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Article

Visualization of Emergency Evacuation Physical Behavior under Multi-Agent Decision-Making

1
Intelligence and Automation in Construction Fujian Province Higher-Educational Engineering Research Centre, College of Civil Engineering, Huaqiao University, Xiamen 361021, China
2
Department of Physical Education, Xiamen Institute of Technology, Xiamen 361021, China
3
College of Civil Engineering, Huaqiao University, Xiamen 361021, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(9), 5509; https://doi.org/10.3390/app13095509
Submission received: 2 April 2023 / Revised: 23 April 2023 / Accepted: 25 April 2023 / Published: 28 April 2023

Abstract

:
Emergency evacuation simulation is significant for architectural design and emergency plan implementation. To explore the influence of evacuees’ physical behavior and evacuees’ decisions on the evacuation process, as well as to address the problems of traditional emergency evacuation models with insufficient detail of the situation (realism), low reusability, poor operability, and lack of subsequent scalability, this paper first analyzed pedestrian characteristics in emergencies. To describe pedestrian decision-making in an emergent evacuation situation, a multi-agent design based on decision theory was proposed, solving the multi-agent decision-making problem in an emergency evacuation environment by the A* algorithm. Then the designed multi-agent was embedded into the social force model by AnyLogic software. Finally, the model reproduces the pedestrian evacuation process in an emergency evacuation situation on the built platform, depicting three kinds of typical behaviors: pedestrian partnering, obstacle avoidance, and exit competition. In addition, this study also analyzed a large student apartment building by example and proposed corresponding optimization solutions to improve its evacuation capacity through simulation results.

1. Introduction

In the event of an accident in a highly populated place, internal evacuation is very difficult, and mass casualties due to evacuation problems are very likely to occur [1]. The physical behavior of pedestrians during emergency evacuation falls under the category of evacuation dynamics, which is particularly prone to panic due to the limited and crowded environment in such crowded building environments, thus affecting evacuation efficiency and causing unnecessary casualties due to stampedes [2]. Therefore, an engineer is required to analyze the fire safety design of the building, and in such analysis usually, the engineer compares the output of the fire modeling with the estimated evacuation time of the building to assess whether there is enough time for the occupants to evacuate the structure [3,4]. However, evacuation time is susceptible to the physical behavior of evacuees, and the importance of behavioral factors in emergency evacuation was discussed by Mohler as early as 1964, and these behaviors include partnering behavior, obstacle avoidance behavior, and exit competition behavior [5], which has received extensive attention from scholars in the fields of physics, psychology, computer science, and sociologists [6,7]. Schatz et al., discussed the need to incorporate evacuation behavior into evacuation planning and modeling to support the incorporation of physical behavior (individual or collective) into evacuation models [8,9], but due to the complexity of physical behavior, there is a plethora of research on physical behavior during evacuations.
With the rapid development of computer simulations, researchers have introduced these physical behaviors into simulation models for the evaluation of fire safety design of buildings and solutions for behavioral factors [10]. For such problems, evaluation models at this stage are divided into two main categories: macroscopic and microscopic [11,12,13,14,15]. Macro is mainly studied for theoretical purposes, analyzing pedestrian movement characteristics, bottleneck effects, and crowding phenomena using more advanced model effects. However, macro models usually consider the crowd as a whole and ignore the interactions between pedestrians and pedestrians and pedestrians and the environment. Microscopic models, on the other hand, address detailed studies, such as human–person interaction forces. There have been many studies on microscopic models, including the cellular automata model [13,16,17,18,19,20], social force models [15,21,22,23,24,25,26,27,28], and lattice gas models [29,30]. However, the difficulties of evacuation research are reflected in the large arbitrariness of pedestrian movement, the many factors that influence their behavior, and the complex walking behavior. The evacuation process and the realism of existing models can be greatly limited from the perspective of pedestrian factors, such as pedestrian psychological state and command execution. Crowd behavioral understanding is critical in a wide range of applications because crowd action essentially consists of a continuous decision-making process based on a vast array of factors, such as the pedestrian’s destination, interactions with nearby pedestrians, and interactions with upcoming events. In addition to the number of factors that influence pedestrian decision-making, how humans consider these factors before making a decision is also underutilized. Humans do not simply act on them. They also anticipate future states and drive current actions backward. A typical example is when two people traveling in orthogonal directions are constantly positioning themselves about each other to predict whether they will collide. Therefore, it is significant to focus on methods and techniques for safe evacuation assessment [1]. However, most of the current emergency evacuation models have problems such as insufficient detail situation (realism), low reusability, poor operability, and lack of subsequent scalability hardly support the above work effectively.
In response to the abovementioned problems, the purpose of this study was to apply the multi-paradigm modeling idea method to the field of emergency evacuation and propose a new emergency evacuation modeling method. The methodology uses the AnyLogic software developed based on the social force model as a secondary development platform, adding a multi-agent based on decision theory to the social force model so that evacuated individuals can make autonomous decisions. The model fully considers various influencing factors in the evacuation process, takes the case building as the physical environment, and establishes an overall evacuation model to observe the evacuation process. It lays the foundation for further understanding the evacuation law of people under disaster scenarios, provides new ideas and technical support for fire simulation exercises and emergency plan development in multi-scheme buildings, and provides a certain degree of reference for building fire performance design in the early stage of building planning.

2. Theoretical Basis

2.1. Pedestrian Characteristics in Emergencies

The process of emergency evacuation is a reflection of people’s behavior in the event of an emergency, so it has a close connection with human psychology. In the case of emergency emergencies, the stimulation of certain specific factors throughout the process leads to some more typical psychological reactions of people. These mainly include panic, subordination, affinity, etc.
(1)
Panic
People feel nervous and fearful because of sudden and dangerous surroundings, named panic. Pedestrians are unable to think normally and calmly during panic [2]. Panic can disrupt the pedestrians’ proper judgment and make them incapable of responding effectively to unexpected events, leading them to adopt unwise practice strategies or misbehave. Fear of pedestrians can be more intense when the distance between the hazard and the pedestrian is closer. At the same time, the escape process in the face of certain dangerous conditions of the irritation, usually due to excessive panic and intensive panic and lead to irrational self-preservation behavior in the evacuation process, thus occurring crowding, pushing, and even trampling and other dangerous behavior of the main reason.
(2)
Following the crowd
In an emergency, pedestrians are unable to react in time and will assume that it is safe to be with the public. Individuals will automatically follow the crowd of most pedestrians and lack independent and correct thinking to follow blindly, which may exacerbate the emergency and cause secondary accidents such as stampedes [31].
(3)
Affinity
When people’s safety is threatened, they will choose and flee to a safer area as soon as possible. In this process, people tend to develop dependency psychology, which leads to many people gathering. Therefore, without effective identification or proper guidance during the evacuation process, pedestrians will flee to where the crowd is congregating, thus leading to longer evacuation times [31].

2.2. Social Forces Model

In 1951, Helbing, a German transportation scientist, put forward the concept of social force: the interaction between the driving force of personnel themselves, the force between personnel, obstacles, and other built environments [2,3]. Then, based on the laws of system dynamics, he and his partners constructed a Social Forces Model to simulate human movement and other behaviors throughout the evacuation process [32]. The social force model mainly quantifies the factors affecting pedestrian movement through the expression form of the force. According to the analysis of Newton’s second law, the behavior trend in the movement of people is expounded [2,3]. According to reality, a variety of social forces can be set to keep a certain distance between people. The mathematical expression of this model is shown in Equations (1)–(4). In this formula: m α is the quality of personnel a; w α is the speed that people like in this environment; F α t is the resultant force on personnel; ξ is an uncertain random variable; F α 0 is the driving force; F α β is the interaction between people; F α β is the force between people and other objects; F α i is attraction; f ( t ) α β s o c is the psychosocial forces; f ( t ) α β p h is physical strength.
m α d w α d t = F α t + ξ
F α t = F α 0 t v α , v α 0 e α + β F α β e α , r α r β + B F α B e α , r α r B + i F α i e α , r α r i , t
F α 0 t v α , v α 0 e α ) = m α 1 τ α ( v α 0 e α v α
f α β r α β = f ( t ) α β s o c + f ( t ) α β p h
Since it was proposed, the social force model has been widely concerned and recognized, especially in the field of emergency evacuation has been widely promoted and used. This model can decompose and set the interaction force of each person, and reflect the different roles of different people in the evacuation simulation process. Compared with the cell model of cellular automata, the force of the agent in the social force model is continuous, and the information of people in the group can be arbitrarily specified, so the simulation results are more accurate. Secondly, the model can also reflect the congested state of crowd evacuation, making the evacuation process and result more real. In addition, the formula expression of the model is simple and clear, and the parameters have a certain stability, which can reflect the phenomenon of companion effect and bottleneck competition in the evacuation simulation experiment, and adjust the expected speed of personnel to make them constantly change their state (normal state → panic state), which is more suitable for the actual situation of evacuation.
Therefore, more and more evacuation studies have been conducted through social force models and applied to various scenarios [21,22,23,24]. For example, Parisi introduced an automatic deceleration-stop mechanism to study the effect of the distance between two bodies on the velocity [33], and Frank studied the impact of indoor structures and other appurtenances on the evacuation of pedestrians based on the social force model [34]. Sticco et al. used analytical techniques and numerical simulations, and appropriate correction of friction coefficients was performed so that the density and flow relations output by the fundamental social force model matched those in pedestrian dynamics [35]. Stuart proposed a method for adjusting pedestrian interactions and combining it with the social force model to obtain simulation results [36]. Köste et al. presented a simple yet moderated [37]. Priscila Saboia modified the social force model with a moving grid to achieve softer and more coherent motion trajectories [38]. Osama Moh’d Alia proposed a technique for solving the social force model based on harmonic search [39], which increased the convergence speed and improved the performance of the harmonic search algorithm to solve the social force model, which has the disadvantage of being computationally intensive.

3. Model Design Methodology

3.1. Model Design Ideas

According to the different roles played in the model, the whole model system is divided into two steps: evacuation agent design and evacuation environment construction. The evacuated individual is constituted by the Agent-Based Model and Simulation (ABMS), and the multi-agent decision algorithm is embedded into it by Java code. The evacuation environment is a metamodel of the building environment built by the AnyLogic platform, modeling the evacuation event by Discrete Event Model and Simulation (DEMS) in the AnyLogic platform, and finally combining the designs of evacuated individuals with the evacuation environment.

3.2. Multi-Agent Design Based on Decision Theory

3.2.1. Multi-Agent Type and Internal State Module

Human variability is reflected in many aspects, such as age, body shape, personality, physiology, must-be tolerance, etc. In this essay, intelligent bodies are roughly divided into three categories: adults, older people, and children. The state of the intelligent body can be expressed as panic value, physiological state, psychological state, personality, etc., and the action strategy of the next moment is decided according to its state and the perceived information. The internal state of the intelligent body is described in this paper mainly for the physical and emotional panic values, and this paper stipulates that the panic value of the intelligent body is not considered or set to 0 under normal circumstances, and the calculation of the panic value of the intelligent body can be expressed by Equation (5) when in an emergency
C d a n g e r = a e d + b e 1 / ρ
where is the distance between the person and the hazard source; ρ is the perceived density: a,b is the scaling factor, a + b = 1. The description of physical strength should be related to the speed of the intelligent body, which simultaneously and inversely affects the speed of the intelligence. The value of physical strength can be calculated by Equation (6).
λ t + 1 = λ t × e x p { { v t k × s i n [ π 2 × | λ t λ m a x | ] } × r }
where k,r indicates the control parameters; from the equation, we can see that when the human speed is high, the rate of physical exertion will be quick, but with the continuation of the movement and the decline in physical energy, through the rapid breathing to obtain more oxygen, physical energy, and corresponding replenishment, the human physical exertion rate will then slow down. Determination of maximum speed: The walking speed of humans in the traditional model is a fixed value, which does not reflect the variability of intelligent body W and the speed is influenced by many factors. In this study, we propose that the maximum speed of an intelligent body at each step is related to its own physiological and imperative state W and crowd density, as shown in Equation (7).
v m a x = ( 1 + 2 C d a n g e r ) e ε × ρ / λ × v a v e r a g e
where ρ is the perceived density; ε is the coefficient of determination, taken as ε = 1.26; average is the average speed of the person, randomly taken between [1.2, 1.5] m/s for adults and [0.58, 1.2] m/s for the older people and children, to reflect the variability between intelligence; Cdanger is the panic degree, which indicates that the more nervous the intelligent body is, the faster the escape speed. This study proposes that in normal conditions, each intelligence takes a random fixed value in the corresponding Vaverage, and the default speed is Vmax when various actions performed in emergencies are not specified.
Multi-agent perception is a particularly relevant module for simulation. All information in the computer simulation environment can be obtained through the environment model, so the key to the perception model is how to simulate the functional limits of the human organism human being, through the perception-oversensitive body, to obtain the information that can be perceived by the senses and filter out the information that cannot be perceived. The intelligent body can perceive information such as distance, type, and state about other objects through the perception model. The principle of the visual filter is to determine whether an object can be perceived based on the relative position of each object in the environment to the human eye, which involves determining whether the target is within the perceptual field of view and additionally considering whether the subject is obscured by another object in the line of sight to the human eye.
In practice, the human perception range should be a sector with a left–right distance smaller than the distance ahead, while the perception radius R of the multi-agent is shown in Equation (8):
R D = ( 1 C d a n g e r ) × k v
The Cdanger panic level is a value between [0, 1], depending on the perceived danger; kv is a unit of visual separation, used to indicate the strength of visual ability; and male symbolizes the size of indicators. In general, kv is taken as 60, but when it is perceived that he is in an emergency, the perceived distance should be reduced due to the increase in panic, and objects at a slight distance will be ignored. The focus factor is used to reflect the intelligence’s attention to an object within the line of sight, and the focus factor of object A can be expressed as shown in Equation (9).
f A = a O A × F O A × F + b O A + c V a V b
Here, O A is the vector from the intelligent body to object A; Va is the speed of movement of object A; a, b, and c are the scale factors of each, and the various intelligent bodies have different scale factors to reflect the individual differences of the respective intelligently bodies. The intelligent entity chooses its heading according to the size of the focus factor of the perceived object, and the tendency is to head toward the perceived object with the highest focus factor to obtain more accurate information about the environment and to provide a reference for decision-making behavior.

3.2.2. Behavioral Decision-Making Model

Decision-making is the fundamental problem of artificial intelligence, which aims to study how to reach a goal state from an existing one. The decision-making gives a sequence of actions or a behavioral strategy for each step that will achieve the goal. The basic behaviors of the general population can be summarized as global goal behavior, group behavior, follower behavior, random behavior, collision avoidance behavior, escape behavior, helping behavior, queuing behavior, waiting behavior, competition behavior, etc. Intelligence makes behavioral decisions by using behavioral selection mechanisms and behavioral rules through perceived information and their states, and the behavior of decision-making may be a basic behavior or a series of the fundamental behavioral sequence The behavior of decision-making may be basic behavior or a series of basic behavior sequences, or formed by the fusion of several basic behaviors in a series of technologies. The design process of each basic behavior pattern is described below.
(1)
Global target behavior based on an improved algorithm
Crowd movement is always goal-driven. Goal behavior is one of the basic behaviors of crowd behavior, which enables the crowd to reach the specified target location. This is a path planning problem, and the performance of the path planning is directly related to the superiority of the multi-agent path selection and smoothness of the movement, which is greatly dependent on the merits of the planning algorithm, how to quickly and accurately plan an efficient path in various scenarios and make it have the ability to cope with the dynamic changes of the scene is the path planning algorithm should solve the problem.
Path planning can be divided into global path planning based on a priori complete information and local path planning based on sensor information, depending on the level of knowledge of the environment. In particular, global path planning is static, and partial path planning is dynamic from the point of view of whether the information about the obstacles is acquired statically or dynamically. Global path planning requires all the environmental information to be available for path planning based on all the information in the context map; local path planning only requires the sensors to collect the ambient information in real-time, understand the context map information, and then determine the location of the location map and its local obstacle distribution, so that the optimal path from the current node to a child target node can be selected.
In a static world where global map information is known, searching forward and looking both can be effective. However, in a dynamic environment where it is necessary to retry the shortest paths to an unknown map, a forward search is also likely to result in a nonoptimal search path, leaving a backward search is a reasonable way to deal with this situation. In dynamic settings, where it is necessary to repeatedly try to find the shortest path to an unknown map, forward search is likely to result in a decision that runs counter to the optimal decision, and backward search is a good way of dealing with this situation. In contrast, incremental algorithms in forward search can only provide distance information from the current point to the start point and heuristic estimates to the target and give no guarantee that unsearched areas are passable.
However, these algorithms can be divided into heuristic and incremental categories. Heuristics can direct the search direction to the target point at each search, overcoming the limitation of non-heuristic algorithms that traverse irregularly in all and every which and can typically drastically improve search efficiency. However, the search will be counterproductive if the heuristic path is blocked.
A heuristic search is a “smart” search using heuristic functions to guide the search, typically such as the A* algorithm and genetic algorithms. Incremental search is the reuse of information from previous searches to achieve efficient search, significantly reducing the scope and time of the search, exemplified by the LPA*, D* Lite algorithms, etc.
Among the traditional path planning algorithms, the implementation principles and application scope of the various algorithms vary considerably, as shown in Table 1 for a comparative distinction between five typical algorithms (Dijkstra, A*, D*, LPA*, D*Lite) in terms of search principles and application scope, etc.
The positive and negative search directions are mostly related to the ability to handle dynamic planning; heuristic search offers an increase in time performance and avoids global blind search; incremental search represents a secondary use of iterative information and is mostly used to improve the efficiency of the algorithm.
To this end, this study designed this behavior using the A* algorithm to find the global path to the target point. The A* algorithm searches for a minimum cost path in the discrete space, i.e., it calculates the position corresponding to the minimum value of the cost function F = G + H in each iteration. In the A* algorithm, the estimation function H from the current position to the target position is crucial, and it directly affects whether the final path is optimal or not. To achieve the rapidity and path optimization of the algorithm, this study divides the estimation function into two parts: one is the shortest distance cost HD for the current position of the intelligent body to reach the target, and the other is the choice preference cost HP for the intelligence body, and the formula for HP is Equation (10).
H D = χ × ( x s x g ) 2 + ( y s y g ) 2
where χ is the depletion per unit distance and (xs,ys), (xg,yg) are the starting and ending points of the intelligence, respectively. HD can meet the requirements if there are no obstacles in the environment or the terrain is relatively simple. The crowd behavior is complex, however, and the environment in which the intelligent body is located, its behavior pattern, internal state, and walking direction should be considered in path selection. If the calculated path is far from the actual one by determining the evaluation function only, this study proposes the preference cost HP for compensation. It can be expressed as Equation (11).
H P = i = 1 n γ i × ω i
where γ denotes the preference factor and ω denotes the preference weight. Only the influence of current motion direction and previous direction, current direction and target direction, and channel width on the path cost function when passing through a narrow channel are considered in this paper. The corresponding preference factors γ1, γ2, γ3 are calculated by Equations (12), (13), and (14), respectively.
γ 1 = 1 2 × ( 1 c o s ( θ c u r r e n t θ p r e v i o u s ) )
γ 1 = 1 2 × ( 1 c o s ( θ c u r r e n t θ t a r g e t ) )
γ 1 = 0 1.1 W i d t h p a s s a g e / W i d t h a g e n t × 10 i f     W i d t h p a s s a g e < W i d t h a g e n t i f     W i d t h p a s s a g e > W i d t h a g e n t × 1.1 O t h e r
where θcurrent, θprevious, and θtarget are the current direction of travel, previous orientation, and target orientation of the intelligent body, respectively, Widthpassage is the width of the channel, and Widthagent is the width of the Intelligent Body. Finally, the cost function F is obtained in Equation (15).
F = G + χ × ( x s x g ) 2 + ( y s y g ) 2 + γ 1 ω 1 + γ 2 ω 2 + γ 3 ω 3
The optimal path or no solution is finally achieved by a heuristic search of the space based on the principle of taking the minimum of the cost function F. The specific algorithm imported into AnyLogic software is shown in Table 2 below.

3.3. Evacuation Environment Construction

The modeling process is divided into two major parts: the model construction of the host environment and the model construction of the object behavior. (1) The AnyLogic simulation physical environment is primarily made up of walls, stairs, passages, exits, and so on. The modeling of the environment also contains starting target line, arrival target line, floor conversion module, and other spatial markers. It is mainly divided into the following three segments. Segment 1: The CAD plan of the model to be created is imported through the function of CAD guide, followed by the use of walls, rectangular walls, circular walls, and rectangular areas to build fixed facilities such as internal and external walls, stairs, platforms, and passages. Segment 2: Specify the front and back locations of people, the properties of the facilities, and the specific paths for people to travel through the target lines, area services, and paths modules in the pedestrian library. Segment 3: Define and set detailed parameters for different walls and fixtures. PedGrounds of different heights are created to create different levels, and PedChangeGrounds are utilized to connect the dimensions so that people can move between PedGrounds. (2) AnyLogic object behavior modeling is mainly to make the object from the appearance to the disappearance of the entire processes of movement by creating the form of a flowchart. The module mainly consists of PedSource (pedestrian generation), PedSink (pedestrian disappearance), PedGoto (going to the target), PedAreaDescriptor (limited area), PedChangeGround (floor conversion), etc. The entire simulation process is set up by connecting all the required modules with connectors according to the simulation’s real-time situation. We established the parameters of the behavior object by matching the behavior module with the space module. Since the software is designed based on the social force model, it is only necessary to specify the position of some of the nodes of the human, and not to set the complete movement route. The modeling process is shown in Figure 1

4. Behavioral Evacuation Simulation Model Design and Analysis

In an emergency evacuation, the behavioral characteristics of pedestrians are an influential factor in evacuation efficiency. This study mainly analyzed the factors affecting the behavioral traits of pedestrians in an emergency evacuation, focusing on the influence of pedestrians’ factors and typical environmental structures on evacuation, such as companionship behavior, obstacle avoidance behavior, and exit competition behavior.

4.1. Simulation Model Design of Partnering Behavior Evacuation

We used a large museum as a simulation object to analyze the partnering phenomenon. As shown in Figure 2, brown rectilinear lines were used as the inner and outer walls of the museum building, rooms R1–R15 represent different exhibition halls inside the museum, and a colored multi-agent is used to represent the personnel in the emergency evacuation process of the museum. In the emergency evacuation process, all the personnel eventually fled the museum by the main exit. The social force model-based partnering behavior is shown in green in this figure.

4.1.1. Simulation Idea

Once the emergency evacuation simulation starts, the evacuation path is unique; all people will leave through this exit, and the evacuation will be successful when all people have left. In the simulation evacuation process, it is assumed that the total number of people in the museum is 500, with 50 people in the central area and the remaining 450 people in the galleries.
The service level of the evacuation result uses HCM2000 as the standard, as shown in Table 3, and is divided into six classes according to different density, speed, flow rate, and space occupation, with A being the best service level class, which is reflected in fast evacuation speed, short evacuation time and low congestion, and vice versa, F being the worst service level.

4.1.2. Analysis of Simulation Results

Using the group creation function in the PedSource property, the expression uniform_discr (2,3) is used to reflect the evacuation crowd of the partnering model; setting that each group is mainly composed of 2–3 people, the group formation is carried out in a group manner, setting the interval time as exponential (3)s. Figure 3a shows the evacuation process under the normal mode (non-partnering behavior). Figure 3b shows the evacuation process in the partnering mode. On the contrary, in the evacuation under companionship behavior, due to the companionship-seeking behavior of the personnel in the evacuation progress, the bottleneck is mainly at the main exit of the museum, and the congestion at other locations is low due to the bottleneck effect. Comparing the HCM2000 level of service criteria table [40], the level of service for people at the exit location at this point is level E and level D at the central area. On the other hand, the evacuation under companionship behavior, due to the companionship-seeking behavior of personnel in the evacuation flow, leads to a large orange area with severe congestion already at the exit of each room as well as at the central location, which, however, is more severely congested at the exit location, with a level of service E. Obviously, to a certain extent, the resulting congestion is in a more forward position with the congested area expanding.
The whole evacuation process time is shown in Table 4. It can be seen that the evacuation time in the companion mode is longer than that in the normal operation due to the activities of seeking and waiting in the evacuation process, the crowding at the exit, and the long waiting time due to the wide range of the bottleneck effect.

4.2. Evacuation Simulation Model Design for Obstacle Avoidance Behavior

4.2.1. Simulation Ideas

In the research process of traditional evacuation, most scholars only set part of the fixed building structure and building supporting the building with a view that the channel in the evacuation process is unobstructed. However, in an actual emergency, as people may carry objects with them in the evacuation process, portable items may fall in the passage under crowded evacuation conditions, resulting in the reduction of the speed of the rest of the people in evacuation due to avoiding these items, which in turn affects the rate and evacuation level of the whole evacuation process. In the simulation experiment, a rectangular building with a length of 30 m and a width of 3 m was set up to allow a dense flow of people to pass through this channel and to detect the change in speed of people before reaching the scattered obstructions, as well as the effect of the density of scattered obstacles on the evacuation efficiency and the capacity of this section. The size of the barrier was determined as 55 × 30 × 15 cm according to the actual standard book bag size, and the position of the obstacle was assumed to be fixed after scattering to improve the operability of the simulation.

4.2.2. Analysis of Simulation Results

We used the wall in the pedestrian library of AnyLogic software to establish the channel and set the start line and target line on the left and right side, used the rectangular wall to draw the scattered obstacles, set multiple target detection lines in the forward direction, set them to pedGoTo, entered the code in Table 5 to obtain the speed, and finally used the variables to obtain the specific speed value.
As shown in Figure 4a, the effect of scattered items on speed is explored through simulations. To measure the influence of different distances on the travel speed of personnel before approaching the obstacle, four speed test lines (from left to right are detection lines 1,2,3,4) were set at various locations in front of the scattered object, and the measured speed can be observed, as well as the change of velocity of personnel in the process of travel before encountering the obstacle. From the simulation process diagram in Figure 4a, it can be observed that the avoidance behavior of the personnel occurs before reaching the z obstacle, which is the same as the ideal state of changing with distance as elucidated in the social force model. According to the changes of the four detection lines in Figure 4b, it can be found that the personnel will show changes in velocity only when they are about to approach the obstacle, and their response to the object’s velocity is more delayed. The congestion in the evacuation that leads to obstructed vision and the blind following behavior when moving forward can amplify the degree of congestion caused by the obstruction.
In addition, we further explored the impact of scattering density on the ability to pass by adding obstacles, as shown in Figure 5 for the simulated evacuation of the channel under different density obstacles, by setting different densities 0/m2. 0.1/m2, 0.2/m2, 0.3/m2) of scattering items inside the corridor to study its impact on the ability of personnel to pass. As shown in Figure 5, when evacuees run from the starting line on the left side to the ending line on the right side, there will be apparent avoidance behavior before reaching the obstruction, resulting in a greater density of human flow near the obstacles and blockage phenomenon, resulting in a lower evacuation speed of personnel at the obstacles. As shown in Figure 6, according to the relationship between different densities of obstructions and the number of people passing, the different densities of objects have varied effects on the capacity in the corridor, and the density decreases as it increases from 0 to 0.3 obstructions per square meter. Considering that in the actual student apartment evacuation process, the book bags carried by the personnel may be dropped during the emergency evacuation process, thus causing more adverse effects.

4.3. Exit Competitiveness for Evacuation Simulation Model Design

The bottleneck mouth blockage phenomenon occurs very readily at the exit, mainly due to the high escape velocity of personnel in the emergency evacuation process and the contraction of space at the exit, resulting in pushing and shoving and crowding each other at the exit, causing a significant decrease in the capacity of the exit and the bottleneck phenomenon of overcrowding, which in turn seriously reduces the evacuation efficiency of personnel [41]. Under normal conditions without emergencies, personnel tends toward lower travel speeds, so the collision crush effect at constricted exits is more moderate [42]. However, in emergencies, the evacuation speed of personnel is too high, and the resulting blockage crush is more severe.

4.3.1. Simulation Ideas and Experimental Analysis

The first floor of an apartment building is selected as the object of study of exit competition behavior. The first floor of this apartment mainly consists of a central hall and a corridor, with a total of 750 people needing to evacuate from the exit on this layer, and 250 people on each side of the veranda and at the stairway in the middle. The simulation model is set up in Figure 7a by setting up four detection lines (No. 1, No. 2, No. 3, No. 4) at different locations to measure the speed of people in different directions at each position and the change of the passage situation over time. Then, three scenarios of the normal exit mode, optimization at exit bottlenecks, and setting up evacuation flow lines were simulated. As shown in Figure 7b, students always crowd each other and form a crowding equilibrium at the exit bottleneck, then evacuees can continue to pour into the exit when the crowding balance is broken, and so on.
The data results of the number of exit passers obtained from the simulation experiments are shown in Figure 8a, which shows that when the simulation started, the growth rate of test line No. 4 was faster, the trend of changes in test lines No. 1, No. 2, and No. 3 was more consistent around 150 s, mainly due to the bottleneck effect of the exit caused by excessive congestion. The evacuation speed at the exit is shown in Figure 8b because the start of the evacuation at the exit is relatively smooth, and the evacuation speed at the four test locations is relatively fast; with time, the exit congestion phenomenon leads to the reduction of the evacuation speed, and 1,2, and 3 test line speeds change trend gradually and consistently until the end of the evacuation.

4.3.2. Simulation Experiment Optimization and Result Analysis

Since the bottleneck effect of congestion is caused by the sudden width reduction at the exit, this paper investigated the evacuation capacity of different corner radii at the exit on this basis. The right-angle-shaped exit channel was mainly changed to a circular arc channel with a radius of 1 m and a radius of 2 m. By establishing a detection line at each of the three model exit locations and comparing the right angle (r = 0) exit with two arc-shaped exits (r = 1 and r = 2) on the evacuation capacity and speed, the best exit setting method was obtained. After simulating experiments on the modified exits, the data obtained are shown in Figure 9 and Figure 10, and the different corner radius settings have various effects on the evacuation situation. The improved model is significantly less crowded; the radius of the corner exit to complete the evacuation of all personnel time was reduced markedly, and the time consumption was the least of the three. The corner exit with a radius of 1 had a slight improvement relative to the evacuation capacity of the right-angle exit. The evacuation speed of personnel in the three different shapes of the exit channel was also significantly different and accelerated with the increase of the radius of the corner radius.
To further improve the evacuation efficiency at the exit during the emergency evacuation, Figure 11a was used to complete the evacuation more efficiently by adopting specific evacuation flow lines for the evacuees. Three different evacuation flow lines were set up according to the evacuation flow from a single direction, which can divert and evacuate the congested people at the exit. The results show that evacuees can effectively reduce the congestion at the exit bottleneck when evacuating by setting up specific diversions of evacuation paths. From the comparison of the data in Figure 11b, it is clear that the evacuation effect is the same for both cases at the beginning of the evacuation, and when the bottleneck effect occurs at the exit with too many people, the capacity and efficiency of the exit with the set flow path were significantly improved compared with the original model.
Both the corner curvature set up at the exit and the fixed flow line setup can reduce the bottleneck effect at the exit and improve the evacuation capacity and efficiency of the channel. However, that the installation of flow lines requires the introduction of fences and other equipment to divide the flow area, as well as the need for staff to guide the evacuation work to ensure that evacuees evacuate according to a specific flow line. However, in practice, this mode is not appropriate for the emergency evacuation of small places under unexpected conditions [43], and the results achieved in this way are not evident. Therefore, in the exit of non-large places, it should be chosen to improve the evacuation efficiency by setting the corner arc, while two optimized ways can be used together at the evacuation exit of large places.

5. Example Analysis

5.1. Simulation of Apartment Construction Environment Analysis

According to the description of evacuation basics and the analysis of the characteristics of the social force model and the simulation process of the software, a multifunctional large apartment building was selected for the study, whose building structure, safety channels are relatively diverse, and the number of floors and occupants is also quite large. The large apartment building has six levels, including 137 dormitories; the first level consists of 22 rooms, the number of these rooms on the remaining five floors is 23, and the number of occupants in each room is 8, as shown in Figure 12.

5.2. Establishing the Simulation System

5.2.1. Selection of Simulation Parameters and Indicators

According to past studies, there is a potential danger when the area occupied by each person in the evacuation process is less than 0.28 square meters, and if the space occupied by each person is less than 0.25 square meters, crowding and collision will occur in case of emergency, leading to dangerous behaviors such as severe trampling accidents. Therefore, the minimum density to ensure the safety of people’s lives during actual evacuation is 0.28 m2 [44]. Since the human movement characteristics serve as a significant observed phenomenon in the evacuation process and can fully reflect the flow state of personnel pooling during the evacuation, the per capita density and speed during evacuation serve as important factors for safe evacuation assessment. The internationally used service index for pedestrian evacuation density (People Density Service Level Evaluation Index from Fruin’s Pedestrian Planning and Design) was used as a criterion in the experiment, as detailed in Table 6 [45].
The evacuation speed of personnel is an essential parameter in the assessment of safe evacuation [46], which in practice is mainly determined by factors such as age, and considering the study scenario as a university apartment building, the study population was set to young people aged 18–25 years (speed setting: 1.37 m/s for men; 1.24 m/s for women). According to the results of the above research and simulation, it can be seen that the evacuation was adversely affected by the companion mode and the scattering of objects. Therefore, to complete the simulation of the evacuation of the apartment building in an ideal way, the simulation scenario was set to the non-companion mode without carrying any belongings in the process, and the best evacuation effect can be obtained under this condition. In addition to that, the evacuation was carried out when the gathering of people was high, and the number of evacuees in the simulation experiment was set according to the maximum number of people in the apartment building according to the actual situation. The details are shown in Table 7.

5.2.2. Modeling the Physical Environment of the Simulation Experiment

The wall frames of the large apartment building were modeled by Anylogic software at a scale of 1:1 to ensure the accuracy of the virtual experimental environment. The layout of the different floors of the apartment building is shown in Figure 13. Before modeling the behavioral flow of pedestrians, the evacuation path of all people should be clarified. Therefore, by dragging in a collection of intelligence in MAIN and setting its element class as TargeLline, the target lines targetLine1, targetLine2, and targetLine3 at the three exits of the dormitory building are subsequently added to this collection for the proximity route. Then, we continued to add Pedestrian in MAIN, entered the Pedestrian page, and added a function named findTarget in its page, setting the return value type as TargeLline, and entered the code in Table 8 inside the function body. Finally, we returned to the main body MAIN and set the target line position of the target module in PedGoto to a dynamic value, and completed the setting by entering the function code ped. findTarget() to compile. Thus, in the case of an emergency, all personnel will follow the designed evacuation routes and instructions and select the most suitable evacuation route according to the personnel’s independent judgment of the distance and proximity of the evacuation route to complete the evacuation. Finally, the physical environment was combined with the attributes of each module in the pedestrian evacuation process, and the corresponding parameters were set for evacuation simulation.

5.3. Analysis of Simulation Results

5.3.1. Evacuation Time

Considering that student apartment buildings are relatively dense residential places and that emergencies are sudden and frequent, student apartment buildings in most universities are equipped with sensitive emergency alarm devices that can detect the occurrence of an emergency and issue an alarm in time, so a detection time of 10 s and a pre-action time of 15 s will be set. By the simulation run of the apartment building model, the time required to complete the evacuation at the highest number of people gathered was obtained, as shown in Figure 14.

5.3.2. Evacuation Status of Each Floor Exit

In the evacuation analysis of the whole building, the evacuation situation of each floor stairway location and exit should also be counted, so it is also necessary to set the corresponding test line at the station of each floor exit stairway location to obtain detailed information of the respective data of each floor exit. Figure 15 shows the folding line diagram of each floor exit of a large apartment building.
For large apartments with relatively complex staircase structures, although both internal safety evacuation staircases will be open for use during an emergency evacuation when evacuation occurs, internal evacuees are not aware of the number of evacuees at the staircase exits and will generally choose the nearest staircase exit to leave; however, in the case of equal distance from two exits, personnel will usually select the appropriate exit according to their subjective ideas for evacuation [47], and this may lead some personnel to choose the more crowded exits. According to the analysis of the above evacuation line drawing, the exits on the second floor and above were congested to a certain extent after 150 s, and the evacuation speed was slow. In addition, according to the evacuation situation at the exits of the floors, the evacuation time at the first stairway exit was shorter and fewer people were evacuated through this stairway compared to the second stairway exit. When choosing the evacuation exit, the number of rooms near the second exit and the stairway was higher, resulting in a serious blockage. Therefore, when the evacuation time is compared with the evacuation timeline graph, it can be seen that when the evacuation time reached 510 s, the first exit was evacuated, while the second stairway on the fourth floor was still in the evacuation state, which caused the first exit to be idle after 510 s, while the second stairway and the exits were still congested, resulting in a waste of resources in the evacuation process.

5.4. Improvement Measures and Simulation Results

In response to the problems that emerged during the evacuation simulation in the previous paper, this study proposes measures such as zoning evacuation, increasing safety exits, optimizing the alarm broadcast system and evacuation signs, strengthening the grid management, and conducting simulation verification for the proposed improvement solutions, expecting to optimize the emergency evacuation efficiency of apartment buildings further.
Proposal 1: Based on the above-performed evacuation data analysis, the simulation experiments only used distance as the criteria for selecting routes and exits, ignoring the following problems: (a) the internal structure of the building; (b) the uneven utilization of evacuation exits in different evacuation paths; and (c) the internal evacuation channels are too few, leading to heavy congestion, which significantly reduces the evacuation efficiency.
Option 1: According to the previous simulation experiments, the two exits are not blocked when evacuating the first floor; therefore, the improvement plan is to choose the nearest exit for the upper floor personnel to leave after arriving at the first floor. Option 2: Based on Option 1, the personnel on the second to sixth floors were equally distributed to the two stairways for evacuation. The 92 people on each floor located near the first stairway exit left by this stairway exit, and the remaining 92 people exited by the second stairway exit. Option 3: Based on Option 1, make the personnel on the first, third, and fifth floors choose the nearest access exit to leave, while the personnel on the second, fourth, and sixth floors are distributed equally for evacuation. Option 4: Based on Option 1, the width of its two evacuation staircases is appropriately widened. Option 5: Based on Option 1, the vacant activity room on the right side of the large apartment building is changed into an evacuation safety stairway, and the personnel on each floor above the second floor are evenly distributed to choose the one closer to themselves for evacuation from the three evacuation stairways. According to the proposed five improvement plans, the structure of this experimental model was modified and redistributed according to the number of people, and the experiments were run in turn to collect the data obtained, as detailed in Table 9.

6. Discussion

By the final results from the improved scenarios, it can be seen that scenario 5 has the shortest total evacuation time, and the evacuation efficiency was improved by about 21.29% compared to the status quo, from 11 min to 10 min. It can be seen that in the abovementioned scenarios, only by increasing the safety channels can we maximize the safe evacuation of people. However, the current evacuation process still has the problem of uneven utilization of evacuation channels, so when people are not evenly distributed according to the shortest path to evacuate, it is easy to cause a large number of people to crowd at one evacuation channel, while another evacuation channel is unattended, which not only causes a waste of resources but also seriously affects the evacuation efficiency; to solve this problem, we need to increase the number of evacuation managers and optimize their evacuation management. For example, we can (i) increase the frequency of daily emergency evacuation drills and arrange appropriate guidance personnel, reducing unnecessary congestion time and guaranteeing evacuation efficiency; (ii) according to the lack of evacuation management personnel in the evacuation process, corresponding evacuation management personnel should be set up in the evacuation process, etc.

7. Conclusions

In response to the problems of large randomness of pedestrian movement and the many factors affecting their behavior and complex walking behavior in evacuation research, this study proposes a multi-agent design method based on decision theory, using the multi-agent modeling simulation method to model the evacuated individual subsystem and set up the panic value, physiological state, and personality of evacuees. Based on the multi-agent type and internal state module, the multi-agent decision-making problem in the emergency evacuation environment was solved by the A* algorithm, which enables the multi-agent model to simulate the decision-making of evacuees in real situations and makes the evacuation more realistic. Finally, JAVA code was coded to embed the improved multi-agent into the social force model via AnyLogic software to realize the evacuation process. The data from the evacuation process was fed back in real-time through line graphs and pictures by setting up functions, events, etc.
The simulation reproduces the pedestrian evacuation process in an emergency evacuation situation on a constructed platform, representing three types of behavior typical of pedestrians in groups, obstacle evasion, and exit competition. In addition, an exemplary analysis of a large student apartment building was carried out in this study, with appropriate optimization solutions proposed by the simulation results to improve its evacuation capacity. However, the multi-agent setting for evacuation managers was missing during the study. Therefore, the second step will be to step up the research on multi-agent and strengthen the multi-agent design of evacuation managers to strengthen the evacuation capacity. Additionally, we should try to combine multi-agent with other evacuation models to compare the evacuation simulation capability between different models.
This study considers the problem of evacuee behavior and decision-making and, using decision theory carries out a multi-agent design based on human intelligence to explore the impact of multiple basic behaviors on the evacuation process. However, there is still a lack of behavioral fusion, so further exploration of behavioral fusion and behavioral selection mechanisms is needed to achieve both behavioral complexity and high intelligence to achieve a more efficient evacuation process. In addition, how to achieve a natural transition between the basic behaviors of the crowd needs to be investigated in future work.

Author Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by C.W., C.Z., K.X., Y.T. and H.Z. The first draft of the manuscript was written by C.W. and C.Z.; Writing—original draft, C.Z.; and all authors commented on previous versions of the manuscript. All authors have read and agreed to the published version of the manuscript.

Funding

The authors gratefully acknowledge the financial support provided by the Fujian Provincial Department of Science and Technology (Grant Number: 2021I0014) and the Xiamen Municipal Construction Bureau (Grant Number: XJK2022-1-7).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

All data, and models, generated or used during the study appear in the submitted article.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Flow diagram of the AnyLogic evacuation experiment.
Figure 1. Flow diagram of the AnyLogic evacuation experiment.
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Figure 2. Group model diagram (Companionship is represented by the green markings indicated by the arrows.).
Figure 2. Group model diagram (Companionship is represented by the green markings indicated by the arrows.).
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Figure 3. (a) Non-partnered behavioral density level of the service graph; (b) partnered behavioral density level of the service graph.
Figure 3. (a) Non-partnered behavioral density level of the service graph; (b) partnered behavioral density level of the service graph.
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Figure 4. (a) Simulation process diagram of obstacle detection (The coloured dots are multi-agent, the orange rectangle is an obstacle); (b) Personnel speed and time chart.
Figure 4. (a) Simulation process diagram of obstacle detection (The coloured dots are multi-agent, the orange rectangle is an obstacle); (b) Personnel speed and time chart.
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Figure 5. (a) Barrier-free (0 pcs/m2) channel map; (b) scattered items with a density of 0.1 pcs/m2; (c) scattered items with a density of 0.2 pcs/m2; (d) scatter channel map with a density of 0.3 pcs/m2. Scatter channel diagram (The coloured dots are multi-agent, the orange rectangle is an obstacle).
Figure 5. (a) Barrier-free (0 pcs/m2) channel map; (b) scattered items with a density of 0.1 pcs/m2; (c) scattered items with a density of 0.2 pcs/m2; (d) scatter channel map with a density of 0.3 pcs/m2. Scatter channel diagram (The coloured dots are multi-agent, the orange rectangle is an obstacle).
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Figure 6. Capacity change plot with density.
Figure 6. Capacity change plot with density.
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Figure 7. (a) Setting diagram of the test line (the direction of the arrow is the direction of evacuation.) at the exit; (b) safety exit competition simulation experiment diagram (The coloured dots are multi-agent).
Figure 7. (a) Setting diagram of the test line (the direction of the arrow is the direction of evacuation.) at the exit; (b) safety exit competition simulation experiment diagram (The coloured dots are multi-agent).
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Figure 8. (a) Capacity time map of different locations; (b) speed time map of different positions.
Figure 8. (a) Capacity time map of different locations; (b) speed time map of different positions.
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Figure 9. Simulation process diagram of the three improvement schemes (The coloured dots are multi-agent, the direction of the arrow is the direction of evacuation.).
Figure 9. Simulation process diagram of the three improvement schemes (The coloured dots are multi-agent, the direction of the arrow is the direction of evacuation.).
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Figure 10. (a) Capacity time diagram of the three schemes; (b) speed time diagram of the three schemes.
Figure 10. (a) Capacity time diagram of the three schemes; (b) speed time diagram of the three schemes.
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Figure 11. (a) Improved evacuation flow diagram (the direction of the arrow is the direction of evacuation.); (b) capacity time diagram of the two models.
Figure 11. (a) Improved evacuation flow diagram (the direction of the arrow is the direction of evacuation.); (b) capacity time diagram of the two models.
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Figure 12. (a) The first floor of a large apartment building; (b) Standard floor plan.
Figure 12. (a) The first floor of a large apartment building; (b) Standard floor plan.
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Figure 13. Large apartment model diagram.
Figure 13. Large apartment model diagram.
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Figure 14. Evacuation line diagram of large apartment buildings.
Figure 14. Evacuation line diagram of large apartment buildings.
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Figure 15. (a) Exit line chart of the first floor of a large apartment building; (b) exit line chart of the second floor of a large apartment building; (c) exit line chart of the third floor of a large apartment building; (d) exit line chart of the fourth floor of a large apartment building; (e) Exit line chart of the fifth floor of a large apartment building; and (f) exit line chart of the sixth floor of a large apartment building.
Figure 15. (a) Exit line chart of the first floor of a large apartment building; (b) exit line chart of the second floor of a large apartment building; (c) exit line chart of the third floor of a large apartment building; (d) exit line chart of the fourth floor of a large apartment building; (e) Exit line chart of the fifth floor of a large apartment building; and (f) exit line chart of the sixth floor of a large apartment building.
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Table 1. Comparison of five typical algorithms for path planning in terms of search principles and scope of application.
Table 1. Comparison of five typical algorithms for path planning in terms of search principles and scope of application.
AlgorithmSearch DirectionHeuristicIncrementalScope of Application
DijkstraPositive SearchNoNoGlobal information known, static planning
A*Forward SearchYesNoGlobal information known, static planning
D*Reverse SearchNoYesPartial information known, dynamic planning
LPA*Forward SearchNoYesSome information is known, assume the rest is free to access, dynamic planning
D*LiteReverse SearchYesYesPartial information known, assume remaining free access, dynamic planning
Table 2. Input to AnyLogic’s multi-agent decision Java pseudocode.
Table 2. Input to AnyLogic’s multi-agent decision Java pseudocode.
Multi-Agent Decision Setting Pseudo-Code
1Create two tables, the OPEN table holds all the nodes that were generated but not examined, and the CLOSED table records the nodes that have been visited. Calculate the cost function F for the starting point and place it in the OPEN table.
2While (OPEN! =NULL)02.
3{
4 Take the node with the smallest cost function F from the OPEN table n
5  if (n node == target node){
  break;
6 }
7else for(Each child node X of the current node n){
8 Computing the cost function F for each child node
9   if (X in OPEN)
10   if (The cost function F of X is smaller than the F of the node in the OPEN table){
11      Change the node n to the parent of X and update the estimate in the OPEN table
12       }}
13      if (Xin CLOSE){
14       if (The cost function F of X is smaller than the F of the node in the CLOSEtable){
15        Change the node n to the parent node of the X “ update the estimate in the CLOSEtable,
        and put the node X into the OPEN
16       }}
17       If (X in not both){
18       Change the node n into the parent of X and calculate the cost function F of X
19       }}
20     end for
21     Node n is inserted into the CLOSE table;
22       Order nodes in the OPEN table by the size of F/small in the stack
23End While
Table 3. HCM2000 Service Level Standards.
Table 3. HCM2000 Service Level Standards.
Service
Levels
Space
(m2/Person)
Flow Rate
(Person/min/m)
Velocity (m/s)Density
(Person/m2)
A>5.6<16>1.30<0.18
B3.7–5.616–231.27–1.300.18–0.27
C2.2–3.723–331.22–1.270.27–0.45
D1.4–2.233–491.14–1.220.45–0.71
E0.75–1.449–750.75–1.440.71–1.33
F<0.75Unlimited<0.75>1.33
Table 4. Time of evacuation in both modes.
Table 4. Time of evacuation in both modes.
ModeReaction Time (Set)Prepare for Escape TimeTime to
Action
Total Evacuation Time
Non-partner mode10 s15 s98.85 s123.85 s
Companion mode10 sThe 20 s114.47 s144.47 s
Table 5. Get the speed code.
Table 5. Get the speed code.
Obtain the Speed Code
Sudu = ped.getSpeed();
sumOfSudu = ped.getComfortableSpeed();
Sudu1 = sumOfStudu/self.coumtPeds();
Plot.updateDate();
Table 6. Personnel Density Service Level Evaluation Indicators.
Table 6. Personnel Density Service Level Evaluation Indicators.
EquipmentDensity (People/m²)V (m/s)Flowrate (People/(m·min))
Horizontal channel0.43~2.150.51~1.270.55~1.37
Stairs1.08~2.690.36~0.760.33~0.87 (lower limit)
0.44~0.98 (upper limit)
Table 7. Student apartment building capacity table.
Table 7. Student apartment building capacity table.
Apartment Building TypeFloorNumber of Occupants of the Apartment BuildingTotal
Large apartment building11761096
2184
3184
4184
5184
Table 8. Function body input code.
Table 8. Function body input code.
Function Body Input Code
double dis = infinity
TargetLine tline = new TargetLine();
for (TargetLine tl;main. collection)
{
 If (this.distanceTo(tl.getx(),tl.getY( )) < dis)
 {
  dis = this.distanceTo(tl.getx( ),tl.gety( ));
  tline = tl;
 }
}
return line;
Table 9. Improved program data table.
Table 9. Improved program data table.
FloorThe Situation of Each FloorOption 1Option 2Option 3Option 4Option 5
Sixth floorNumber of evacuees at No. 1 stair7992929262
Consumed time139.68184.37183.64180.87127.85
Number of evacuees at No. 2 stair10592929261
Consumed time229.15207.38205.42203.58124.49
Fifth floorNumber of evacuees at No. 1 stair154184167184124
Consumed time260.81290.89276.59285.93240.73
Number of evacuees at No. 2 stair214184201184121
Consumed time305.40282.71298.73276.87231.91
Fourth floorNumber of evacuees at No. 1 stair240276259276186
Consumed time372.16439.01403.98430.73320.79
Number of evacuees at No. 2 stair312276293276183
Consumed time509.31443.20481.30436.91316.67
Third floorNumber of evacuees at No. 1 stair319368338368248
Consumed time447.73498.48482.85489.68405.16
Number of evacuees at No. 2 stair417368398368244
Consumed time514.28487.67498.92478.36400.92
Second floorNumber of evacuees at No. 1 stair398460430460310
Consumed time500.30579.24544.75565.43468.85
Number of evacuees at No. 2 stair522460490460305
Consumed time600.57558.97573.49553.90459.09
Exit 1Number of evacuees483543510543310
Consumed time523. 60589.87575.94579.68497.94
Exit 2Number of evacuees613553586553786
Consumed time626.17586.96609.42577.57520.29
TotalTotal evacuees1096
Total evacuation time626.17589.87609.42579.68520.29
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Wang, C.; Zhu, C.; Xiao, K.; Tang, Y.; Zhen, H. Visualization of Emergency Evacuation Physical Behavior under Multi-Agent Decision-Making. Appl. Sci. 2023, 13, 5509. https://doi.org/10.3390/app13095509

AMA Style

Wang C, Zhu C, Xiao K, Tang Y, Zhen H. Visualization of Emergency Evacuation Physical Behavior under Multi-Agent Decision-Making. Applied Sciences. 2023; 13(9):5509. https://doi.org/10.3390/app13095509

Chicago/Turabian Style

Wang, Chen, Can Zhu, Kun Xiao, Yutong Tang, and Haidong Zhen. 2023. "Visualization of Emergency Evacuation Physical Behavior under Multi-Agent Decision-Making" Applied Sciences 13, no. 9: 5509. https://doi.org/10.3390/app13095509

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