An enhanced multi-attribute crowd evacuation model incorporating the effects of environmental impact factors

Abstract

We propose an enhanced floor field model (FFM) to analyze the behavioral characteristics of crowds with varying attributes proportions during evacuation. This model governs pedestrian movement through the Dynamic Floor Field (DFF) and the Static Floor Field (SFF). The DFF takes into account individual factors such as the gender, familiarity with the environment, and social relationships of evacuees, which influence safe evacuation. Concurrently, the SFF encapsulates the impact of environmental factors like obstacles, exits, and guidance effects. Subsequently, this refined FFM was applied and validated using a sports center evacuation scenario. The results demonstrated that the enhanced FFM accurately replicated evacuees' asymmetric behavior and queuing, and aligned well with other models when the number of evacuees fluctuated over time. In the absence of guidance, both environmental familiarity and gender emerged as primary factors influencing partial evacuation. Additionally, the gender of pedestrians significantly affected the overall evacuation. Notably, compared to pre-existing environmental information available to evacuees, the implementation of guidance to augment pedestrians' environmental familiarity resulted in a more efficient evacuation. The FFM model and these findings could be instrumental in simulating personnel evacuation and formulating emergency management strategies in crowded areas.

1. Introduction

With the rapid acceleration of urbanization and population growth, there has been a notable increase in high-rise buildings and large civic and recreational venues in urban areas. These crowded places often face significant challenges during emergency evacuations, such as fires, earthquakes, and human-induced accidents. The high pedestrian density and complex building structures often lead to considerable casualties and property losses. During such incidents, pedestrian evacuation is considered as an emergency response, with the primary aim of minimizing damage [1]. Therefore, effective pedestrian evacuation in emergencies is crucial for public safety. Consequently, scholars across various fields have analyzed the behavioral characteristics of evacuees and their influencing factors. These analyses have led to improvements in evacuation models, the conduct of experiments and computer simulations, and the formulation of diverse evacuation measures and incentive strategies [[2], [3], [4]].

Existing evacuation theory models can be broadly categorized into macro and micro models [1]. Macroscopic models typically focus on overall evacuation processes, providing statistics and insights into collective behavior, while they may not capture individual-level interactions, avoidance behaviors, or goal-oriented actions. The Flood-Filled Algorithm [5], generally classified under the umbrella of macroscopic models, predominantly serves to identify connectivity and populated regions within images or areas. However, it does not extend its analysis to individual-level micro behaviors and decisions. This limitation suggests that in environments characterized by complexity or high congestion, the accuracy of evacuation results generated by this model may be compromised. Microscopic models, with their detailed characterization of evacuee behavior, can yield highly accurate evacuation results [3]. Among these microscopic models, the cellular automaton and social force models are the most extensively studied. The cellular automaton model is a dynamic system that evolves over a discrete time dimension within a space composed of discrete, finite-state cells, following specific local rules. In 2001, Bursedde et al. [6] proposed an improved version of this model, known as the floor field model (FFM), which has been widely used in evacuation modeling and simulation analyses. Several studies have explored the influence of environmental factors on evacuation, such as exits [[1], [2], [3]], the spread of fire [4], evacuation scene boundaries [7], obstacles and guidance personnel [8]. These studies have improved the methods for setting static floor field (SFF) values in the floor field model. Other research has improved the setting of field values for the dynamic floor field (DFF), taking into account factors such as behavioral characteristics [9,10], panic psychology [11], and emotional contagion [12].

The method of setting field values for floor fields typically involves calculating the probability of evacuee movement. However, most studies have not yet considered the practicalities of setting the movement possibilities of evacuees. The initial FFM specifies that pedestrians only move towards the cell with the smallest floor field value around them at a given moment [13]. When the floor fields have the same value and are located around the same evacuating pedestrian, most of the previous FFMs [[2], [3], [4],[7], [8], [9],11] set the probability of pedestrians moving toward the surrounding cells with the same field value. However, when pedestrians move to one of the cells with the same floor field value at the next moment, the probability is determined as 1, while the likelihood of moving to the other field values with the same floor is 0. This discrepancy is not equal. Hence, there are inherent disadvantages to the pedestrian movement rules set out above, the underlying causes of which are as follows:

• (1)SFF value setting. Evacuating pedestrians at different distances from exits and obstacles exhibit different evacuation behaviors [13,14], indicating that the environmental forces on pedestrians are related to the evacuees' location. Existing studies have less considered the changing pattern of environmental forces on evacuees at different location points within the scenario, ultimately resulting in the same field value of the SFF [1,2].
• (2)DFF value setting. Crowd dynamics involve a nonlinear system with heterogeneous individuals. In practical evacuations, crowd evacuation behavior is influenced by the attributes of pedestrians [15]. Previous studies on FFM have neglected the issue of pedestrian specificity, instead treating pedestrians as equally attributed cells, resulting in identical field values for the DFF.

The introduction of pedestrian-specific characteristics and the consideration of the relative conditions between pedestrians and their environment into evacuation models have been subjects of interest within the field of evacuation modeling research. Social force models are extensively utilized in pedestrian evacuation modeling due to their accurate representation of pedestrian idiosyncrasies and the degree of interaction forces between pedestrians and their environment. The social force model, initially put forward by Helbing et al. [16], takes into account factors such as pedestrian rushing, crushing, panic, and visual range, enabling it to mimic typical human behavior during an evacuation. Some previous studies have investigated the influence of environmental factors such as exits [13], obstacles [14], and guidance [17] on evacuation, utilizing the social force model. Conversely, other studies have examined the influence of individual attributes such as the health status of evacuees [18], social relationships [19], emotional state [20], and familiarity with the environment [21] on evacuation, also based on the social force model. However, the above studies have not incorporated the multi-attribute characteristics of actual evacuees and have neglected the interaction between these attributes. For instance, social relationships can affect evacuees’ familiarity with the environment [19], gender may be associated with personnel attention [22], and the conservative or aggressive psychology of evacuees can relate to their familiarity with the environment [23]. Pedestrians influenced by multiple attributes align more closely with actual movement speed and exit selection behavior [24,25]. Therefore, studying evacuees with a single attribute tend to be more one-sided and fails to accurately represent the actual evacuation situation of evacuees with diverse attributes.

This paper enhances the configuration of SFF values in four unique evacuation scenarios, taking into account the environmental impact on pedestrians, which includes exits, obstacles, and guidance personnel. It introduces non-uniform variations in SFF values to accurately represent the diverse influences of the environment on individuals. The social force model is utilized to calculate the force exerted by individuals with varying attributes, which in turn is employed to establish DFF values. A distinctive non-uniform floor field model, tailored to the behavioral characteristics of individuals in a sports center, is developed. This model is then used to simulate evacuations in the sports center, offering valuable insights into modeling evacuations for individuals with different attributes and enhancing emergency management.

2. Model description

2.1. Former FFM

The FFM segments the evacuation scene into numerous square equal-area square cells. It stipulates that each cell can accommodate a unique pedestrian at any given time and each cell corresponds to different SFF and DFF values.

The SFF value S_i,j varies with the evacuation environment. In the initial FFM, the SFF value magnitude is only related to the Euclidean distance from the pedestrian to the exit [6]. The SFF value starts from 0 at the exit and uniformly increases from the exit to each adjacent cell. The difference between adjacent cells' SFF values in each direction is 1. The formula for calculating this method's SFF value is shown in Eq. (1).

$$S_{i,j}=\mathit{min}\left(S_{i-1,j-1}+S_{i-1,j}+S_{i-1,j+1}+S_{i,j-1}+S_{i,j+1}+S_{i+1,j-1}+S_{i+1,j}+S_{i+1,j+1}\right)+1\text{.}$$ (1)

The magnitude of the DFF D_i,j varies with the position of the evacuees and the evacuation time. In the initial FFM, the magnitude of the DFF is related to the number of adjacent cells around the pedestrian, the diffusion coefficient of the DFF α, and the attenuation coefficient of the DFF β [6]. The formula for the field value of the DFF is shown in Eq. (2).

$${D_{i,j}}^{t+1}=\left(1-\alpha \right)\left(1-\beta \right){D_{i,j}}^t+\frac{\alpha \left(1-\beta \right)}{4}\cdot \left({D_{i+1,j+1}}^t+{D_{i+1,j}}^t+{D_{i+1,j-1}}^t+{D_{i,j+1}}^t+{D_{i,j-1}}^t+{D_{i-1,j+1}}^t+{D_{i-1,j}}^t+{D_{i-1,j-1}}^t\right)\text{.}$$ (2)

In the FFM, the probability of a pedestrian moving toward the surrounding cells is determined by combining the DFF and SFF values, the sensitive parameters of the DFF values k_s, and the sensitive parameters of the SFF values k_d. The pedestrian moves in the Moore-type field (Fig. 1(a)), with the maximum probability (Fig. 1(c)) in the surrounding direction (Fig. 1(b)). The spatial probability of each cell is calculated is shown in Eq. (3).

$$Pi,j=C\xi i,jexp\left[ksSi,j+kdDi,j\right]\text{.}$$ (3)

where P_i,j indicates the probability of a pedestrian moving toward the cell(i,j), and C is a normalization factor. When ζ_i,j = 1, the cell is occupied by pedestrians; when ζi,j = 0, the cell is not occupied by pedestrians.

Fig. 1.

Pedestrian movement rules. a. Moore-type field of the pedestrians. b. Possible movement directions of the pedestrian. c. Transition probabilities of the pedestrian.

2.2. Improvement of the SFF

This paper considers the center of the exit, obstacles, and guides as the center of a circle, using concentric circles with radii that are integer multiples of the length of the exit, obstacles, and guides. The overlapping area of the cell space and the circle is the base for setting the SFF values. We employ a method to set the SFF values under three different evacuation scenarios, as depicted in Fig. 2 [(a) - (c)].

Fig. 2.

Diagram of static floor field setup. a. No obstacles and no guide. b. Obstacles but no guide. c. Presence of obstacles and guidance personnel.

The equation for the field value of the SFF is shown in Eq. (4).

$$Suv=\sum _{i=1}^m\pi l{i}^{2}Sli+\delta 1\sum _{j=1}^p\pi h{j}^{2}Shj-\delta 2\sum _{k=1}^f\pi {\phi }^{2}Sk\text{.}$$ (4)

S_uv represents the SFF value considering the joint influence of obstacles and guide personnel; δ₁ and δ₂ are particular variables. There are obstacles or guidance personnel in the evacuation scene δ₁ = 1, and no obstacle or guidance personnel in the evacuation scene δ₁ = 0. l_i represents the radius of a circle centered on the cell of the exit and the overlapping area between this circle and the element with radius l_i is represented by S_li. Moreover, m represents the number of circles with the exit radius, h_j represents the circle's radius centered on the obstacle cell, and the overlapping area between the circle and the element with radius h_j is represented by S_hj. p represents the number of circles with the obstacle radius, φ represents the radius of a circle centered on the cell of the guiding effect, the overlapping area between the circle and the element with radius φ is represented by S_k, and f represents the number of circles with the guide radius.

2.3. Improvement of the DFF

2.3.1. Improved pedestrian interaction forces

The DFF value is influenced by the interaction among pedestrians [6]. In a practical evacuation, the different attributes of the evacuees result in variations in the forces acting between the pedestrians. To enable the FFM more accurately depict the real force conditions of evacuees, we employ the following equation to determine the magnitude of the DFF values. This is based on the calculation of pedestrian interaction forces in the social force model. The interactions between pedestrians, as described by the social force model, encompass psychological repulsion and physical friction. The formula for calculating the psychological repulsion is shown in Eq. (5).

$$\overrightarrow{{f_{nl}}^{soc}}=An\exp \left(\frac{rn+rl-dnl}{Bn}\right)\overrightarrow{enl}\text{.}$$ (5)

where $\overrightarrow{{f_{nl}}^{soc}}$ represents the psychological repulsion of pedestrians; $An$ indicates the force strength; $Bn$ represents the constant of the action range; $\overrightarrow{enl}$ is the unit vector, representing the direction of force from pedestrian n to pedestrian l; r_n represents the radius of pedestrian n, r_l represents the radius of pedestrian l, and d_nl represents the distance of the centroid between pedestrian n and pedestrian l.

The equation for the body contact force between pedestrians is shown in Eqs. (6), (7).

$$\overrightarrow{{f_{nl}}^{ph}}=kg\left(rn+rl-dnl\right)\overrightarrow{enl}+\mu g\left(rn+rl-dnl\right)\Delta \overrightarrow{vn{l}^t\cdot }\overrightarrow{tnl}\text{.}$$ (6)

$$g\left(rn+rl-dnl\right)=g\left(x\right)=\{\begin{array}{l}x,x\ge 0.\\ 0,x<0.\end{array}$$ (7)

where $\overrightarrow{fn{l}^{ph}}$ indicates the body contact force between pedestrians; k is the coefficient of body extrusion force; g is the gravity parameter; μ is the sliding friction coefficient; $\Delta \overrightarrow{vn{l}^t}$ is the relative tangential velocity, which is tangential to a unit vector, and the perpendicular direction is $\overrightarrow{tnl}$.

For moment t, pedestrians within the evacuation scene can be considered fixed; so, we set $v{n}^t=0$. Also, there is no overlap between pedestrians in the FFM, so when $rn+rl-dnl=0$ the repulsive force of pedestrians reaches a maximum, inter-pedestrian repulsion decreases with increasing pedestrian spacing. The equation for calculating body contact forces between pedestrians is shown in Eq. (8).

$$g\left(rn+rl-dnl\right)=g\left(x\right)=-\frac{\lambda }{x}\text{.}$$ (8)

where $\lambda$ is the repulsive force decay coefficient, and the value range is [0.18–0.3].

2.3.2. Identifying the group and the leaders in the group

This paper determines whether two pedestrians are a small group [26] based on the magnitude of the splitting force between the body contact force and the repulsive force at the pedestrian connection line. It is stipulated that if the physical contact force between pedestrians in the direction of the pedestrian connection line is greater than the repulsive force between pedestrians in the direction of the pedestrian connection line, the pedestrians are in a group; if the reverse is true, the pedestrians are not a group. The pedestrian with the lowest total repulsive force within the group is the group's leader. The formula for judging a small group is shown in Eq. (9).

$$\{\begin{array}{l}\rho a＞\bar{\rho },2ki＜K\text{Form}\mathrm{a}\text{small}\text{group.}\\ \rho a\le \bar{\rho }\text{Not}\text{forming}\mathrm{a}\text{small}\text{group.}\end{array}$$ (9)

where $\rho a$ is the population density that forms the aggregation phenomenon; $ki$ is the number of people within the unit with an angle of less than 90° towards the center personnel in a straight line; $K$ is the number of pedestrians per unit distance.

2.3.3. Determining the familiarity of the environment for evacuated pedestrians

In a multi-exit room, the familiarity of the leader with the exits is an essential factor in pedestrian evacuation. When the leader's familiarity with the exits converges with those around them, the probability of pedestrians moving toward the same exit increases [27]. The transmission efficiency of leaders in transmitting environmental familiarity information to surrounding pedestrians is related to distance; the greater the distance, the less efficient the transmission of information [24]. Evacuees in the vicinity who have a social relationship with the leader are more likely to receive information about the environment [28]. Therefore, the exit familiarity of the leader, the repetition of information between the leader and the surrounding personnel, and the social relationship are the primary bases for setting the field values of the moving floor field in this paper. The environmental familiarity of each evacuee set is given by Eq. (10).

$$F_{ij}=\left(\delta ij\frac{\sum _{a=i-1}^{i+1}\sum _{b=i-1}^{i+1}{d}_{kab}}{\sum _{a=i-1}^{i+1}\sum _{b=i-1}^{i+1}dab}de\frac{Ne}{N}+\xi ij\frac{\sum _{a=i-1}^{i+1}\sum _{b=i-1}^{i+1}{d}_{kab}}{\sum _{a=i-1}^{i+1}\sum _{b=i-1}^{i+1}dab}de\frac{Me}{N}\right)fe\text{.}$$ (10)

where F_ij represents the environmental familiarity of each evacuated pedestrian; δ_ij represents the attenuation coefficient of information transmission between ordinary pedestrians, where the information transmission attenuation coefficient set in this paper is 0.7; d_kab indicates the linear distance between each pedestrian with the same familiar exit around the evacuation pedestrian and the pedestrian; and d_ab indicates the linear distance between the cell of the pedestrian around the evacuated pedestrian and the pedestrian. d_e represents the repeatability of pedestrian exit information and its surroundings; N_e represents the number of individuals in the surrounding cells who have no social relationship with pedestrians; N represents the total number of evacuees in the surrounding cells; ξ_ij represents the attenuation coefficient of information transmission between pedestrians with social relations, where the value range is set as [0.7–1]; M_e indicates the number of individuals with social relations with pedestrians in the surrounding cells; and f_e represents the leader's familiarity with the environment. When the evacuees are in the same group, they are considered to have social relations; otherwise, they are considered not to have social relations.

The formula for the environmental familiarity of leaders within groups is shown in Eq. (11).

$$f_e=\frac{\sum _{q=1}^e\left(rq\times q\right)}{e}\text{.}$$ (11)

where q represents the number of exits familiar to leaders, $rq$ indicates the proportion of the total number of pedestrians who are familiar with the q quantity of exits, and e indicates the total number of exits in the room.

2.3.4. Determination of field values for DFF

The DFF in the model describes the distance subordination behavior of pedestrians to show the mutual attraction and repulsion between pedestrians based on familiarity with the environment. The DFF in the model is calculated by surrounding pedestrian information [28]. The calculation method of the dynamic field in pedestrian transition probability is shown in Eq. (12).

$$D_{ij}=F_{ij}\times {\left|\sum _{\left(i,j\right)}{F}_{ij}\right|}^{-1}\text{.}$$ (12)

The reference values [29] for each parameter of the above social force model are shown in Table 1.

Table 1.

Social force parameters of pedestrians with different attributes.

Familiarity of personnel with the environment	Familiar with the environment		Not familiar with the environment
Gender of personnel	Male	Female	Male	Female
Force intensity constant $An$/N	2000
Action range constant $Bn$/m	0.08
Body compression coefficient $k$/kg·s−2	1.2 × 105
Sliding friction system $\mu$/kg·m−1·s−1	2.4 × 105
Pedestrian radius $r$/m	[0.33–0.41]	[0.3–0.38]	[0.33–0.41]	[0.3–0.38]
Pedestrian expected speed $vi$/m·s−2	[1.30–1.65]	[1.19–1.47]	[0.4–1.35]	[0.3–0.98]

2.4. Personnel attribute settings

2.4.1. Physical indicators

Based on the “Chinese Adult Body Dimensions (GB/T 10000-1988)", Table 2 showcases the parameters for varying body measurements of individuals. This paper takes into account the distinctive attribute characteristics of the population within the sports center. For males, the body weight is randomly distributed within the range of 45 kg–80 kg, while for females, it's randomly distributed within the range of 40 kg–75 kg. The height of males is randomly distributed within the range of 154 cm–180 cm, and for females, it's randomly distributed within the range of 150 cm–170 cm. The radius for males is assigned a random value within 0.33 cm–0.42 cm, whereas, for females, it's assigned a random value within 0.30 cm–0.39 cm.

Table 2.

Physical index parameters of personnel.

Percentile	Male			Female
	18–60 years old			18–55 years old
	Weight/kg	Height/m	Shoulder width/mm	Weight/kg	Height/m	Shoulder width/mm
1	44	1543	330	39	1449	304
5	48	1583	344	42	1484	320
10	50	1604	351	44	1503	328
50	59	1678	375	52	1570	351
90	71	1754	397	63	1640	371
95	75	1775	403	66	1659	377
99	83	1814	415	74	1697	387

2.4.2. Movement speed

Variations in individual attributes, including age, gender, social relationships, physical fitness, familiarity with the environment, and education level of evacuees, as well as differences in the structures, functions, personnel density, and disaster resilience, result in different evacuation speeds for different individuals in varying scenarios [30]. The evacuation speeds assigned to evacuees in this study are delineated in Table 3.

Table 3.

Movement speed of personnel with varying attributes.

Movement State	Male	Female	Children or elderly people
Emergency state, horizontal walking	1.35 m/s	0.98 m/s	0.65 m/s
Emergency state, top-down	1.06 m/s	0.77 m/s	0.40 m/s
Normal state, horizontal walking	1.04 m/s	0.75 m/s	0.50 m/s
Normal state, top-down	0.40 m/s	0.30 m/s	0.20 m/s

3. Results and discussion

3.1. Comparison of models and determination of k_s and k_d

This article takes a small sports center as the research object and infers the simulation analysis of large venues and crowds by changing the crowd density. The competition center is 92.9 m long and 62.3 m wide, with a total area of approximately 5869 square meters and a height of 14.34 m. It comprises three floors and eight exits. The gymnasium includes 2252 seats designed to evacuate 2000 to 3000 people. To comply with the evacuation situation, it sets the gender ratio of sports centers to 3:1, with children and the elderly accounting for 15% of all evacuation personnel.

The new floor field model (NFFM) was applied via MATLAB software to simulate multiple evacuations of 532 pedestrians on the ground floor of the sports center without setting up a guidance role. The floor field values for the evacuation scenario were sized as shown in Fig. 3. The different colors in the figure represent different floor field values calculated according to the improved model.

Fig. 3.

Floor field value of the evacuation scene.

The average evacuation times for the different k_s and k_d are shown in Fig. 4.

Fig. 4.

Average evacuation time varies with k_s and k_d.

In this paper, we constructed the same evacuation scenario for an evacuation simulation based on Anylogic and Pathfinder software, fixed k_s and k_d values, and compared and analyzed the NFFM with other models to verify the model's validity. After simulating the evacuation of pedestrians from the sports center several times by Anylogic, we observed that the average time for all pedestrians to move out of the evacuation scenario of the sports center is 185.13 s. In comparison, that of Pathfinder is 143.8 s, as seen from Fig. 4, when k_s = 0.8 and k_d = 0.5, the evacuation time of the NFFM model was the closest to the Anylogic simulation. Moreover, when k_s = 0.4 and k_d = 0.5, the evacuation time was closest to the Pathfinder simulation.

To select the most suitable k_s and k_d for this sports center scenario, we contrasted the NFFM with the original FFM, Pathfinder built-in model (STM), and Anylogic built-in model (SFM) by calculating the variation in the number of pedestrians within the evacuation scenario.

It can be seen from Fig. 5 that when the relationship between the number of pedestrians remaining in the evacuation scene and the evacuation time is studied, the NFFM fits well with other models. When k_s = 0.8 and k_d = 0.5, the evacuation curve of the NFFM fitted best with the STM and the SFM. The distribution of evacuees based on NFFM under this parameter is shown in Fig. 6 [(a) – (f)].

Fig. 5.

Comparison of evacuation models.

Fig. 6.

Distribution of evacuees when k_s = 0.8, k_d = 0.5. a. T = 13.35 s. b. T = 43.17 s. c. T = 84.84 s. d. T = 109.79 s. e. T = 138.94 s. f. T = 174.36 s.

It can be seen from Fig. 6 that pedestrians showed a symmetrical destruction effect and uneven distribution [21] and queuing [31] during evacuation. Each sub-area exit carried the evacuation sequence of the last evacuation pedestrian: lower right exit > upper right exit > upper left exit > lower left exit.

We divided the evacuation scene into four equal area sub-areas with the same initial density of pedestrians and symmetrical initial distribution based on the evacuation center point and the evacuation exit location. Because the obstacles and exits in the upper left and upper right areas were symmetrically distributed, the evacuation crowd's uneven distribution had nothing to do with obstacles and exits. Because the NFFM determines the floor field value based on gender and familiarity with the environment, we speculated that the uneven distribution of pedestrians was related to the differences in the attributes of pedestrians in the evacuation scene.

It can be seen from Fig. 7 that when the initial density of the evacuation population is the same, the increase in the proportion of men and pedestrians familiar with the environment among the evacuation population in each sub-area promotes the evacuation [[20], [21], [22]]. Moreover, compared with other models, NFFM can better reflect the impact of gender and the proportion of pedestrians familiar with the environment in each sub-area on the evacuation results. This indicated that the difference in pedestrians’ environmental familiarity and gender proportion could significantly affect regional evacuation.

Fig. 7.

Relationship between crowd attribute ratio and evacuation time.

3.2. Effect of the proportion of pedestrian's attributes

In Fig. 7, the changing trend of the male proportion in each region was the same as that of the number of pedestrians familiar with the environment. To explore the main personnel attributes that affect the evacuation of pedestrians, we simulated the evacuation of pedestrians of different genders randomly distributed in the evacuation scene of the sports center and the proportion of pedestrians familiar with the environment. The relationship diagram between the female proportion and the evacuation time is shown in Fig. 8 (a), and the relationship diagram between the proportion of pedestrians familiar with the environment and the evacuation time is shown in Fig. 8 (b).

Fig. 8.

Relationship between the pedestrians attribute proportion with the evacuation time. a. the proportion of female pedestrians. b. the proportion of pedestrians familiar with the environment.

It can be seen from Fig. 8 (a) that at the same gender ratio, the evacuation time of a population increases as the initial population density in the evacuation scenario increases. At the same initial population density, the evacuation time of the population increases with an increase in the proportion of females in the evacuation scenario. The reason behind this phenomenon is that, compared to males, females have slower movement speeds. An increase in the proportion of females in the evacuating population results in a lower average movement speed of the population, ultimately leading to longer evacuation times. The results indicate that both population density and gender distribution are significant factors influencing overall pedestrian evacuation.

It can be seen from Fig. 8 (b) that when the proportion of pedestrians familiar with the environment is the same, evacuation time of the population increases as the initial population density in the evacuation scenario increases. At the same initial population density, the evacuation time of the population exhibits only a slight change with an increasing proportion of pedestrians familiar with the environment in the evacuation scenario. The reason behind this phenomenon is that as the proportion of pedestrians familiar with the environment increases, an increasing number of evacuees quickly move towards the nearest evacuation exits. This results in an elevated local pedestrian density within the evacuation scene, which hinders pedestrian evacuation. Consequently, this leads to no significant variation in evacuation time for different population densities. The results suggest that, in contrast to the proportion of pedestrians familiar with the environment, population density is the primary factor influencing overall pedestrian evacuation.

3.3. Effect of priming on familiarity with the crowded environment

The evacuation results in Fig. 8 (a) and Fig. 8 (b) showed that the increase in the proportion of pedestrians familiar with the environment has no significant effect on evacuation time compared with the gender ratio of the evacuation population. However, in real life, owing to the transmissibility of environmental information, the proportion of pedestrians familiar with the environment gradually increases with the evacuation process. The transmission of environmental information among pedestrians can effectively reduce evacuation time and improve evacuation efficiency [32], which indicates that increasing the proportion of pedestrians familiar with the environment improves evacuation efficiency [33].

To explore the causes of the above contradictions, we considered the differences in the environmental information obtained by evacuees. The environmental information obtained by evacuees in the evacuation process was called available environmental information (AEI), and the inherent environmental information of evacuees before evacuation was called inherent environmental information (IEI). In this study, the proportion of evacuation crowd affected by these two kinds of information was controlled by the difference in the number of guide personnel.

The setting of guide personnel is shown in Fig. 9. Connected adjacent obstacles or walls in the evacuation scene by separation lines and placed one guide personnel on each separation line. Assuming that pedestrians were affected by the corresponding guide when passing through each division line, the number of evacuees passing through each line was calculated according to the arrow direction, as shown in Table 4. Different numbers of guide personnel were set to control the proportion of AEI evacuees. No guide personnel were positioned in the evacuation scene when the proportion of evacuees’ IEI was changed.

Fig. 9.

Position of guide personnel.

Table 4.

Number of pedestrians passed the division line.

Division line number	Passed by quantity	Division line number	Passed by quantity	Division line number	Passed by quantity	Division line number	Passed by quantity
A1	0	A11	0	A21	18	A31	0
A2	41	A12	66	A22	0	A32	0
A3	31	A13	72	A23	0	A33	0
A4	11	A14	72	A24	0	A34	0
A5	83	A15	118	A25	18	A35	91
A6	94	A16	111	A26	21	A36	64
A7	36	A17	19	A27	19	A37	51
A8	49	A18	0	A28	1	A38	52
A9	54	A19	0	A29	18	–	–
A10	0	A20	18	A30	0	–	–

It can be seen from Fig. 10 [(a) – (d)] that when the proportion of pedestrians familiar with the environment increases in different population densities, the pedestrian evacuation time based on the impact of AEI is unchanged. However, the evacuation time of people affected by IEI shows a downward trend. This indicated that the AEI and the IEI have different effects on improving the evacuation efficiency of evacuees. Compared with the proportion of pedestrians who change their inherent familiarity with the environment, using guidance to improve the proportion of evacuees familiar with the environment improves evacuation efficiency.

Fig. 10.

Change chart of crowd evacuation time from different environmental information sources. a. 0.97 p/m². b. 1.36 p/m². c. 1.77 p/m². d. 2.36 p/m².

3.4. Analysis of limitations and deficiencies

Given the complexity of the sports center's personnel composition, venue structure, and the unpredictable safety of personnel, simulations cannot entirely replicate the real-world scenarios of disasters and accidents, leaving room for improvement in the relevant aspects. The comparison between the enhanced floor field model and various other models only takes into account a single factor, that is, the evacuation time. In future research, different factors such as the number of evacuees and the spatial distribution of personnel in actual scenarios can be compared to analyze the strengths and weaknesses of the model. Moreover, the behavioral characteristics of sports center personnel are influenced by factors such as the type of sudden accidents, the degree of harm, and the location of occurrence. This study did not measure the speed changes of personnel in different accident scenarios. In future research, the impact of varying environmental factors on the force of personnel can be further analyzed by examining the speed changes of personnel in sports centers under different accident scenarios.

4. Conclusion

This paper enhanced the method of setting the floor field value by using the force rule observed in crowd evacuation scene. Furthermore, the constructed FFM is employed to simulate pedestrian evacuation in a sport center. The conclusion derived from the results are as follows:

(1) The refined model effectively replicates the asymmetrical evacuation and queuing phenomena and aligns well with other models when the number of researchers fluctuates over time. (2) In comparison to environmental factors such as obstacles, the gender and the proportion of pedestrians familiar with the environment significantly influence asymmetrical evacuation. (3) In the context of region-specific analysis without guidance, environmental familiarity and gender emerge as the primary factors affecting evacuation. Among these, gender exerts a more substantial impact on evacuation. (4) Compared to the information about the evacuation scenario that evacuees possess, using guidance to augment the familiarity of evacuees with the environment can bolster evacuation efficiency. Consequently, it is crucial to develop effective guidance strategies for pedestrians with limited environmental familiarity.

Data availability

The data that has been used is confidential.

CRediT authorship contribution statement

Lingjie Zhu: Writing – original draft, Methodology, Formal analysis, Data curation. Xiaomeng Xu: Writing – review & editing, Supervision, Resources, Project administration, Conceptualization. Jian Wang: Software. Jiahao Chen: Writing – original draft, Validation, Software, Formal analysis. Zhengjia Ma: Writing – review & editing. Qiang Wang: Writing – review & editing, Software, Conceptualization. Qifei Wang: Software.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Nomenclature

Symbol Description

$\alpha$

Diffusion coefficient of the DFF

$\beta$

The attenuation coefficient of the DFF

$C$

Normalization factor

$m$

Number of circles with the exit radius

$P$

Number of circles with the obstacle radius

$f$

Number of circles with the guide radius

$\phi$

The radius of a circle centered on the cell of the guiding effect

$e$

Total number of exits in the room

$k$

Coefficient of body extrusion force

$g$

Gravity parameter

$\mu$

Sliding friction coefficient

$\lambda$

Repulsive force decay coefficient

$N$

Total number of evacuees in the surrounding cells

$q$

Number of exits familiar to leaders

$\rho a$

The population density of the group forming the aggregation phenomenon

$K$

The number of pedestrians per unit distance

$ki$

Number of people within the unit with an angle of less than 90° towards the center personnel in a straight line

$ks$

Sensitive parameters of the DFF values

$kd$

Sensitive parameters of the SFF values

$\delta 1$

Particular variables

$\delta 2$

Particular variables

$li$

The radius of a circle centered on the cell of the exit

$hj$

The radius of a circle centered on the cell of the obstacle

$Sk$

Overlapping area between the circle and the element with radius φ

$An$

Force strength

$Bn$

Constant of the action range

$rn$

The radius of pedestrian n

$rl$

The radius of pedestrian l

$de$

Repeatability of pedestrian exit information and its surroundings

$Ne$

Number of individuals in the surrounding cells who have no social relationship with pedestrians

$Me$

Number of individuals with social relations with pedestrians in the surrounding cells

$fe$

Leader's familiarity with the environment

$rq$

Proportion of the total number of pedestrians who are familiar with the q quantity of exits

$\left(i,j\right)$

The coordinate of the neighbor cell of the pedestrian

$Si,j$

Magnitude of the SFF

$Di,j$

Magnitude of the DFF

$Pi,j$

Probability of a pedestrian moving toward the cell(i,j)

$Fij$

Environmental familiarity of each evacuated pedestrian

$\delta ij$

Attenuation coefficient of information transmission between ordinary pedestrians

$\xi ij$

Attenuation coefficient of information transmission between pedestrians with social relations

$Suv$

SFF value considering the joint influence of obstacles and guide personnel

$S{l}_i$

Overlapping area between the circle and the element with radius l_i

$S{h}_j$

Overlapping area between the circle and the element with radius h_j

$dnl$

Centroids distance between pedestrian n and pedestrian l

$dab$

Linear distance between the cell of the pedestrian around the evacuated pedestrian and the pedestrian

$dkab$

Linear distance between each pedestrian with the same familiar exit around the evacuation pedestrian and the pedestrian

$\overrightarrow{enl}$

Direction of force from pedestrian n to pedestrian l (unit vector)

$\overrightarrow{tnl}$

Tangential unit vector

$\Delta \overrightarrow{vn{l}^t}$

Relative tangential velocity

$\overrightarrow{{f_{nl}}^{soc}}$

Psychological repulsion of pedestrians

$\overrightarrow{{f_{nl}}^{ph}}$

Body contact force between pedestrians