Investigating the Exits’ Symmetry Impact on the Evacuation Process of Classrooms and Lecture Halls: An Agent-Based Modeling Approach

: As the evacuation problem has attracted and continues to attract a series of researchers due to its high importance both for saving human lives and for reducing the material losses in such situations


Introduction
Evacuation problems have attracted a large audience over the time, as emergency situations might occur at any time and in any place, producing a series of damages not only from a material point of view, but even from the magnitude and the number of causalities they might produce.
A series of elements have been considered in the literature related to individuals' behaviors, either in terms of cooperation [1,2] or competition [3], such as, but not limited to: age [4][5][6], social background [7], the degree of familiarity with the environment [8], the degree of selfishness [9], the presence or absence of guidance or authority figures [4,[10][11][12], the occurrence of herd behavior [13], pressure [14,15], emotions [13,16], or by considering different settings of the environment, such as the presence of a single/multiple exit doors [17][18][19], the width of the door [20], the distance to the exit door [21,22], the visibility of the exits [23], the occurrence of different objects [24,25], or limited visibility [26]. The presence of an obstacle in front of an exit has been a controversial and highly studied aspect in the literature. Starting from the pioneer work made by Helbing et al. [27], in which the authors the involved entities and it easily provides them with behavior rules, while observing their emergent behavior [70]. The agent-based modeling has succeeded over the time in properly modeling a wide range of phenomena from different fields, such as transportation [71][72][73][74], information diffusion [75][76][77], complexity and organizational learning [78][79][80], education [81][82][83], social sciences [16,[84][85][86][87][88], etc. The main strength of this type of modeling results from the fact that it allows the investigation of complex phenomena in terms of agents and their interactions [89].
When trying to convert the human behavior into an agent behavior, a main question arises, namely: "How can an agent act similar to a real person in an ABM model?" This question has been tried to be addressed within agent-based models developed over time, in which a series of agents' characteristics and behavioral rules have been enabled in order to build an "as-close-as-possible" behavior of the agents to the persons in real life [89].
To be more specific, according to Wooldridge and Jennings [90], the agents possesses characteristics which make them act similar to humans, such as: • Autonomy: while performing most of their tasks, the agents do not need human direct intervention. • Proactiveness: the agents take action and their actions are oriented through a purpose. • Veracity: the agents cannot provide false information. • Adaptability: they are flexible, meaning that they can adapt to the changes in the environment.

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Mobility: the agents can move towards any direction and they can travel through all environment. • Responsiveness: they became aware or conscious of the environment and act accordingly. • Social ability: the agents can interact with each other. • Rationality: they have goals and they act in order to achieve them.
Throughout the time, these properties have been studied more in depth and it has been stated that instead of "rationality", it is more appropriate to use a "bounded-rationality" property. According to Getchell, this change refers to the similarity between agents and humans, with the specification that agents should be able to behave more "humanly" and not specifically more "rational" [91][92][93][94]. Following the same idea, Wilensky and Rand [89] underlined that decisions with non-optimal characteristic are the ones closer to the reality. Thus, sometimes it is necessary to improve the model by changing it and the restrictions imposed to the agents in order to reduce the agents' knowledge degree in "terms of resources or analytical ability" [89,91]. As for validating such a model, a Pattern-Oriented Modeling (POM) can be used as suggested by [95,96].
Besides the available solutions for crowd modelling, such as: Pathfinder [97] Simulex [98] or EXODUS [99], which need a series of software and user requirements. There is a series of agent-based modeling software, free of charge, which can be used for simulation and for the design of the complex environments needed for depicting a building or a class in the evacuation process. Among them, we can mention NetLogo, which provides a facile way to install the software, to use it and to deeply understand how it works without requiring any advanced programming knowledge [53,[100][101][102][103]. Additionally, the graphical user interface provided by NetLogo is useful in analyzing the persons' movement oriented to the egresses, with the possibility to monitor in real-time the agents who have to take decisions at a certain moment representing a meaningful advantage. The software also has its own limitations, such as the time needed for creating a world similar with the real classrooms. This aspect is caused by the lack of any pre-defined components for modeling evacuation scenarios.

Overview, Design Concepts and Details
Following the ODD (Overview, Design concepts, Details) protocol provided in [109], the model proposed in the paper is discussed in the following, while the graphical interface and few more details related to the model are provided in Section 5.

Purpose
The proposed model aims to investigate if the position of the exit doors has an impact on the evacuation time. It considers classrooms or lecture halls with two evacuation doors, which can either be placed in a symmetrical or in a non-symmetrical position in relation to a horizontal or a vertical axis. To this extent, 18 situations have been considered for the doors' placement in classrooms and lecture halls. The model is grid-based and uses a particular type of agent (the patches) in order to represent the environment (desks, chairs, path-ways, obstacles in the classroom or in the lecture hall), while the evacuees are represented using the turtle agents, which possesses a series of individual characteristics. The model is calibrated using a data field extracted from a previous study, both in terms of persons' and environment's characteristics [6].

Evacuating persons
The evacuating persons represent the main type of entity considered (referred also as "turtles"). The characteristics of the evacuating persons are presented in Table 1. At the beginning of the simulations, the agents are randomly placed in within the environment on the white patches representing the chairs.

Environment
The environment (representing the classroom or the lecture hall, also called "the world") is composed by a set of agents, called "patches", having a series of characteristics as depicted in Table 2. At the beginning of the simulation, each patch agent described as chair can have at most one turtle agent above it.
The environment area is presented in Figure 1. System state variables: A time step of 1 tick represents 2.5 s based on [6]. The size of each patch is equivalent to 0.5 m × 0.5 m of ground based on [6].  The environment area is presented in Figure 1. System state variables: A time step of 1 tick represents 2.5 s based on [6]. The size of each patch is equivalent to 0.5 m × 0.5 m of ground based on [6].

Process overview and Scheduling
At time zero, the evacuation process begins and each of the agents (turtles) heads toward one of the two exits based on the label on each patch and choosing only patches with smaller or equal energy to the one the agent is located on. The speed of each agent depends on its own speed. The value of the speed can be diminished for various periods of time if the agent has other agents in front of it with smaller speeds or it has to overpass a chair section, case in which its speed becomes 0.262 patches/tick [6]. Furthermore, the speed of the agent can reach zero as it is blocked by the flow of agents and has no possibility of changing its coordinates.
On its path to one of the evacuation doors, an agent can encounter different objects (desks, chairs, obstacles) and can jump or overpass them. Desks and overpassed objects cannot be crossed over, while jumped obstacles and chairs can be crossed over and diminish the agent's speed.

Process overview and Scheduling
At time zero, the evacuation process begins and each of the agents (turtles) heads toward one of the two exits based on the label on each patch and choosing only patches with smaller or equal energy to the one the agent is located on. The speed of each agent depends on its own speed. The value of the speed can be diminished for various periods of time if the agent has other agents in front of it with smaller speeds or it has to overpass a chair section, case in which its speed becomes 0.262 patches/tick [6]. Furthermore, the speed of the agent can reach zero as it is blocked by the flow of agents and has no possibility of changing its coordinates.
On its path to one of the evacuation doors, an agent can encounter different objects (desks, chairs, obstacles) and can jump or overpass them. Desks and overpassed objects cannot be crossed over, while jumped obstacles and chairs can be crossed over and diminish the agent's speed.
At a moment of time, two agents cannot have the same coordinates, meaning they cannot overlap.
The simulation ends when all the agents have left the model area using one of the two exits.

Emergence
The population dynamics emerge from the movement of the individual agents involved in the evacuation process. The agents observe the environment (desks, chairs, obstacles, etc.) and the other agents and act accordingly to the given rules.

Fitness
At each moment of time, the agents are seeking patches with smaller (or equal) energy scores.

Sensing
The agents "sense" ("know") the type of patches they are facing, the energy of these patches and the presence of other agents.

Interaction
The agents change their speed based on interaction with other "blocking" agents and they try to minimize their evacuation time by seeking other patches with equal or smaller energy in order to overpass the blocking agents.

Stochasticity
Stochasticity derives from various values for the speeds generated for the agents at the beginning of the simulations, from their positions within the environment, from the interactions between them, from the response they have to the environment conditions (such as the occurrence of the obstacles, desks, walls, etc.). A stochastic approach was needed as, even in real life situations, there is some inherent randomness which derives from various personal characteristics, decisions and environment properties.

Collectives
The individuals are not grouped in any social group.

Observation
The data for the agent-based model is collected based on the simulations made in the literature and listed above. Even more, the model is configurable so, any of these characteristics can be easily adapted to a different environment or different characteristics of the individuals.

Details
Initialization At the start of the simulation run, the agents are randomly created and placed above the patches marked as chairs. The initialization is not the same, the place of the agents is randomized for every new simulation. The values for the agents characteristics are also random and generated at the beginning of each simulation, keeping in mind that for the male agents the average speed should be 1.048 patches/tick, while for the female agents it should be of 1.016 patches/tick as reported by [6].
Furthermore, the environment is generated at the beginning of each simulation and it depends on the characteristics of the classroom set from the interface. The energy of each patch is calculated at the beginning of the simulation and it depends on the distance from the exits (namely, it depends on the exits' positions).

Input
The input data is based on the data extracted from the literature related to the evacuation process [6]. As the model is configurable, a series of elements can be selected from the interface, such as: desks configuration, number of seats on row, number of desks on row, the space on the vertical corridor, the space on the horizontal corridor, the color of the patches representing different elements (such as chairs, exits, desks, etc.), the number of evacuees, the percentage of female evacuees, the position of each exit door, the width for the exit doors, the distance from each door from the nearest corner, the presence of obstacles, the number of obstacles jumped, the number of obstacles bypassed, the maximum distance from the obstacles jumped to one of the exits, the maximum distance from the obstacles bypassed to one of the exits, etc. Other elements can be changed from the code, such as the speed of the male agents, the speed of the female agents, the size of the patches, etc.

Classrooms and Lecture Halls' Configurations
For both the classrooms and the lectures halls, the situation in which there are two evacuation doors has been considered. Regarding the symmetry of the doors' position within the structure of the room, a horizontal and a vertical symmetry has been considered as depicted in Figure 2. Furthermore, the environment is generated at the beginning of each simulation and it depends on the characteristics of the classroom set from the interface. The energy of each patch is calculated at the beginning of the simulation and it depends on the distance from the exits (namely, it depends on the exits' positions). Input The input data is based on the data extracted from the literature related to the evacuation process [6]. As the model is configurable, a series of elements can be selected from the interface, such as: desks configuration, number of seats on row, number of desks on row, the space on the vertical corridor, the space on the horizontal corridor, the color of the patches representing different elements (such as chairs, exits, desks, etc.), the number of evacuees, the percentage of female evacuees, the position of each exit door, the width for the exit doors, the distance from each door from the nearest corner, the presence of obstacles, the number of obstacles jumped, the number of obstacles bypassed, the maximum distance from the obstacles jumped to one of the exits, the maximum distance from the obstacles bypassed to one of the exits, etc. Other elements can be changed from the code, such as the speed of the male agents, the speed of the female agents, the size of the patches, etc.

Classrooms and Lecture Halls' Configurations
For both the classrooms and the lectures halls, the situation in which there are two evacuation doors has been considered. Regarding the symmetry of the doors' position within the structure of the room, a horizontal and a vertical symmetry has been considered as depicted in Figure 2. Due to the situation presented in Figure 3, it has been considered that the diagonal symmetry should not be analyzed as it is very unlikely to find in practice a room which has two aisles on two opposite walls. Moving further on this idea, from all the possible cases regarding the two doors position within the classroom or the lecture hall, we have only kept in analyses of those cases in which the doors are placed on adjacent walls. Furthermore, due to regulations [18,110], the doors cannot be placed too close on adjacent walls, which reduced the number of considered symmetrical cases to the ones presented in Figures 2 and 4. Due to the situation presented in Figure 3, it has been considered that the diagonal symmetry should not be analyzed as it is very unlikely to find in practice a room which has two aisles on two opposite walls. Moving further on this idea, from all the possible cases regarding the two doors position within the classroom or the lecture hall, we have only kept in analyses of those cases in which the doors are placed on adjacent walls. Furthermore, due to regulations [18,110], the doors cannot be placed too close on adjacent walls, which reduced the number of considered symmetrical cases to the ones presented in Figures 2 and 4.
Regarding the case of horizontal symmetry presented in Figure 2, another possible situation is the one depicted in Figure 4, which has been selected to be investigated as it might produce different evacuation times for the situation in which the lecture hall has an elevated floor. Furthermore, the case was of interest due to the fact that the available space in the front of the room in Figure 2 is different from the available space in the back of the room in Figure 4, which might conduct to a difference in the simulations' results. By considering the constraint presented above related to the presence of the exit doors only on adjacent walls, the cases in Figure 5 have not been considered as they are quite improbable to appear in real-life cases. Regarding the case of horizontal symmetry presented in Figure 2, another possible situation is the one depicted in Figure 4, which has been selected to be investigated as it might produce different evacuation times for the situation in which the lecture hall has an elevated floor. Furthermore, the case was of interest due to the fact that the available space in the front of the room in Figure 2 is different from the available space in the back of the room in Figure 4, which might conduct to a difference in the simulations' results. By considering the constraint presented above related to the presence of the exit doors only on adjacent walls, the cases in Figure 5 have not been considered as they are quite improbable to appear in real-life cases.  Regarding the case of horizontal symmetry presented in Figure 2, another possible situation is the one depicted in Figure 4, which has been selected to be investigated as it might produce different evacuation times for the situation in which the lecture hall has an elevated floor. Furthermore, the case was of interest due to the fact that the available space in the front of the room in Figure 2 is different from the available space in the back of the room in Figure 4, which might conduct to a difference in the simulations' results. By considering the constraint presented above related to the presence of the exit doors only on adjacent walls, the cases in Figure 5 have not been considered as they are quite improbable to appear in real-life cases.  Regarding the case of horizontal symmetry presented in Figure 2, another possible situation is the one depicted in Figure 4, which has been selected to be investigated as it might produce different evacuation times for the situation in which the lecture hall has an elevated floor. Furthermore, the case was of interest due to the fact that the available space in the front of the room in Figure 2 is different from the available space in the back of the room in Figure 4, which might conduct to a difference in the simulations' results. By considering the constraint presented above related to the presence of the exit doors only on adjacent walls, the cases in Figure 5 have not been considered as they are quite improbable to appear in real-life cases.  As for the asymmetric position of the exit doors, the cases presented in Figure 6 have been considered, keeping in mind the observation previously made regarding the fact that the doors cannot be placed too close on adjacent walls [18,110].
As for the asymmetric position of the exit doors, the cases presented in Figure 6 have been considered, keeping in mind the observation previously made regarding the fact that the doors cannot be placed too close on adjacent walls [18,110].

Asym-13
Asym-14 Asym-15 1562mm. The desks and seats configurations used for simulating the above exit doors' positioning are: one-block, two-blocks-h, two-blocks-v, three-blocks and four-blocks- Figure 7. The desks and seats configurations used for simulating the above exit doors' positioning are: one-block, two-blocks-h, two-blocks-v, three-blocks and four-blocks- Figure 7.

The Agent-Based Model
The agent-base model has been created using NetLogo [89] and its interface is presented in Figure 8. The types of agents used for creating the environment and the evacuees have been the patches and the turtles. In our case, the patches have been used for representing small pieces of the ground or different objects in the classroom, such as desks, chairs, doors or obstacles. Each patch used in the model possesses a series of characteristics depending on its role in the agent-based model. For example, the patches used to represent the floor receive at the beginning of the simulation a label consisting in an integer number which represents the distance (expressed in patches) to the nearest exit. Even more, the patches representing the floor offer the possibility to other agents to move over their surface at their default speed. The doors are drawn using a special type of patches as they are always positioned in the specific locations selected by using two choosers "exit-1-location" and "exit-2-location", while their width can be selected by using the "exit-width" slider. By default, all the exits are labeled with "0". On the other hand, the patches representing the desks do not have a label and do not allow the

The Agent-Based Model
The agent-base model has been created using NetLogo [89] and its interface is presented in Figure 8. The types of agents used for creating the environment and the evacuees have been the patches and the turtles.

The Agent-Based Model
The agent-base model has been created using NetLogo [89] and its interface is presented in Figure 8. The types of agents used for creating the environment and the evacuees have been the patches and the turtles. In our case, the patches have been used for representing small pieces of the ground or different objects in the classroom, such as desks, chairs, doors or obstacles. Each patch used in the model possesses a series of characteristics depending on its role in the agent-based model. For example, the patches used to represent the floor receive at the beginning of the simulation a label consisting in an integer number which represents the distance (expressed in patches) to the nearest exit. Even more, the patches representing the floor offer the possibility to other agents to move over their surface at their default speed. The doors are drawn using a special type of patches as they are always positioned in the specific locations selected by using two choosers "exit-1-location" and "exit-2-location", while their width can be selected by using the "exit-width" slider. By default, all the exits are labeled with "0". On the other hand, the patches representing the desks do not have a label and do not allow the In our case, the patches have been used for representing small pieces of the ground or different objects in the classroom, such as desks, chairs, doors or obstacles. Each patch used in the model possesses a series of characteristics depending on its role in the agent-based model. For example, the patches used to represent the floor receive at the beginning of the simulation a label consisting in an integer number which represents the distance (expressed in patches) to the nearest exit. Even more, the patches representing the floor offer the possibility to other agents to move over their surface at their default speed. The doors are drawn using a special type of patches as they are always positioned in the specific locations selected by using two choosers "exit-1-location" and "exit-2-location", while their width can be selected by using the "exit-width" slider. By default, all the exits are labeled with "0".
On the other hand, the patches representing the desks do not have a label and do not allow the agents to move over their surface as, in the model, it has been considered that none of the evacuees will decide to jump over the desks [6,18]. The patches used for drawing the chairs area can be overridden by the agents but at a smaller speed than their default speed. This speed has been determined to be 0.262 patches/tick [6]; the tick is the time unit in NetLogo, equal to 2.5 s in real life. Regarding the presence of the obstacles, two types of obstacles have been considered: "jumped" and "bypassed". In the case of jumped obstacles, the patches representing this type of obstacles are colored in pink (see Figure 9) and are labeled accordingly to the distance needed to be traveled by an agent to the nearest evacuation exit, while the speed of the agents when arrived on this patch is equal to the one had when passing through a row of chairs. The bypassed obstacles are marked with red patches ( Figure 10) and they do not contain any label, which force the agents to sidestep them. The presence of the obstacles can be set from the interface by changing the "obstacles" switch to "on" position. The number and the distance to the exits of the obstacles can be set from four sliders available in the interface, while their position is randomly determined at the beginning of each simulation. The size of each patch is equivalent to 0.5 m × 0.5 m of ground. agents to move over their surface as, in the model, it has been considered that none of the evacuees will decide to jump over the desks [6,18]. The patches used for drawing the chairs area can be overridden by the agents but at a smaller speed than their default speed. This speed has been determined to be 0.262 patches/tick [6]; the tick is the time unit in NetLogo, equal to 2.5 s in real life.
Regarding the presence of the obstacles, two types of obstacles have been considered: "jumped" and "bypassed". In the case of jumped obstacles, the patches representing this type of obstacles are colored in pink (see Figure 9) and are labeled accordingly to the distance needed to be traveled by an agent to the nearest evacuation exit, while the speed of the agents when arrived on this patch is equal to the one had when passing through a row of chairs. The bypassed obstacles are marked with red patches ( Figure 10) and they do not contain any label, which force the agents to sidestep them. The presence of the obstacles can be set from the interface by changing the "obstacles" switch to "on" position. The number and the distance to the exits of the obstacles can be set from four sliders available in the interface, while their position is randomly determined at the beginning of each simulation. The size of each patch is equivalent to 0.5 m × 0.5 m of ground.     Turtle agents have been used for representing the students to evacuate. Depending on their gender, the turtle agents are colored in blue (representing the male evacuees) and red (representing the female evacuees). Besides from their color, the turtle agents have different speeds: the male agents have an average speed of 1.048 patches/tick, ranging between 1.024 patches/tick and 1.064 patches/tick, while the female agents have an average speed of 1.016 patches/tick, ranging between 1 patches/tick and 1.04 patches/tick [6]. The position of the male and the female agents within the classroom is randomly determined at the beginning of each simulation. The number of each male and female agent can be set from the interface.
The classroom type can also be set from the interface by specifying the preferred typology: one-block, two-blocks-h, two-blocks-v, three-blocks or four-blocks and the number of desks rows and number of seats on each row.

Simulations and Results
In order to simulate the cases considered above for the symmetric and asymmetric doors position, a classroom consisting of 24 seats and a lecture hall with 96 seats have been examined. The attendance has been considered 100% in each case, with 50% males and 50% females. For each situation, 10,000 runs have been performed and the average evacuation time has been reported. The presence of obstacles has been analyzed by taking into account both the jumped and bypassed obstacles.

Classroom Simulations
The cases to be discussed in this section have been divided into three groups based on the number of aisles one can identify among the group of desks and chairs: the first group is formed by the one-block configuration with no aisle within the group of desks and chairs, the second by the two-blocks configuration as they feature one aisle, while the third one by the three-blocks and four-blocks which presents two aisles either parallel or in cross.

Results for One-Block Configuration
In the case of one-block configuration, the average evacuation time in the case of symmetrical versus asymmetrical exits has recorded similar evacuation values, with small differences in favor of the asymmetrical exists-please see the results presented in Table 3. As the differences are less than 1 s, we can conclude that, in the case in which the desks and seats are positioned in a one-block configuration, there are no major differences among the two clusters of exits positions. On the other hand, by considering the individual configurations from each cluster, it can be observed that Sym-3 provides the best evacuation time from the symmetrical exits group (64.45 s), while from the asymmetrical exits group, the configurations having one door on the middle of the long wall and another one on the short wall in the back of the classroom (e.g., Asym-9, Asym-11, etc.) have provided the best evacuation time.
The evacuation time for the cases in which a jumped object is on the floor compared to the cases in which no object has fallen faces an increase of approximately 1.46%-1.52%, which can be considered minor. Similar values are recorded for the case in which the fallen object can be bypassed (an average increase of 1.83%-2.38%). For the case in which both a jumped and a bypassed object are on the floor, the evacuation time increases on average with 5.26%-5.88%, counting for up to 4 s compared to the case with no objects on the floor.

Results for Two-Blocks Configurations
For the case in which the desks and seats are in one of the two-block configurations, the data in Table 4 has been obtained. Considering the numbers, it can be observed that the evacuation times are higher in the case in which the two blocks are vertical than in the horizontal case. As for the symmetrical-asymmetrical analysis, the differences are small even in this situation. Compared to the one-block situation, in this situation it can be observed that the symmetrical exits group score, on average, smaller evacuation times than the asymmetrical exits group.
Up to 4 s difference can be encounter for the case in which there are one jumped and one bypassed object on the floor (Table 4). Even in this case, the symmetrical exits are preferred to the detriment of the asymmetrical exits.
From the symmetrical exits group, Sym-2 and Sym-3 provide the fastest evacuation times in the two-blocks-h configuration, while for two-blocs-v configuration, only Sym-3 provides better evacuation times. By considering their schemes, it can be observed that the exit doors are positioned either on the long wall or on the short wall in the back of the classroom.
In the situation of asymmetrical exits, the configurations with one door in the front of the classroom provide longer evacuation times, while the configurations with one door on the long wall and one door on the short wall in the back of the classroom (e.g., Asym-7) provide shorter evacuation times.

Results for Three-Blocks and Four-Blocks Configurations
In the situation of three-blocks, similar results to the ones obtained in the case of two-blocks have been determined, showing that symmetrical exits perform slightly better than asymmetric ones (Table 5). Higher differences among symmetrical and asymmetrical doors position are obtained in the case in which one jumped and one bypassed object are on the floor.
Regarding the least performing door combinations, it has been observed that for the three-blocks case, the asymmetrical cases containing a door positioned in the middle of the long wall provide the longest evacuation times (e.g., Asym-1, Asym-3, Asym-5, etc.). The four-block desks and chairs configuration bring higher evacuation times in the case in which the doors are asymmetrically positioned. Even higher differences are recorded for the case in which there are fallen objects on the floor. For example, when there is a jumped and a bypassed object, on average, the evacuation time is almost 9 s longer in the asymmetrical doors case than in the symmetrical ones (Table 5).
For a better picture, in Figures 10 and 11, the average, the minimum and the maximum evacuation time are depicted, all of them calculated as an average over all the symmetrical versus all the asymmetrical cases. It can be observed that the symmetrical configurations perform better, even though there are symmetrical configurations that perform worse than the best asymmetrical configuration. More explicitly, it has been observed, for example, that Sym-1 performs worse than Asym-7. Regarding the least performing door combinations, it has been observed that for the three-blocks case, the asymmetrical cases containing a door positioned in the middle of the long wall provide the longest evacuation times (e.g., Asym-1, Asym-3, Asym-5, etc.).
The four-block desks and chairs configuration bring higher evacuation times in the case in which the doors are asymmetrically positioned. Even higher differences are recorded for the case in which there are fallen objects on the floor. For example, when there is a jumped and a bypassed object, on average, the evacuation time is almost 9 s longer in the asymmetrical doors case than in the symmetrical ones (Table 5).
For a better picture, in Figures 10 and 11, the average, the minimum and the maximum evacuation time are depicted, all of them calculated as an average over all the symmetrical versus all the asymmetrical cases. It can be observed that the symmetrical configurations perform better, even though there are symmetrical configurations that perform worse than the best asymmetrical configuration. More explicitly, it has been observed, for example, that Sym-1 performs worse than Asym-7. Since the differences among symmetrical and asymmetrical configurations are higher in the four-blocks case, an additional analysis in which the number of fallen objects has been conducted. It is known that in the case of an emergency, the situation can become critical very fast and a series of objects might fall due to panic. For example, if 4 jumped and 4 bypassed objects fall instead of no object, the average evacuation time for symmetrical exits is 97.40 s (with 46.64% greater than in the 95  Since the differences among symmetrical and asymmetrical configurations are higher in the four-blocks case, an additional analysis in which the number of fallen objects has been conducted. It is known that in the case of an emergency, the situation can become critical very fast and a series of objects might fall due to panic. For example, if 4 jumped and 4 bypassed objects fall instead of no object, the average evacuation time for symmetrical exits is 97.40 s (with 46.64% greater than in the no object case), while for the asymmetrical exits is 114.54 s (with 63.62% greater than in no object case). It has been observed that, for this particular case, Asym-15 configuration provides by far the highest evacuation time. By considering this configuration, it can be observed that the two doors are placed at a smaller distance one to another (than any of the other cases), which might be a cause of the prolonged evacuation time.
Overall, considering all the above cases, it can be observed that, in most of them, the symmetrical exit doors position provides a reduced evacuation time when compared to the asymmetrical exit doors configuration. In some cases, such as the no-obstacle case, the differences are small (near unnoticeable), while in some other cases, in which objects are fallen, the differences can present some differences (e.g., an increase in evacuation time of 14.77% on average when using asymmetrical doors positions instead of symmetrical for the four-blocks desks and chairs configurations).
By analyzing each door position, it has been observed that from the symmetrical configurations, Sym-3 provides the best evacuation times no matter the desks and chairs configurations, while from the asymmetrical configurations, the "winning" door combination depends on the aisles formed by the desks and chairs position within classroom and in most of the cases, do not contain door in the front of the classroom or doors too close on the same or adjacent walls. Thus, a "safe" choice, would be to use, whenever possible, a Sym-3 configuration.

Lecture Hall Simulations
The results for a lecture hall consisting of 96 seats, all occupied, are presented in the following.

Results for One-Block Configuration
Based on the simulations, the average evacuation times for both the symmetrical and asymmetrical configurations are presented in Table 6. The first observation is that for a larger hall the symmetrical exits cluster presents better average evacuation times than the asymmetrical cluster. This result is opposed to the result obtained in the case of smaller classrooms. Considering the magnitude of the difference (up to 21.63 s), it can be said it is considerable, especially if one takes into account the fact that time is precious in all the evacuation situations. The longest evacuation times are provided by some of the asymmetrical configurations, such as Asym-1, Asym-3, Asym-5, Asym-9 and Asym-10. Considering the positions of these doors, it can be observed that these configurations consist of doors located in a close proximity, either on the same or on an adjacent wall.

Results for Two-Blocks Configurations
Similar to the case of a classroom, in the case of a lecture hall, the two-blocks-h configuration provides smaller evacuation times when compared to a two-blocks-v configuration (Table 7). Time differences of up to 37.41 s are encountered for symmetrical exists situations vs. asymmetrical exits situations in the two-blocks-h and up to 42.68 s in the two-blocks-v.
Considering only the case of the symmetrical exits, Sym-3 continues to provide the smallest evacuation time, while in the case of asymmetrical exits, Asym-14, Asym-2, Asym-4, Asym-8 provide some of the best evacuation times. Even in this case, the asymmetrical configurations that are not performing so good are the same as in the previous case in which the desks and chairs are placed in a one-block configuration. Symmetrical exits cluster brings average smaller evacuation times than the asymmetric exits cluster (Table 8) both for three-blocks and four-blocks seats and desks placement. For the three-blocks configuration it has been observed that the best symmetrical position of the exit doors is Sym-2, this being the only situation in which Sym-3 provides second-best results. By re-running a series of simulations step by step it has been observed that when the aisles are narrower and positioned vertically, Sym-2 provides the best evacuation times when compared to other symmetrical doors configurations. From the asymmetrical configurations, Asym-1, Asym-3, Asym-5, Asym-9, Asym-10, Asym-13, Asym-14 and Asym-15 provide the highest evacuation times.
In the four-blocks configuration, the differences among the two clusters, symmetrical and asymmetrical, can be up to 66.83 s ( Table 8). The best-performing symmetrical configuration is Sym-3 in this case, while a series of asymmetrical configurations provide very high evacuation times. Among the best performing asymmetric configurations, one can name Asym-14, Asym-2, Asym-4, Asym-7, providing comparable results with symmetrical configurations, but higher than Sym-3.
As in some of the cases, the methods configurations listed as "best" are quite close when analyzing the mean evacuation time and given the stochastic nature of the agent-based modeling used in this case, an ANOVA analysis (analysis of variance) is conducted. Given the fact that both the number of considered situation and the number of simulations performed was large (10,000 times for each configuration), it has been decided to run the ANOVA on a random chosen case and, if the results are not convincing, to proceed with some other cases.
Since the last discussed situation was four-blocks, it has been decided to take the test on this case. The ANOVA test has been performed by considering all 18 configurations in the simple case in which there were no jumped and no bypassed objects. The null hypothesis (H 0 ) states that the mean average of the evacuation times obtained for the 18 configurations is the same [111][112][113].
The data in Table 9 has been obtained. Based on the data in Table 9 it can be observed that the recorded p-value is less than the significance level of 0.05, which rejects the null hypothesis. To this extent, it can be safely assumed that there is at least one inequality. Furthermore, it can be observed that F (266577.3) is greater than F-crit (1.622828), which sustains the conclusion mentioned before, namely that at least one mean evacuation time is significantly different than the other evacuation times.
At this point, one might be interested to see which one of the 18 configurations considered significantly differs from the other configurations. To this extent, a t-test can be performed between any of the two configurations [114]. Given the fact that the number of t-test needed to be performed is relatively high (combinations of 18 taken 2, namely 153 tests), it has been decided to perform only one t-test between the best symmetric configuration (Sym-3 for the four-blocks situation) and the best asymmetric configuration (Asym-7). The null hypothesis of the t-test states that the means of the evacuation times for the two configurations (Sym-3 and Asym-7) are equal. Table 10 provides the computed data for the t-test.
In order to decide on the acceptance of the null hypothesis, the value for tStat (−139.7250142) should be compared with tCritical two-tailed value (1.960201264). If tStat < -tCritical two-tailed value, then the null hypothesis is rejected. Considering the values in Table 10, the null hypothesis is rejected.
Additionally, a Bonferroni post-hoc testing can be performed. The Bonferroni test considers all the possible pairs of situations (153 in our case) and adjusts the significance by dividing the 0.05 value to the number of the possible pairs. As a result, the test shows whether there is 95% chance that the two considered groups to be significantly different. The Bonferroni test is useful as it overprotects over Type 1 error (when one believes that there is a difference between two groups, but there is not) while increases the probability of Type 2 error (when one believes that there is no difference, but, in fact, there is a difference). In our case, as we are interested in not having a Type 1 error, the Bonferroni test can be applied [115]. As a result, by dividing 0.05 to 153, we get 0.000326797, a value that is larger than the P(T ≤ t) two-tail value of 0.000, which shows that the two groups are significantly different.
Based on the results obtained on lecture halls, it can be observed that most of the symmetrical exits configurations provide good evacuation times, along with some of the asymmetrical exits configurations, such as Asym-2, Asym-4, Asym-6, Asym-7, Asym-8, Asym-11, Asym-12 and Asym-14. On the other hand, there are some asymmetrical configurations that might produce very high evacuation times compared to the methods mentioned above. For example, Asym-5 configuration for the four-blocks desks and seats placement provides an overall average evacuation time with 157.05 s (approximatively 2 min and a half) more than Sym-3 configuration.

Concluding Remarks
The paper analyses whether the evacuation doors' symmetry has an impact on the evacuation process. To this aim, 18 possible evacuation doors configurations for classrooms and lecture halls have been considered, divided into two clusters: symmetrical and asymmetrical, along with five desks and chairs configurations in terms of placement. Based on an agent-based model created in NetLogo, these configurations are easily adjustable depending on the size of the classroom/lecture hall and by considering various variables such as the size of the exit doors, the presence of jumped, bypassed obstacles, the type of agents and their various speeds. Besides the interest of including human behavior into the model as much as possible (by varying the speed of each agent and by randomly placing them inside of the classroom/lecture hall at the beginning of each simulation), the study presents some limitations related to not considering the group evacuation cases or "evacuation with a friend", which are planned to be addressed in a future work.
Using the agent-based model, a series of simulations have been performed and the results have been analyzed in terms of evacuation time. Two types of rooms have been considered: a classroom with a capacity of 24 seats and a lecture hall with a capacity of 96 seats.
Based on the simulations, it has been observed that in most cases, the three configurations listed under the symmetrical cluster provide an average evacuation time smaller than the average evacuation time of the asymmetrical configurations.
Furthermore, it has been observed that the asymmetrical doors configurations cluster can be split into two subgroups: one that provides comparable evacuation times with the ones received when a symmetrical door configuration is used (here one can include the following configurations: Asym-2, Asym-4, Asym-6, Asym-7, Asym-8, Asym-11, Asym-12, etc.), and another one that provides higher evacuation times (e.g., Asym-1, Asym-3, Asym-5, Asym-9, Asym-10, Asym-13, Asym-15, etc.). These two groups are not excluding each other as it has been observed that the performance of the methods can be related, to a certain extent, to the desks and chairs placement in the classroom. For example, Asym-14 provides good evacuation times for the classrooms and lectures halls in which the desks and chairs configuration is one-block, two-blocks of four-blocks, but poor evacuation times for the three-blocks configuration.
Another result observed based on the simulation is that in the case in which the number of fallen objects (jumped or bypassed) increases, the asymmetrical configurations with doors close one to another provide poor results in terms of evacuation times. A similar situation is reported for the lecture halls with asymmetrical configurations in which the doors are located in general in close proximity, either on the same or on the adjacent walls.
On a general note, it has been observed that the symmetrical configurations and the asymmetrical ones having the door placed at larger distances succeed in providing the best evacuation times, no matter what the desks and seats placement is in the classroom or lecture hall. Among them, the symmetrical ones, especially Sym-3 and Sym-2 configurations, provide, in general, some of the smallest evacuation times. There are also cases in which some of the asymmetrical situations provide the best evacuation time, with small differences when compared to the symmetrical situations. As a result, if one has no possibility of simulating the evacuation classroom/lecture hall in a controlled environment, he/she can simply opt for a symmetrical door configuration which can provide either good or the best results depending on the other characteristics of the room and on the desks and seats configurations.
The agent-based model is configurable and can be accessed at the following link: https://github. com/liviucotfas/exits-symmetry-impact.