Pedestrian Evacuation Modeling Using Agent-Based Model and Social-Force Model

Good emergency management is essential in planning events that have the potential to endanger lives, one of which is preparing for an effective and efficient evacuation. Evacuation evaluation using a fire drill is not optimal because it does not describe the emergency. Therefore, agent-based modeling is carried out to see interactions between individuals and their environment during evacuation. ABM (Agent-Based Modeling) is combined with a social-force model, which is the source of the agent’s movement style toward goals and avoiding obstacles. The simulation is carried out using NetLogo 6.3.0 software, which can represent agents spread across a 2-dimensional room with variations in room size, exits, and the number of agents involved. Several characteristics are given to the agent to cause heterogeneity, including age categories in the form of children, adults, people over 70, and people with disabilities, which will determine the agent’s walking speed. The measurements observed were the average duration of evacuation and the average speed of agents. From the simulation results, it can be concluded that using the social force model will lead to the emergence of collective behavior, such as clogging and arching in agents. The exact population density in different room areas will affect the evacuation duration, whereas a larger room area will cause the agent to travel a greater distance to the exit. An increase in evacuation duration will accelerate rapidly at low densities and slow down as density increases.


Introduction
Evacuation simulation models enable the analysis of the behavior of numerous individuals without the need for real-world testing.Various approaches have been developed to address evacuation problems, such as mathematical models, cellular automaton, lattice gas models, fluid dynamics, social force models, game theory, and animal experiments [1].These approaches are conventional simulation models that assume agents have homogeneous characteristics.However, one drawback of these approaches is that idealized environments may only sometimes represent the dynamic characteristics of real-world societal evacuation behavior, which can lead to deviations in analysis results [1] [2].
Agent-based evacuation models distinguish themselves from conventional simulation models by treating each individual as an autonomous agent with unique characteristics and behaviors.Agents can take action based on their situation and environment.The diversity in individual behaviors can lead to the emergence of phenomena or patterns within collective behavior.One advantage of agent-based evacuation models is their ability to model individuals' decisionmaking and social behaviors, as well as how these behaviors are influenced by the structural characteristics of buildings [3].
The selection of simulation methods is highly contingent upon the preferences of the modeler and the specific requirements of the model.Zia integrates agent-based modeling with Moore's neighborhood model, taking into account variables such as Hops (the shortest distance to the exit) and Doms (the direction toward each exit corresponding to the shortest distance of cells) [4].Delcea validates simulation results by comparing them with scenarios executed in the real world, relying on 18 students across two types of classroom layouts-classical and collaborative classrooms-to assess the impact of classroom spatial design on the evacuation process [5].The social force model is one of the most commonly used local motion models based on the assumption of self-driven particles.This model is implemented in evacuation models by systematically changing the ideal speed of agents over time using a vector quantity known as the social force model.Therefore, the social force model is employed to represent the effects of the environment (interactions among agents and agent-environment interactions) on each agent [6].
Numerous publications utilizing the social force model have made the assumption of a homogeneous population, neglecting individual characteristics or behaviors of the involved individuals [7].In this study, the authors combined agent-based modeling with the social force model to depict human behavior in evacuation situations during building fires.The choice of the social force model was based on its flexibility, where each force can be separated and analyzed individually.By combining agent-based modeling and the social force model, each agent can have unique characteristics that reflect their individual social and physical forces.Each agent will move at a constant speed but can respond to random disturbances by adopting other agents' average direction of motion in their environment.

Social-Force Model
The Social Force Model (SFM) is a modeling framework for pedestrian behavior based on sociopsychological and physical forces [8].SFM assumes that all pedestrians behave like particles and utilize force vectors to describe their intrinsic forces and motivations.Essentially, SFM operates on principles similar to Newton's second law, which explains the motion of objects.In SFM, the existing effects will influence the decisions of the agent and result in specific actions.Therefore, in each SFM equation, the agent's mass, m α remains constant throughout the simulation.Furthermore, the effect f or force in each type of SFM can be interpreted as an acceleration function that influences the agent's motion.

The Driving Effect
The driving effect, denoted as ⃗ D α , ensures that agent α moves in accordance per its desired speed v 0 α and moves in the direction of its desired destination ⃗ e 0 α .
With τ α representing the relaxation time that modulates how quickly an agent reaches its ideal speed ⃗ v 0 α (t) = v 0 α ⃗ e α (t), a smaller value of τ α makes the agent behave more aggressively, leading to a more significant value for ⃗ D α .Without other effects, an agent takes τ α seconds to reach its ideal speed.When the magnitude of the actual velocity ⃗ v α is greater than the ideal velocity v 0 α , the driving effect will slow down the agent.Conversely, the driving effect will accelerate the agent when the actual velocity is smaller than its ideal velocity.

The Obstacle Effect
Pedestrians maintain a distance from boundaries like walls or roads and avoid obstacles or other objects.This results in a repulsive effect described by the obstacle effect as follows.The repulsive effect generated will cause agents to move away from obstacles, as indicated by the term −∇ ⃗ r αi .
U αi represents the repulsive potential, which decreases exponentially with the distance between agent α and the nearest object i to agent α (|⃗ r αi |).

The Territorial Effect
Generally, pedestrians tend to feel uncomfortable when unfamiliar individuals approach their personal space.Therefore, pedestrians tend to maintain a certain distance from other pedestrians.This repulsive effect is described as the territorial effect.
The closer a pedestrian gets to a stranger, the stronger the repulsive effect ⃗ T αβ becomes.This effect is directly proportional to the repulsion potential v αβ , similar to the obstacle potential U 0 αβ .In his research, Helbing defined the repulsion potential as follows.
This potential feature σ as the characteristics length for the territorial potential, where σ = 0.3 m.The parameter b represents the semi-minor axis of an ellipse that takes into account the distance between agent α and agent β, |⃗ r αβ |, as well as the velocity of agent β, ⃗ v β .When agent β has a higher velocity, it will require more space for the next step, s β = v β ∆t, so b will increase.The distance between the agents is defined as

The Attractive Effect
Pedestrians can also be attracted to objects or other pedestrians (e.g., relatives, family, friends).
Helbing describes the attractive effect as follows.
Representing the distance between agent α and object i as ⃗ r αi = ⃗ r α − ⃗ r i , the magnitude of the attractive effect | ⃗ A αi | decreases with time t as the agent loses interest in object i.Since the attractive effect is often neglected in most studies, it is not considered in this research.

Effective Field of View
The territorial and attractive effects have larger values for objects visible in the direction of the agent's motion ⃗ e α than for objects located behind agent α.Helbing introduced the concept of perception weights (w ϕ ) to account for this difference.Here, 2ϕ represents the effective field of view angle, and c ϕ is the weight factor for situations outside the effective field of view, where 0 < c ϕ < 1, and objects behind the agent have a progressively smaller constant value.Therefore, w ϕ is defined as follows in the equation provided.
As a result, the territorial effect ⃗ T αβ and the attractive effect ⃗ A αi will be as follows.

The Total Effects
The sum of the four effects described results in the motion of an agent that complies with Newton's second law.
Helbing assumes that all the effects influencing the decision-making of agents occur simultaneously.Therefore, the total effect can be obtained by summing all the existing effects.Additionally, there are two additional assumptions.First, the mass m α of each agent can be considered constant.Second, the sum of the four effects ⃗ f is related to the force ⃗ F = m ⃗ f , which leads to an adjustment of Newton's second law as follows.
Furthermore, the motion equation for agent α can be formulated by summing all the effects as follows.
The agent's preference velocity, denoted as w α , is computed from the sum of all the effects and optional fluctuations.The fluctuations in this equation represent random behavioral variations that may occur.Random fluctuations come into play when there are two equally valid decisions, such as deciding whether to pass an obstacle on the left or right side.In Helbing's simulation, fluctuations are assumed to be 0.
Next, the desired new velocity ⃗ w α (t + ∆t) is determined by calculating the change in the current velocity ⃗ v α (t) due to the total effect ⃗ f α (t).
The position of agent α is described by the vector ⃗ r α , which is defined as follows. d⃗ In this simulation, each agent is constrained by the maximum allowable speed (v max α ).This constraint is applied by reducing the actual velocity ⃗ v α from the preferred velocity ⃗ w α .Here, the unit vector ŵα is defined as ŵα As a result, the new position of each agent α is calculated for each time step iteration as follows.

Simulation
Generally, the steps of agent movement during the evacuation simulation process can be seen in Figure 1.
Helbing introduced several parameter values for the social force model chosen based on compatibility with empirical data, as presented in the Table 1 [8].In the simulation, these parameters are adjusted using sliders before the simulation process commencess.The conversion between international units and NetLogo units is necessary based on predefined assumptions.In this simulation, the assumption employed is that 1 meter is equivalent to 2 patches, and 1 second is valued at 5 ticks.
Table 1.Parameter values of the social-force model.

Variable
Value The independent variables used in this simulation are the number of involved agents and the size of the room used.The age distribution is as follows: 81% are adult agents, 15% are older agents whom over 70, 3% are child agents, and 1% are agents with disabilities, based on research conducted by Cotfas [9].Population density was calculated by dividing the total number of agents by the area used.
The world used is in the form of a two-dimensional square grid composed of equally-sized cells.This world is represented in Cartesian coordinates with the x and y axes.The simulation  .Each cell is assumed to be 0.5 meters, and one tick in the simulation equals 0.2 seconds.Four categories of agents are defined with different walking speeds as shown in Table 2. Due to continuous agent movement, each agent or turtle can occupy one cell or be between two or more cells.Agents can access information about the cells they occupy and the surrounding cells.Neighbor agents can be either those located around the cell occupied by agent i or agents located at a distance based

Result and Discussion
The simulation was conducted using NetLogo 6.3.0 software [13] for several scenarios, consisting of four types of room sizes (81 m 2 , 100 m 2 , 225 m 2 , and 400 m 2 ) with varying numbers of agents based on their population densities, with each scenario simulated 100 times.The initial position of each agent is determined randomly.The simulation focuses on the pedestrian evacuation scenarios without prescribing a specific duration, allowing for a dynamic exploration of evacuation dynamics.Figure 3 is the simulation world interface used in the simulation scenario of 400 agents in a room with a size of 225 m 2 .Here is the interface of the simulation world that is used.Figure 4 compares simulation results for each density in different room sizes and the regression data as a logarithmic function.The figure shows that at low population densities, the increase in total evacuation time accelerates rapidly and slows down with increasing density.This is consistent with the findings of a study conducted by Pauls [10] in which the function to determine  the total evacuation time exhibits non-linear growth and can generally be formulated in the following equation.
The maximum capacity value that can be accommodated is obtained by dividing the room area by the occupant load factor for each type of building [11].According to the IBC, the occupant load factor for buildings used for assembly without seating is 0.464 square meters or approximately 2.1 persons/area.Therefore simulations were conducted using a room size of 225 square meters with higher densities to examine the impact of population numbers exceeding the maximum occupant limit set by the IBC.
It can be observed in Figure 5 that the increase in evacuation time slows down significantly after exceeding a density of 2 person/m 2 and tends to reach a stagnant value.This aligns with the IBC recommendation that the maximum density a room can accommodate to ensure safety and security is typically around two persons/m 2 [11].Furthermore, this is consistent with research conducted by Fruin [12], which explains that pedestrian mobility decreases as population density in an area increases.The total evacuation time can be formulated in a general exponential equation.
The average simulation speed is obtained from the average speed of all agents throughout the entire evacuation process from t = 0 until the evacuation process concludes.Figure 6 shows that the average speed data obtained from the simulation results follow a 4th-order polynomial trend and aligns with the formulation of speed based on density influence as previously described by Predtechensskii and Milinskii [10].The graphical representation in Figure 6 includes the x-axis representing density, while the y-axis depicts velocity.This observation provides valuable insights into the relationship between density and speed, crucial for understanding pedestrian dynamics in evacuation scenarios.Furthermore, the agreement between the result and the formulation proposed by Predtechensskii and Milinskii [10] highlights the robustness of their theoretical framework.Thus, the density-dependent speed function can be formulated in the following equation.

Conclusion
From the simulation results, it can be concluded that pedestrian evacuation simulations using agent-based modeling methods can emerge collective behaviors such as arching and clogging.Additionally, differences in room size with the same density will result in different total evacuation times but with the same data trends.At low population densities, the increase in total evacuation time will accelerate rapidly and then slow down as the population density increases.The duration of evacuation is highly influenced by the number of agents involved and the initial positions of the agents.The lack of real-world data on evacuations makes it challenging to validate agent-based modeling.Further experiments or modeling using an agent and environmental characteristics that better represent actual conditions are necessary to expand the scope.

10th
Asian Physics Symposium (APS 2023) Journal of Physics: Conference Series 2734 (2024) 012032 on the declared characteristics within the simulation.An illustration of the simulation is shown in Figure 2.

Figure 2 .
Figure 2. The illustration of the NetLogo world used for the simulation.

Figure 3 .
Figure 3. Simulation of 400 agents in a room with size 225 m 2 when a) t = 0, b) t = 26, and c) t = 159.

Figure 4 .
Figure 4. Comparison of total evacuation time with agent population density.

10thFigure 5 .
Figure 5.The average total evacuation time (ticks) in a room of size 225 m 2 .

Figure 6 .
Figure 6.Comparison of total evacuation time with agent population density.

Table 2 .
The average walking speed of pedestrians according to age category.