et al. proposed an improved social force model to simulate an environment with a restricted field of view. They then investigated the impact of the number and location of emergency signs and self-organizing behavior on evacuation efficiency [35]. The above work however does not consider the impact of people’s behavior and psychology on the social force models.

The behavior and psychology of people have been partly addressed by the researchers. For instance, l.Z. Yang et al. [36] applied a cellular automata model to simulate evacuation through building structure changes, person location settings, kin attraction, and route selection. They then derived the effect of kin behavior on the evacuation. Furthermore, Daoliang Zhao [37] applied a two-dimensional cellular automata model with the addition of a go-with-the-flow mentality (abbreviated as GWC) divided into directional GWC (DGWC) and spatial GWC (SGWC). This model was then used to simulate the evacuation of people from different rooms. To further enhance the uncertainty of the movement, Ning Ding et al. [38] introduced several key physical factors as well as the psychology of evacuees by adapting the cellular automaton. They further proposed a split and recombination network and made comparisons with the firefighting videos to confirm the validity of their model.

Although they further solved the problems in the centrality and behavior of the social force model, they still needed to improve the authenticity of the model’s psychology and behavior.

In general,although the above all studies show the impact of changes in the field of vision on the evacuation of people, further investigation is still needed. In terms of the field of vision, the influence of trapped people’s psychology on evacuation efficiency and the influence of obstacles in the field of vision on evacuation efficiency also need to be further investigated. To address the above problems, this document proposes an evacuation model for personnel considering changes in the field of vision. The main contributions of this paper are as the following.

In this paper, we consider the interaction between people and things and combine cellular automata with a behavioral heuristic model, using cellular automata controls personnel direction and using social force model controls personnel movement speed. This model relates the forces on pedestrians to the distance people move, reflecting the role of forces in the actual evacuation process and improving the computational efficiency of the combined model.

The static and dynamic field parameters are redefined so that they are no longer fixed, but variables related to the changes in the field of view. Using this approach we then establish a connection between conformity in psychology and the field of view and improve the improve the authenticity of the model’s psychology and behavior.

The field of view of people in eight directions is considered and the method of determining obstruction to human movement in cellular automata is improved. We combine it with the characteristics of the field of view addressing the problem that obstacles can affect the number of people and their position in the field of view under certain circumstances.

The evacuation process of the model is analyzed by changing the size of the field of view and the number of evacuees and compared with traditional evacuation models including the social force and cellular automata models.

3 Model

3.1 Field model

In this paper, a Moore-type cellular automaton is used to model evacuation. A 2D plane is also used to simulate the experiment. The experimental environment considered is a library, where people are relatively sparse compared to other densely populated sites. In this paper, considering the reference to resistance psychology in [39], in this case, the distance between the personnel radii determined in the evacuation process should be increased. Each lattice includes 1 m×1 m units. The surrounding direction probabilities are shown in Fig. 1. Therefore,

Fig. 1

Target cell next movement direction.

$P_{ij} = N^{- 1} e^{k_{s} S_{ij} + k_{d} D_{ij}}$ (1)

$N = \sum_{i} \sum_{j} e^{k_{s} S_{ij} + k_{d} D_{ij}}$ (2) where P_ij is the probability of pedestrian movement to the adjacent areas in the ground field model, N is the regularization factor, i, j represent the horizontal and vertical coordinates of the pedestrian location, respectively, k_s, k_d represent the static and dynamic field parameters, respectively. Furthermore, D_ij is the field value of the dynamic field, and S_ij is the field value of the static field:

$\begin{matrix} S_{ij} = & min_{(i_{Ts}, j_{Ts})} {max_{(i_{l}, j_{l})} {\sqrt{(i_{Ts} - i_{l})^{2} + (j_{Ts} - j_{l})^{2}}} \\ - \sqrt{{(i_{Ts} - i)}^{2} + (j_{Ts} - j)^{2}}} \end{matrix}$ (3) where (i_Ts, j_Ts)∈ { (i_T1,j_T1) , …, (i_T1, j_T2) } is the horizontal and vertical coordinate of the exit, and (i_l, j_l) is the coordinate of the farthest distance from the exit.

In this paper, we consider herd mentality to characterize the psychology of evacuation. Based on [40] the field value of the dynamic field, D_ij, is calculated. For t = 0, the field value of the dynamic field is $D_{ij}^{0} = 0$ . If pedestrians move from one cell to the next, the calculation steps are as the following.

1. Imprinting of the moved fields

$D_{ij}^{t + 1 / 3} = D_{ij}^{t} + 1$ (4) where $D_{ij}^{t + 1 / 3}$ indicates the first step dynamic field value.

2. Calculating the dynamic fields of attenuation and diffusion

$\begin{matrix} D_{ij}^{t + 2 / 3} = & (1 - λ) * (1 - δ) * D_{ij}^{t + 1 / 3} \\ + λ * \frac{1 - δ}{8} * (D) \end{matrix}$ (5)

$\begin{matrix} D = & D_{i, j - 1}^{t + 1 / 3} + D_{i + 1, j - 1}^{t + 1 / 3} + D_{i - 1, j - 1}^{t + 1 / 3} + D_{i + 1, j}^{t + 1 / 3} \\ + D_{i + 1, j + 1}^{t + 1 / 3} + D_{i, j + 1}^{t + 1 / 3} + D_{i - 1, j + 1}^{t + 1 / 3} + D_{i - 1, j}^{t + 1 / 3} \end{matrix}$ (6) where λ, δrepresent the diffusion and attenuation coefficients, respectively both set to 0.5 in this paper, D indicates the first step dynamic field value in the adjacent area. $D_{ij}^{t + 2 / 3}$ indicates the second step dynamic field value

3. Normalising the equations:

$D_{ij}^{t + 1} = D_{ij}^{t + 2 / 3} / \sum_{i} \sum_{j} D_{ij}^{t + 2 / 3}$ (7) where $D_{ij}^{t + 1}$ indicates the last step dynamic field value

3.2 Dynamically changing field parameter

In cellular automata, k_s, k_d denote static field parameters and dynamic field parameters respectively. These parameters indicate the sensitivity of the field in a fixed environment, which is generally a constant value [5]. In this paper, we assume that the environment is changing during the evacuation. Therefore, the sensitivity of both field values is changing with the surrounding situation. In this paper, the static and dynamic field parameters are therefore substituted by variable parameters related to the field of view.

The static field is set as the path service, k_s indicating the degree of pedestrian dependence on the path service. The dynamic field D_ij is also the field related to the herd mentality, hence k_d is the degree of personnel dependence on the herd mentality.

Xu Yang et al. [41] used the vector calculation method to study the influence of the position of other people in the field of view on herd mentality. The same approach can be applied to the calculation of the degree of dependence of people on the herd mentality k_d. Based on the original formula, this paper adds the number of people and field of vision area as the following

$O_{r} = \sqrt{(i_{t + 1} - i_{t})^{2}} + \sqrt{(j_{t + 1} - j_{t})^{2}}$ (8)

$o_{kr} = \sum_{k \in n} \sqrt{(i_{t + 1} - i_{kt})^{2}} + \sqrt{(j_{t + 1} - j_{kt})^{2}}$ (9) where i_t+1, j_t+1 are the horizontal and vertical coordinates at the next moment, i_t, j_t are the horizontal and vertical coordinates at that moment, n is the person in the field of view, and i_kt, j_kt are the horizontal and vertical coordinates of the other persons in the field of view.

$cos (β)_{ij} = \frac{O_{r} o_{kr}}{∥ O_{r} ∥ ∥ o_{kr} ∥}$ (10) where O_r is the direction vector of the pedestrian’s movement at the next moment, and o_r is the sum of the direction vectors of the other persons within the field of view.

$k_{d} = M^{- 1} \sum_{x = 0}^{M} cos (β)_{ij} \frac{n}{S}$ (11) where X is the number of other people in the field of view, M is the number of directions set, n denotes the number of people present in the field of view, and S is the number of squares in the field of view that account for the cellular auto-field site.

Experiments showed that when faced with other people or obstacles on the path, people tend to choose the path in which obstacles are furthest from them in their field of vision or the one without an obstacle [42, 43]. The motion heuristic model [44, 45] also determines the level of service of each path to a person. This model accurately infers the merits of the path in each direction and the degree of dependence k_s of the person on the path, to obtain service as the following

$L_{s} = (d_{max}^{2} + f^{2} - 2 d_{max}^{2} f cos (α_{0} - α))$ (12)

$k_{s} = L_{s} / M$ (13) where f is the distance of the individual to the nearest person in his/her field of view, d_max is the longest distance in the field of view of the person in case of a burst, and M is the number of directions set. α₀ is the direction of the target exit, α is the direction of the centerline of the field of vision, and α₀ - α is the included angle formed in two directions.

3.3 Distance that people move

In this paper, the direction of movement of the person is determined by a modified cellular automaton model with probabilities. Then the exit gravitational force and the resistance between the people and between the people, and the obstacles are calculated by the social force model, and the behavioral heuristic model respectively to obtain the combined force. The pedestrian’s speed is calculated via the Newtonian mechanics’ formula multiplied by the number of unit steps. In the new model, by using cellular automata to control the moving direction of personnel and social force model to control the moving distance, the combination of cellular automata and social force model is realized. If these two models are combined to determine the direction, it will not only greatly increase the computing pressure of the computer, but also reduce the calculation proportion of the herd mentality in the new model and reduce the calculation speed. Therefore, the division of labor between the two models can enhance the performance of conformity psychology in the new model, which can improve the computational efficiency. The integer part of the value is taken as the number of squares that can be moved at the next moment to determine the position (see Fig. 2). In Fig. 2, solid black squares represent the pedestrian, and shaded squares represent the direction and position in which the pedestrian may be able to move. This paper makes the calculation easier by taking the integer part of the moving distance. This is in line with the applicability of cellular automata to large-scale calculations. Rounding by distance results in a certain loss of moving distance. To compensate for this loss we enlarge the scale of the cell lattice and choose 1m×1 m units.

Fig. 2

Distance traveled by pedestrians.

As shown in Fig. 3, pedestrian movement is mainly influenced by the exits. Therefore, the gravitational force on the person is calculated using the method of attraction from the social force model [24 , 47] proposed by Helbing et al.:

Fig. 3

Pedestrian force diagram.

$\vec{f_{α}} = A_{i} e^{(r_{i} - d_{m}) / B_{i}} \vec{n_{im}} cos θ$ (14)

In the above, A_i denotes the intensity of social exclusion, B_i denotes the degree of attenuation, r_i is the acceptable radius of resistance, d_m denotes the distance between the person and the exit, θ denotes the angle between the pedestrian and the vertical normal to the door, $\vec{n_{im}}$ is the exit, and m denotes the normalized vector pointing towards pedestrian i.

The resistance to persons is mainly reflected in the interaction forces between people and people and objects. Therefore, this paper introduces the calculation of contact forces in the behavioral heuristic model:

$\vec{f_{β}} = kg (r_{i} + r_{j} - d_{ij}) \vec{n_{ij}}$ (15)

$\vec{f_{γ}} = kg (r_{i} - d_{γ}) \vec{n_{γ}}$ (16) where k denotes the obstruction effect in the case of determining physical interaction, g is 0 if the pedestrian is not in the field of view, and 1 otherwise, r_i denotes the radius of the person, r_j denotes the radius of other persons in the field of view, d_ij is the distance between the center of masses of the pedestrians, d_iγ denotes the distance between the center of mass of the pedestrian and the obstacle, $\vec{n_{ij}}$ is the normalized vector pointing from pedestrian j to pedestrian i, and $\vec{n_{i γ}}$ denotes the normalized vector of the obstacle γ pointing to pedestrian i. The combined forces are shown in Fig. 3 and are as follows

$\vec{F} = a \vec{f_{α}} - b (\vec{f_{β}} + \vec{f_{γ}})$ (17) where a, b are the number of weights, a + b = 1 and b = n/(Sf), n is the number of people in the field of view of the person, S is the number of squares of the field of view, and f is the distance of the nearest person in the field of view. Using coefficient b, we incorporate the effect of the number of people and the distance of the first person in the field of view on the resistance. The closer the other people are to the pedestrian, the higher the weighting coefficient and the greater the resistance.

In this paper, the traditional kinematic equations are used to combine force and velocity. Through the kinematic equations, we obtain the velocity: $\vec{v} = \vec{v_{des}} - \vec{F} t / m$ , where t is the buffer time, m is the mass of the pedestrian, $\vec{v}$ is the velocity after resistance in each direction, and ${\vec{v}}_{des}$ is the initial velocity of the pedestrian:

$\vec{v_{des}} = min (\vec{v_{0}}, \frac{d_{max}}{t})$ (18)

This formula limits the speed within the maximum field of view of the pedestrian, preventing overlap between persons and between the person and obstacles. Here, $\vec{v_{0}}$ is the maximum operating speed.

3.4 Handling of obstacles in the field of view

To improve the accuracy of the model’s field of view representation, this paper changes the field of view range by changing the number of field grids in each of the 8 directional fields of view (see Fig. 4). If the field of view range is 4, the grids in the green, blue, yellow and black areas are selected. If the field of view is 3, the grids in the blue, yellow and black areas are selected. If the field of view is 2, the grids in the yellow and black areas are selected.

Fig. 4

Field of the view calibration chart.

In dealing with the obstacle problem, it is necessary to target the obstacles in the personnel’s field of view. Otherwise, in calculating the dynamic and static fields the presence of obstacles result in the unavailability of the information in the field of view area as shown in Fig. 5. For number 1, number 3 is within the field of view to influence the actions of number 1, whereas number 2 is within the field of view of number 1 but he is blocked by the obstacle and cannot influence number 1. If the judgment rule of number 2 is not redefined, the model records and calculates the information of number 2. Therefore, new rules are required to determine how the number and location of obstacles in the field of view can affect other personnel.

Fig. 5

Special cases.

For the handling of the obstacle problem, we consider a case with a field of view of 4. For the judgment by personnel after facing complex obstacles in the new field of view conditions, we propose a solution as shown in Fig. 6. According to the principle of the smallest to largest and the order of arrows from left to right, the person’s field of view is numbered and calculated. This is used to mimic the person’s response to objects in the field of view.

Fig. 6

View order diagram.

The process of judging each arrow is shown in Fig. 8. Here the information about each arrow is gathered and the computer imitates the way people obtain information about the outside world. Since the model needs to determine the location and number of people and obstacles within the field of view, the judgment of people and obstacles is required. Therefore, this paper sets up the field that is used for the judgment in conjunction with the judgment of the process in Fig. 8 (see Fig. 7). The field sets the location where the obstacle appears as 0 and infinity. The point is judged to be infinity if it is identified as an obstacle. The other field sets the location of people as 0 and 1, and when the point is judged to be 1 it is identified as an evacuee. When it is judged to be 0, the location is also considered vacant.

Fig. 7

The obstruction field.

Fig. 8

Judgment Flow Chart.

3.5 Update rule

The overall update rules are as based on the following steps.

Step 1: Set the location of the pedestrians. Randomly distribute the locations of pedestrians within the field.

Step 2: Judge and obtain the position and number of other people and the position of obstacles according to the field of view characteristics.

Step 3: Calculate the static field, dynamic field, and their parameters according to the location and number of other people and the position of obstacles.

Step 4: The direction of pedestrian movement is obtained by calculating the probability of the pedestrian moving to the adjacent area, and the direction corresponding to the largest probability is considered as the direction chosen by the pedestrian.

Step 5: Calculate the force on the pedestrian by using the information obtained in step 2.

Step 6:Obtain the distance that the pedestrian moves.

Step 7: Set t = t+1.

Step 8: Determine whether the evacuation of the pedestrian is complete. If so, the cycle is terminated, otherwise, Steps 2 to 7 are executed again.

Step 9: End of the cycle.

4 Results and analysis

This experiment was programmed using Python to set up a 30 m×50 m library venue. The center of the door is located as (0, 25) and its width is 5 m, the radius of the person is 0.5 m, and the thickness of the wall is 0.5 m. We further assume the same length of pedestrian view for the same field of view. The distribution of people is also assumed to be uniform, as shown in Fig. 9.

Fig. 9

Map of the considered environment in the experiments.

4.1 Impact of change in the field of view on evacuation

In this paper, we set the number of evacuees to 200. The values of k_s,k_d and evacuation time are then calculated for different field-of-view ranges and presented in Table 1. It is seen that the evacuation time decreases by increasing the field of view. Therefore, the size of the field of view is an essential factor affecting the speed of evacuation.

Table 1
Average value of k_s, k_dat different fields of views

Field of view Evacuation Time k_s of Average value k_d of Average value

2 60s 0.204345797 0.248310042

3 47s 0.376034951 0.296171793

4 45s 0.446756585 0.397246743

Field of view	Evacuation Time	k_s of Average value	k_d of Average value
2	60s	0.204345797	0.248310042
3	47s	0.376034951	0.296171793
4	45s	0.446756585	0.397246743

For a small field of view, k_s< k_d, evacuation times are longer and people tend to rely on herd mentality to choose their path. For a larger field of view, k_s> k_d, evacuation time becomes shorter and people rely on path services to choose their paths. This indicates that if people rely on path services, evacuation is facilitated, whereas when they rely on herd mentality, evacuation is hindered. We also note that k_s increases by increasing the field of view, while increasing k_d negatively affects the evacuation. This implied that the level of route service determines evacuation efficiency and this psychology plays a certain role in promoting evacuation.

4.2 Impact of the number of people on the evacuation

Figure 10 shows the time required to evacuate people versus the number of evacuees. The required evacuation time is seen to tend to increase when the number of people grows from 100 to 700 with the same field of view. Furthermore, for larger fields of view, the evacuation time reduces. Also, the time required to evacuate fluctuates within a certain range as the number of people increases from 700 to 1,000. The time required to evacuate people in different fields of view is also similar, hence by increasing the number of people up to a certain threshold, the density of people increases, and the efficiency of exit utilization decreases. This results in a congestion phenomenon that is not affected by changes in the field of view.

Fig. 10

Relationship between the number of people and evacuation time.

4.3 Comparison with traditional evacuation models

Here we compare the proposed model with the traditional evacuation model, i.e. the traditional social force model and the traditional cellular automata model. For comparison, in this paper, the following simulation experiments are conducted.

1. Comparison with the traditional social force model in terms of evacuation time

In this paper, we obtain the time required to evacuate people under different models and the number of evacuees for a range of fields of view starting at 3. The results are shown in Table 2. It is seen that by increasing the number of evacuees, the time required for evacuation increases for all three models. Nevertheless, the time required for evacuation based on the new model and the traditional cellular automaton is much shorter than that required for the traditional social force model. This indicates that the new model is more efficient than the social force model.

Table 2
Time required to evacuate for different models with different numbers of people

Types of models Time required to evacuate 200 people Time required to evacuate 300 people Time required to evacuate 400 people

New Model 47s 68s 90s

cellular automata 43s 65s 83s

Social Force Model 968s 1990s 2784s

Types of models	Time required to evacuate 200 people	Time required to evacuate 300 people	Time required to evacuate 400 people
New Model	47s	68s	90s
cellular automata	43s	65s	83s
Social Force Model	968s	1990s	2784s

2. Comparison with the traditional social force model on crowd evacuation states

Figure 11 shows that, at 10 s, the evacuation of the three models is approximately the same. From the 20 s onwards, the new model and the traditional cellular automata model both begin to gather people towards the exit. However, people in the traditional social force model are still in a stray state. This phenomenon is the new model and cellular automata have a description of people’s behavior and psychology, that is, the “field model". In the process of calculation, the “field model” features can enable cellular personnel to quickly gather, forming traffic flow, arches, and other organizational phenomena in the lane. Therefore, the new model and cellular automata field model help people evacuate with a high degree of organization, which is closer to reality than the traditional social force model.

Fig. 11

Evacuation diagrams for different evacuation models at different times.

Combining the evacuation time and the evacuation situation, the following results can be obtained. For the same number of people, the new model has the same dynamic field as the traditional cellular automaton, i.e., the herding effect. Therefore, during the evacuation process, the cellular people can follow other cellular people to the exit more quickly. The computation time is also faster, and the new model has the same computation efficiency as the traditional cellular automaton. The new model has the same computational efficiency as the traditional cellular automaton, thus facilitating the simulation of large-scale evacuations.

3. Comparison with the traditional cellular automata model in the context of different population distributions

Table 2 shows that the new model is slightly better in terms of evacuation time than the traditional cellular automaton. Therefore, this paper analyzes the variables of the model and chooses to study its population distribution. Different scenarios of crowd distribution are analyzed for the crowd distributed on the left flank and the crowd distributed on the right flank. The main obstacles affecting the evacuation of the left wing are the seats, which are sparsely distributed and have a rather small size. The main obstacle affecting the evacuation of the crowd on the right wing is the bookshelf, which is characterized by large and dense obstacles. The considered site is as described above with a population of 200 people (see Fig. 12).

Fig. 12

The people distribution map.

The heat map for evacuating the crowd on the right flank is shown in Fig. 13. If the obstacle is a bookshelf, the difference between the two is the density of people on the vertical normal to the exit. This density is greater in the traditional cellular automaton than in the new model. This is attributed to the Manhattan distance algorithm used by the traditional cellular automaton for the calculation [14 , 49] resulting in a singularity in the route chosen by the people, and thus as a whole, the difference is not significant.

Fig. 13

Heat map for evacuation of the personnel on the right flank.

From the thermal diagram of left-wing personnel and right-wing personnel evacuation under different obstacles, we can draw the following conclusions: The main difference between the new model and the cellular automata in terms of evacuation occurs in the evacuation of sparse obstacles on the left side. The heat map for the evacuation of the crowd on the left flank is shown in Fig. 14. It is seen that the new model has darker-colored thermogram branches than the traditional cellular automata, with more personnel choosing to penetrate the gaps between the obstacles. At the exits, the new model appears to have larger arches and more extensive areas with a darker color. Therefore, compared to the traditional cellular automaton, the new model has a higher density of people at the exit and less efficient use of the exit results in a slightly longer evacuation time. It can be concluded from the left model that the model appears to have a larger arch compared to the traditional cellular automaton. This indicates that adding the socio-mechanical model to the new model results in greater resistance to people at the exit (which caused congestion) than that of the traditional cellular automaton. Therefore, the new model performs more competitively.

Fig. 14

Heat map for evacuation of personnel in the left wing.

4. Comparison of the new model with the cellular automatan model for the amount of entry and exit within the obstacle population

In Fig. 15 the green shear head is the approximate direction of the evacuation of people on the left flank. In Fig. 15, line 1 is (0,20) to (24,20) which is the entrance line into the obstacle cluster. Also, line 2 is (0,3) to (24,3) and (24,3) to (24,20), which is the exit line out of the obstacle cluster. The flow in and out of the left flank obstacle cluster is obtained and the results are shown in Fig. 16.

Fig. 15

Design drawing of the inlet and outlet flow lines.

Fig. 16

Inbound and outbound flow statistics at different times.

In Fig. 16(a), between 4∼23 s, the import flow of the new model is greater than that of the conventional cellular automaton. This suggests that in the new model more people chose to penetrate the obstacles. Figure 16(b) also suggests that between 4∼27 s, the new model has a larger exit flow than the traditional cellular automaton model hence taking a shorter time to reach zero and become stabilized. Therefore, more people arrive near the exit in the new model than in the traditional cellular automata. Therefore, the new model can calculate the gap movement probability between obstacles when dealing with obstacles, which is greater than that of the traditional cellular automata. The new model is more realistic than the traditional cellular automata in dealing with sparse obstacles.

The thermal evacuation map of the left flank crowd and the flow of people entering and exiting the left flank crowd obstacle cluster show that the new model has a faster arrival time at the exit due to the intersection of the sparse obstacles. This causes the exiting crowd to gather and form an arch-shaped area hence increasing the evacuation time. Nevertheless, in terms of evacuation routes, most people reach the exit through the interspersed obstacles more realistically. compared with the cellular automata, the new model can more likely calculate the evacuation route between obstacles. Therefore, the new model is more humanized for the obstacles.

5 Conclusion

5.1 The results of this research are listed in the following

(1) By increasing the field of view, the path becomes relatively clearer, hence the evacuees tend to rely more on the path level of service. This results in a shorter evacuation time. However, by decreasing the field of view, information on the path decreases, hence the evacuees tend to follow the herd mentality. This results in a longer evacuation time. Therefore, the route service level is essential in determining the efficiency of evacuation. Herd mentality is one of the main causes resulting in evacuation difficulties when the field of view is poor. By increasing k_d which is increased by increasing the field of view, evacuation time decreases, suggesting that herd mentality helps the evacuation process where people are dependent on the level of service of the path.

(2) As the number of evacuees increases, the evacuation time increases. After the number of evacuees reaches a certain threshold, the evacuation time does not increase but keeps fluctuating within a certain range which is not affected by the changes in the field of view.

(3) The new model is experimentally compared with the traditional cellular automaton and the social force model. In terms of evacuation time, the new model takes a shorter time compared to the social force model, and it requires shorter computational time enabling this model to be used in simulating systems with large numbers of evacuees of people. Compared to the traditional cellular automaton model, the evacuees in the new model are also able to move well through gaps between small, sparsely distributed obstacles, hence this model is more realistic than the cellular automaton.

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A study of evacuation model based on personnel vision change

Abstract

Keywords

1 Introduction

2 Literature review

3 Model

3.1 Field model

4 Results and analysis

Table 1 Average value of k s , k d at different fields of views Field of view Evacuation Time k s of Average value k d of Average value 2 60s 0.204345797 0.248310042 3 47s 0.376034951 0.296171793 4 45s 0.446756585 0.397246743

5.1 The results of this research are listed in the following

References

Table 1
Average value of k_s, k_dat different fields of views

Field of view Evacuation Time k_s of Average value k_d of Average value

2 60s 0.204345797 0.248310042

3 47s 0.376034951 0.296171793

4 45s 0.446756585 0.397246743