Analyzing emergency evacuation scenarios in Ghana based on different groups profiles in a classroom

Abstract It depends on both the pedestrians and the building whether they can be evacuated from a building safely and quickly in any situation. Understanding pedestrian behavior is crucial when designing buildings for safe evacuation in emergencies like earthquakes and fires. Since this topic has yet to be fully explored in Ghana, we conducted experiments in a classroom to capture the characteristics of pedestrian movements during an emergency. In this experimental study, students were asked to pretend to evacuate during an emergency. The simulation and comparison of the evacuation of students from a classroom were conducted using a multi-grid model in our study. The study examines several factors that influence evacuation characteristics. These factors include pedestrian density, speed, time, door width, body mass index, and classroom capacity. The paper describes in detail all study phases, including planning, preliminary work, observational studies, empirical data collection, and statistical analysis. It thoroughly examines pre-movement time, group density, and velocities for groups and individuals moving through doorways, traveling distances, and walking in educational settings. A person’s state of mind and psychological abilities are also taken into account, as well as their level of emotional involvement in the movement. The obtained results are also discussed for evacuation planning in educational institutions under different conditions.


Introduction
In an evacuation situation, human behavior is complex, but it is an essential activity for human survival.An evacuation occurs when a person leaves locations where they have been meeting their spiritual and social needs.Therefore, their behavior is a form of interaction with their environments that is common to all organisms and is associated with their activities and ability to adapt to their environments.
There have been many studies of pedestrian dynamics in urban traffic studies, including Control models with optimal outcomes (Campanella et al., 2009), Models of social forces (Helbing et al., 2000(Helbing et al., , 2002)), Models based on lattice gas (Fu et al., 2012;Xu et al., 2012), cellular automata models (LA & Tc, 2012;P. Song et al., 2019), comparison of the model of simulation (Kholshevnikov et al., 2009;Zhang et al., 2020), and Analyzing human panic behavior through agent-based modeling (Trivedi et al., 2018).It is imperative to understand pedestrian behavior patterns in evacuations so that they can improve evacuation procedures and relevant regulations.The choice of the route pedestrians makes while leaving an area impacts evacuation efficiency.A situation in which pedestrians cannot adequately select routes for evacuation could result in a phenomenon in which most people would congregate on a few paths.In contrast, most paths would be occupied by just a few people.An inefficient evacuation may result from this scenario.The development of an intelligent pedestrian evacuation guide sign requires an understanding of pedestrian route choice behavior.It provides dynamic information to pedestrians for evacuation via the intelligent guide sign.Models for pedestrian routes can be continuous or discrete, depending on the pedestrian's route choice.To model pedestrian route choice in continuous space (Campanella et al., 2009), used optimal control theory.Users were assumed to maximize their predicted utility while walking.
Jams and crowds have caused numerous pedestrian accidents trampled during the last few years.Evacuating pedestrians from buildings has received much attention as pedestrian flow has become an exciting topic.There has been considerable attention paid to students' safety evacuations in classrooms.Its conceptual simplicity and ease of computer implementation have made it an especially appealing choice for academic researchers to use for numerical investigations.The cellular automata model proposed by (Fu et al., 2012;Zheng et al., 2008) allows pedestrian evacuation to be simulated by considering both positional and fire danger grades to determine movement rules.Based on the simulation results, the model can accurately simulate evacuation behaviors, such as blockage and curving at departure.In a room with fixed obstacles, pedestrian evacuation times were examined using bi-dimensional cellular automata (Varas et al., 2007).Two single doors in place of one double door did not increase evacuation times significantly.The above research cannot accurately replicate the evacuation process when pedestrians are distributed heterogeneously.It is common for people to assemble in dense concentrations in some building regions.Studying the exit choice behaviors and movement rules of pedestrians in an obstacle-filled classroom and pedestrians moving in groups in a classroom, we investigated the effects of density distributions of pedestrians, the time taken to evacuation, and pedestrian speed as again the groups.
According to the experimental results, some previous studies still need to create appropriate models.Additionally, many evacuation models are raw grid models used for simulations and compared with experimental results.In addition, limited studies have been conducted that address evacuation from spaces with multiple obstacles, such as theaters, classrooms, etc.Under such conditions, predicting crowd behavior using models should be built based on the characteristics of the crowd.Using simulations and experiments, we investigate how students evacuate a classroom with one and two exits.In a classroom, we recorded the experiment with a video camera.In the experiment, we investigate the typical evacuation behavior and the basic models that could quantify this behavior.

Work related
Data are collected both in the real world (Aik, 2011;Liu et al., 2009) and in virtual environments (Duives & Mahmassani, 2012).In virtual environments, perceptions may differ, leading to different participant behaviors.Nevertheless, we show that pedestrians can optimize their travel time in both cases by dynamically selecting appropriate exits.Pedestrian behavior at the tactical level determines the choice of exit, according to the models.In previous work, the shortest path was considered a suitable solution for congestion-free situations (SMÃ et al., 2006).In congested situations, the exit that minimizes travel time may not be the closest one.The predominant model is therefore based on travel time and distance to the exit (Ulrich et al., 2018;van der Wal Cn et al., 2021).Additionally, other factors, such as the choice of route, are considered (Aik, 2011), socioeconomic factors (Duives & Mahmassani, 2012), type of behavior (selfish or cooperative, see (Liu et al., 2009)), and presence of smoke, visibility, herd effect, or In emergencies, the faster-is-slower rule may apply (Aik, 2011;Helbing et al., 2000;Liu et al., 2009).The models are developed in different ways.Statistical models such as log-IT or prob-IT are sometimes used in their research (Aik, 2011;Liu et al., 2009).Some other approaches are based on the notions of pedestrian rationality and objective function from game theory (Hoogendoorn & Bovy, 2004;SMÃ et al., 2006).In this way, individual travel time or marginal costs are minimized, and iterative methods like possible to optimize user or system performance with the Metropolis algorithm or neural networks (Crociani & Lämmel, 2016).
When traffic is congested, it is challenging to estimate travel times.Can solve the problem by simulating modeling pedestrians in operation.Due to the link between the exit model and simulation, the application is computationally complicated.Density and travel time have strong correlations.According to traffic theory literature, there is a well-established association between traffic flow and density ref (Helbing et al., 2000).(Aik, 2011;Liu et al., 2009).Density levels near exits are a parameter in some recent dynamic models (Aik, 2011;Liu et al., 2009).Density replaces travel time in these models.Unlike travel time, the density level is easy to measure and does not require simulation.Therefore, it can implement a density-based model more efficiently than an equilibrium-based model.

Experiment setup and behavior observation
In 2021, an experiment was conducted in Ghana's upper west region at a senior high school as shown in Figure 1, the experimental area occupies the first half of the classroom, which is 9.15 meters long by 7.15 meters wide.There are seven rows and five columns of desks and chairs, which are 1.05 meters long and 0.40 meters wide.A total of 35 students can be seated at the desks and chairs, arranged in seven rows while numbered in a specific order.Each column of desks has a number on it; there are two doors in the classroom, and the two doors have equal diameters of 1.6 m wide.There are two exits on the right and left sides of the classroom, with two doors.As shown in Figure 1, There is a ratio of about 1: 1 between the two outlet widths.There are five rows, and the aisles are numbered from left to right.In the third case, we look at the class's original arrangement of chairs and tables.The classroom has two digital camerasone on the left side of the front (opposite the exit) and one at the left rear.Throughout each of these experiments, students were instructed to exit the room quickly by using the short route.They briefly explained the evacuation procedure to the evacuees before the study and instructed them to act as if they were in an emergency (Al, 2020).used video graphic methods to collect the data for the study.A BLENDER software tracker extracted data from the video recordings and manually calculated them.We analyzed the data using OriginPro2021 (liner fitter), Matlab, and Microsoft Excel (Vanumu et al., 2018).Observations of the experiment based on the video recording include the following:

Camera 2 position Camera 1 position
• Evacuation time(s): The evacuation time refers to how long it takes for people to evacuate from the moment the evacuation order is issued until the last evacuee can either leave the evacuation zone or reach a safe place.The time each student leaves a classroom is considered the exit time.
• Pre-evacuation time(s): Between the first verbal warning and the time when each classroom began to evacuate.Upon hearing the alarm, some students begin securing their property instead of fleeing quickly.Additionally, people respond differently when they hear an alarm.There are significant differences in the pre-movement times for students in this case.Compared to other buildings, classrooms, theaters, etc., have more obstacles.To reach the aisle, pedestrians must follow or wait for pedestrians in front of them.Therefore, the pre-movement time has an essential effect on evacuation.
• Average velocity(m/s): Throughout the evacuation procedure, students constantly modify their velocity dependent on the area in front of them.Students could move a different distance in an equivalent amount of time depending on the distance remaining.The student walks at his free walking speed or maximal speed if the gap size is large enough.
• Exit control.According to the theory, two pedestrians can successfully pass through the exit depending on its width.However, the exit is sometimes controlled by only one pedestrian (as indicated by figure 2(a,b) in both situations, one pedestrian is ahead of the other pedestrians in the middle of its exit.There needs to be a more efficient use of the exit width.
• Distance(m) The path's length between two points determines their distance.
Based on these phenomena in the experiment, an evacuation model was developed, which could predict similar outcomes in the future.

Simulation and model characteristics
During our experiment, we found that the dimensions of the doors, obstacles in the classroom (tables and chairs), and the walkway (aisle) did not correspond to integral multiples of the pedestrian's scope (0.4 m).Additionally, it has been detected that pedestrians are dislocated, monopolizing the exit and continuously adjusting their velocity as they make their way from one point to another.Simulating the evacuation process in detail is possible thanks to the smaller grid size (W.Song et al., 2006); the building is difficult to divide into raw lattices where one grid is the same size as a pedestrian.However, this problem can be solved by the multi-grid model.An update procedure that uses a new method was developed to upgrade the multi-grid model considering the pre-movement time.
Analyzed experimental data from evacuations, such as individual travel time, group travel time, and total evacuation time to identify the correlation between evacuation time and the characteristics of evacuees.Pedestrians traveled at an average speed.The main results of this study are presented here.Because of this, we pay special attention to the groups' time of exit, where the crowds from the back of the class exceed the classroom exit's capacity.Due to the force, there will be congestion at the exit (Yang et al., 2011).
During the study (Najmanová & Ronchi, 2017;Xie et al., 2018;Yang et al., 2011), the evacuation time at each seat was defined as the time between when the students started the experiment and when they left the classroom under the five arrangements at the exit.

Model basic rules
The design and construction of a building and its construction and equipment should be designed to ensure that the building and its people will not be adversely affected in an emergency.People need to be evacuated successfully in such situations.
According to the raw grid model, each student occupies just 0.4 m × 0.4 m of the area in a dense crowd; this is typical for pedestrians.The space occupied by pedestrians is divided into 8 × 8 small grids Figure 3(b) to improve accuracy and reflect actual conditions.Each point represents a distance of 0.05 m from the previous one.The grid is divided into two dimensions.Depending on the pedestrian's walking speed and the area occupied, the pedestrian moves a different number of grids in each time step.
In this scenario, a pedestrian won't remain static and will move three grids.This will make it more in line with the fact that pedestrians almost usually use the space to get away if they can.The fact that pedestrians try to flee as soon as possible is consistent.Pedestrians are simulated by biased-random walkers moving forward and backward in the preferred direction.Figure 1.illustrates three or four preferred directions based on classroom characteristics.One of the preferred directions from the left (right) seating area, pedestrians can see horizontally to the right (left).At the same time, the preferred direction for pedestrians in the aisle area is toward the exit.Pedestrians prefer to walk one way.For determining the possible pedestrian configurations and their transition probabilities, see Ref (Tajima et al., 2001).We have also considered the pedestrian's main time.Updating our model involves five steps, including updating the pedestrian position.They inform rules are practical to each pedestrian by the new modernized procedure, which is explained in greater detail in section 4.2.
(1) This test aims to determine whether This time is greater or equal to the pedestrian's premovement time.If yes, proceed.Otherwise, update the next pedestrian.
(2) Based on the transition probabilities, we decide which direction the pedestrian will move during this time step.
(3) A pedestrian move toward the target based on his direction, the free movement velocity, and the number of unoccupied grids.
(4) Slowdowns randomly occur.During this time step, each moving pedestrian will stop randomly.
(5) They are removing pedestrians from outside.All pedestrians at the exit are taken out of the update chain.

New update procedure
Different types of updates are used in evacuation simulations: parallel updates, mixed sequential updates, and ordered sequential updates.According to the parallel rule, all pedestrians are updated simultaneously, and conflicts are resolved when more than one person attempts to reach a similar cell simultaneously.At each step, they only enter one object cell at a time; the others remain in their early positions.Conflicts during an evacuation will most likely occur due to the number of people in the classroom and obstacles (tables, chairs).The sequence number determines how pedestrians are updated.
In contrast to the latter, the former assigns a unique number to each person at a given time phase, while the latter assigns a random sequence number to each person at a given time phase.Based on experimental observation, the pedestrian determines the pedestrian's motion tendency.The method of modernizing has been simplified; the new and straightforward position-based approach is used.The pedestrians' positions are updated each period phase based on the distance between their present position and the center of the output.A modernized triangular field is distributed from the middle of the exit, as shown in Figure 3(b).The first grid in matrix 3(b) corresponds to the center of the exit and is the first grid to be updated; each grid is represented by a number representing its update priority.The lesser the number, the more recent the update is.The same priority grids are updated at random.This update procedure can simulate an endless queue with dense crowds (Zhang et al., 2008).

Simulation of model
Models are run according to the exact scenarios as experiments.During the experiment, the premovement time of each student was recorded and input into the model.Students moved to the exit almost without hesitation, so we chose a time step of 4s and a drift of 0.99.Each time step, a student can move up to six grids in the seating area or aisle area due to the change in speed in the evacuation procedure.In the absence of other pedestrians, the speed is 0.76 m/s, equivalent to 0.75 m/s in the test.Furthermore, based on the observation in the experiment and the division of the time phases, 0.1 is set as the random deceleration probability.

Results and analysis
We'll go over the simulation findings from the model mentioned above.Two screenshots from the simulation utilizing the multi-grid model we created are shown in Figure 5.The simulation (Figure 4(a)) allows for the observation of monopolizing exit and the dislikable queue, which is not possible with a conventional raw lattice CA model.Further, the adopted updating mechanism may have contributed to the continuous pedestrian flow that developed as the majority of students entered the aisle (Figure 4(b)).Another prominent feature of the created multi-grid model is seen in Figure 6, 7, 8 specifically the varied pedestrian velocity.In this diagram, we are concentrating on a student and computing his velocity from the start of the movement to its conclusion using simulation and experiment, and comparing the outcomes.While in the experiment, the velocity is calculated once every second, in simulation, it is calculated every time step (0.4s).The simulation and experimental results show that the model is applicable because they are in good agreement with one another.The arrival time of each student at their respective initial seat in the experiment and simulation is shown in Table 1.This arrival time was defined as the interval between the alarm sounding and the moment the corresponding student arrived at the exit of the classroom (Nagai, Masahiro Fukamachi, et al., 2005).It demonstrates that the majority of the outcomes from simulations match the experiment quite well.Due to their prolonged premovement delays, pupils in Row 5 have a substantially longer evacuation time than other  students.Additionally, Table 2 displays the relative errors of these data based on calculations.All pupils start to move and flee in order to measure the impact of pre-movement time on the overall evacuation time at time t = 0.In the experiments and simulations, Tables 1 and 2 (a) & (b), respectively, Each student's arrival period is calculated as the period between the alarm sounding and the student's departure from the classroom (Nagai, Fukamachi, et al., 2005).The results of most simulations are in good agreement with the experiment.The students in row 5 and column 7 have much longer evacuation times of 7.92s than the rest due to their long lead times.That is when it comes to a single exit, but when there is a double exit, row 3 and column 7 students will have a much more extended evacuation period of 7.68s than the others because there is a double exit in use.Simulate the process again without considering the lead time of each student.The students begin to move at the time (t = 0).The model outcomes are relatively near to the experimental outcomes when entering the lead period of each student into the model.
The model arrival time is compared with the result of the experiment.In Figure 10, 11 , 12 , 13 and 14 the student velocity and time compared with individuals and groups to the order in which the students left the classroom.In addition, the experimental results are inconsistent with the number of pedestrians evacuated per unit of time.The simulation result is compared with the experiment when lead time is considered.

Single-exit scenario
When choosing a route, the distance to the exit is the only factor to be considered.Since there was no way out of the classroom other than through only one exit, it created a bottleneck in the exit.
As a safety science concern and as a concern for any public facility, the ability to evacuate safely and efficiently during an emergency is of primary importance.It is still not uncommon for fatalities to occur due to too long or hampered evacuations during safety hazards.Numerous studies have been conducted on this topic, as it has been deemed necessary.Yet, the effect of groups on evacuations remains a subject of much uncertainty and controversy, with reports of positive effects and indications of negative ones (Bode et al., 2015).At least two factors can explain the current situation.
Human behavior may be to blame for the unclear state of things.According to a dedicated review (Thalmann et al., 2000), human behavior matters significantly in the outcome of building emergencies, both when choosing a seepage way and interrelating with other evacuees.In (Bernardini et al., 2019), varied appearances of common add-ons are reported as influencing emergency response.In addition, human behavior is always dependent on the environment in which they live, the building environment in which they are housed, and emergencies involving their lives (Thalmann et al., 2000).Social groups can also have opposite effects in this regard (Wang et al., 2021).The cooperative behavior of persons within minor groups can positively influence evacuation.Nevertheless, the slower speed of groups, particularly those shaped within intimate relationships, can hamper general evacuation and disrupt the mass flow.The inner unity of the groups may result in less attentiveness to others, which could lead to more competitive behavior between groups (Schadschneider et al., 2018).Evidence suggests that door width, classroom occupancy, and the number of students in a classroom contribute to the time it takes students to evacuate.The evacuation time is nonlinearly correlated, where the total evacuation time of 8.56 � 0.02s with a velocity of 1.68 � 0.06 m −1 exponentially decreases up to 1.68 � 0.01s with a velocity of 0.96 � 0.01 m −1 when a single door width is open, but then remains constant afterward.As a result of the bottleneck trajectories situation, pedestrians are forced to push and crush one another.Additionally, the evacuation experiment showed "faster-is-slower" behavior.

Two-Exits Scenario for individual
Figure 12 shows a scenario illustrating how pedestrians choose routes to different locations based on the multi-grid model.As seen in Figure 14, the north and south walls of the room have identical width exits one and two.
Though the parameter changed, pedestrians' choices of exits were not significantly different.When considering two exits, pedestrians' choices barely change when traffic congestion is present.Almost equally, pedestrians choose exits one and two with different times and velocities.The total time and velocities were between 1.6 � 0.02s to 7.68 � 0.1s and velocities of 0.96 � 0.03 m/s and 1.37 � 0.02 m/s respectively.There is no difference in width between exit one and exit two; therefore, pedestrians must decide which exit to pick depending on their intention to leave the classroom.Considering the nature of the two exits, most pedestrians have always gathered near both exits.Based on the observation of pedestrian space, we may figure out why the possible algorithms are outlined in (Kretz, 2009;LA & Tc, 2012).cannot adjust the ratio of pedestrians choosing both exits by using that information but can see as a u-shape or V-shape when moving in groups (Nicolas et al., 2021).
In these empirical results, exploring the correlation between velocity, group size, and time is incredibly stimulating.These dependencies are shown in Figures 11(a,b), 13 and 14 based on the data presented.At low group size, the discrepancy in velocity by size tends to decrease as number increases; this suggests that large groups appropriately adapt their configuration to dense settings.They studied only two-person groups (dyads) in these experiments.Individuals tried to keep close in these dyads, which may explain some differences.There is a difference of less than 1.2 m/s in speed between individuals and dyads in Figure 15, which means that the flow of mass involvement of both constituents shouldn't differ from the flow of an atomic mass.

Groups and individuals exiting on a single exit
Two pairs were considered as group in the research.

Groups and individuals exiting on double exit
The choice of passenger exits did not differ significantly, regardless of the parameter change.
Congestion barely affects pedestrians' choices when two exits are available.Exits one and two had almost equal pedestrian traffic with different times and velocities (Figure 13b).The total time and velocities were between 1.60s and 7.68s, with 0.96 m/s and 1.37 m/s, respectively.Since exit one and exit two are the same widths, pedestrians choose which exit to take depending on how they intend to get out.There have always been pedestrians near both exits because of the nature of the two exits.
Observing pedestrian spaces may help us to understand why the possible algorithms described in (LA & Tc, 2012) work.Based on the information, it is possible to adjust the ratio of pedestrians choosing both exits.Still, it can be calculated based on moving in groups in the U-or V-shape.
The results demonstrate that moving in groups or pedestrians helping individuals impacts the results.However, this result cannot be generalized and may significantly impact evacuation times if there are more differences between groups.
From Figures 13(a,b) we compared the experiment with the simulation model, and we release that both have similarities; in both scenarios, It was easier for pedestrians to get to the exit fastest than those moving in groups, for example, individual moving time and velocity were given as  (Perozo et al., 2010); as the number of participants increases, pedestrians' routes gradually become more complicated.
Additionally, it would be helpful to know how you would organize groups larger than two people taking between three or four people trying to help each in an unlikely scenario.Each group member would want to help everyone simultaneously, which would be challenging.Most likely, group members only consider those in their immediate surroundings when they need help.As a result, two to four-person clusters emerge within the group.

Behavioral factor
The study found that the two age and gender groups (between 16 and 18 years and between 19 and 21 years) differed in terms of travel speed, passage through doors, and behavior.There was not much difference in behavior between the younger and older students during the evacuation.Still, when considering gender, the male students were more active than their female counterparts (about 20% of the female students ran during the evacuation, compared to the male 80%).Several factors may be responsible for this.Many of the female students hesitated and seemed confused or surprised when they were evacuated.While male students felt relaxed and ran for the exits, Still, some students needed the opportunity to run due to the crowds.These numbers are also influenced by the fact that many female students were not afraid of injury when they ran.I also observed that some stopped at the door to go back and pick up their caps when they fell off their heads or onto their shoes.Other behaviors, such as general evacuation, were interesting to observe.
The observation of other behaviors known from general evacuation theory was attractive.Although their group room had a direct exit to the outside, some children went directly to the main door when they received evacuation instructions.People use their familiar routes and exits in an emergency, even though there may be safer or closer alternatives.This phenomenon is known as the belonging theory.The students in the building were also worried about their friends.People can behave this way when they refuse to evacuate without their family or friend, although in this case, the students did not act on their concern but only expressed it (P.Song et al., 2019).

Conclusion
In this study, one of the goals was to provide insight into specific movement parameters and provide unique data sets during the experiment.They used three variables to describe student  movement: evacuation time, distance, and travel speed.The evacuation process is quantified using a multi-grid model.In this scenario, a pedestrian won't remain static and will move three grids.This will make it more in line with the fact that pedestrians almost usually use the space to get away if they can.The fact that pedestrians try to flee as soon as possible is consistent.They can move different grids according to the student's allowed motion speed and the space in front of them at each time step so that they can adjust their velocity accordingly.As a result, a new update procedure was introduced and determined to be appropriate for simulating this situation.
Based on the new model, the typical features are reproduced.We compare experimental results with those from the developed multi-grid model to further investigate the impacts of lead time on evacuation and velocity.Results agree with the model.Evacuation time and the propagation of the evacuation period are related.There is a bottleneck approach from pre-movement to the exit when considering a single exit but with a different approach with two doors exit.An exciting aspect of our experiment is that the simulation results were similar to the experimental results.Observations indicate that this phenomenon might be explained by coordination between the students that maximizes the effect of the student movement time.The total evacuation time may increase if such a phenomenon becomes weak and uncoordinated in panic situations; this could explain the "faster-is-slower" behavior.
Students' movements and behaviors during the evacuation were mainly influenced by the number of pedestrians, door width (m), classroom capacity, and escape route design.There was discussion about the likely impact of student knowledge of escape routes.We should conduct future research to understand students' behavioral patterns in different age groups and research in other parts of the world, particularly Africa.You are free to: Share -copy and redistribute the material in any medium or format.Adapt -remix, transform, and build upon the material for any purpose, even commercially.The licensor cannot revoke these freedoms as long as you follow the license terms.
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Figure
Figure 1.Shows the schematic classrooms used for the experiments with two exits, north and south door.

Figure
Figure 2. (a) shows a Snapshot of a single-door exit sitting arrangement, (b) single-door exit evacuations, (c) a Snapshot of two doors exit sitting arrangement (d) Two doors exit evacuations.Both doors have the same diameters of 1.6 m.

Figure 3 .
Figure 3.An improved version of the multi-grid model, (a) Implementation of a discretized model.According to the model, a pedestrian occupies a grid of 8 × 8 grids and can change better distances every time phase.(b) the diagram shows the informed procedure for every time phase; modernized is turned from minor to too big with the grid.At the exit, the grid is modernized first (Zhang et al., 2008). .

Figure
Figure 4. Using our developed multi-grid model, here are some simulation snapshots.(a) t = 7.68s (b) t = 8.56s.

Figure
Figure 5. Velocity and time relationship of the individual moving trajectories base on one exit scenarios.
Figure 7. Velocity and time relationship of pedestrian's trajectories in groups base one exit scenario.

Figure
Figure 10.Shows the image time phases of a simulation showing people on the floor and existing scenario of one door.

Figure
Figure 11.(b) (i) Shows the individual times for two exit with widths of 1.6m open for the students, and (ii) shows individual velocity for two exit with widths of 1.6m each open for the students.

Figure
Figure 12.(a) (i) Shows the individual times for one exit with widths of 1.6m open for the students, and (ii) shows individual velocity for one exit with widths of 1.6m each open for the students.

Figure
Figure 13.(b) (i) illustrates groups and individual times for two exits with widths of 1.6m open for the students, with (ii) shows groups and individual velocity for two exits, (b) (i) shows two exits for time and (ii) for velocity for groups and individual.

Figure 14 .
Figure 14.The classroom with two double-door exits, with the best locations for the doors.

Figure
Figure 15.Illustrates the distance and time graph for groups and individuals in a graph.

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