On the basis of data analysis of the evacuation abilities of each vulnerable group, the study conducted evacuation simulations using a computational model previously developed and tested by the authors [
42], thereby comparing evacuation performance results in terms of response and movement under different conditions. The simulation model was built using AnyLogic 7 software, which was developed by AnyLogic Company. The software provides a pedestrian library, which uses a social force model that allows individuals to move according to the pre-assigned rules in the given environment [
43]. An example of a screenshot during the simulation is presented in
Figure 1.
3.2.1. Model Description
The evacuation model translated the survey results on evacuation ability into data on evacuation behavior and performance, including time required for each vulnerable group to make an evacuation decision (i.e., response time) and exit the building (i.e., movement time) in a variety of evacuation conditions. The study opted for an agent-based modeling approach to simulating evacuation behavior, enabling the representation of autonomous agents with perception, interpretation, and decision-making abilities.
Figure 2 illustrates the overall process of an agent’s behavior with regard to the critical elements that affect his or her evacuation performance. A more detailed description of this process and the associated variables for the three critical elements—(1) perceived risk, (2) wayfinding ability, and (3) evacuation velocity—will be provided in the subsequent section.
At the sound of the initial fire alarm, each agent initiates an assessment of situational risk or establishes perceived risk (1 in
Figure 1). The process of establishing an individual’s perceived risk, which is the result of running through a risk perception sequence, functions as a critical factor in predicting the time needed for a building occupant to arrive at an evacuation decision [
19,
44,
45]. The higher the level of perceived risk, the more quickly evacuees engage in protective action such as evacuation decisions [
18,
32,
44,
45,
46,
47,
48]. On the other hand, when perceived risk is lower than the threshold which leads to an evacuation decision, evacuees may exhibit passive behavior by pretending that the situation is non-threatening [
18,
32,
49,
50] or searching for additional information about possible emergency situations [
14,
16,
22,
32,
51,
52]. These findings suggest that perceived risk is directly associated with the response time of each individual agent in the evacuation model.
Once an agent makes the decision to evacuate, his or her movement time is affected by exit/route selection (2 in
Figure 1) and velocity (3 in
Figure 1). Although familiarity with the layout of the building has no effect on whether or not a person attempts to leave the building immediately, it does influence the time that it takes for evacuees to locate the routes and exits available to them [
53]. In addition, being able to perceive and interpret informative evacuation signage helps building occupants find the nearest route and exit for egressing the building.
During an actual evacuation, the velocity of the evacuees is affected not only by mobility but also by the level of risk that each individual perceives [
42]. For example, a person would walk out of a building at a leisurely pace if he or she considered the situation to be relatively secure [
42,
54]. However, the same person would likely accelerate his or her exit from the building to maximum speed if the situation were to become life-threatening and if the amount of stress caused by those threatening conditions were to exceed a certain threshold value [
54]. Therefore, the central mechanism of the model used in this study stipulated that changes in an agent’s level of perceived risk would affect his or her decision-making and trigger behavioral changes that encompass normal (i.e., not responding to emergency cues) and investigating (i.e., searching for additional information about possible emergency situations) approaches before the evacuation decision has been finalized and evacuating at walking speed (i.e., moving toward an exit at walking speed), and evacuating at accelerated speed (i.e., moving toward an exit at maximum speed) after the evacuation decision has been finalized [
32,
42,
44,
46]. Because individual levels of perceived risk operate on an arbitrary scale [
46], the model assumes that perceiving no risk in a situation (i.e., normal state) represents value 0 and a perceived risk greater than thresholds 1, 2, and 3 would cause an agent to move on to the ensuing behavioral states of investigating, evacuating at walking speed, and evacuating at accelerated speed [
42].
3.2.2. Model Variables
As previously stated, the critical elements that affect an individual agent’s evacuation behavior and performance include (1) perceived risk, (2) wayfinding ability, and (3) evacuation velocity.
Figure 3 illustrates how each element is affected by the agent’s cognitive abilities and mobility within the model.
The first element, perceived risk, is established as a result of the perception of fire-related cues, the interpretation of these cues and their meaning, the assessment of situational risk, and decision-making based on behavioral state [
18,
32,
42,
44,
46]. The model for this study considers smoke, fire alarms, and the behavior of other people to be fire-related cues that an individual agent may perceive and interpret during an evacuation [
18,
42]. Recognizing indirect fire cues such as fire alarms or other people demonstrating protective behavior has a prolonged effect on shifting individual levels of perceived risk [
18,
32,
42,
44,
46]. For instance, repeatedly seeing people perform a more active response to the emergency at hand (e.g., running toward an exit) than one’s own response (e.g., investigating the situation) would increase one’s perception of the risks involved in the situation [
42,
44,
46]. However, being surrounded by passive responders (e.g., people continuing to engage in their daily work routine) after the fire alarm has sounded may decrease perceived risk level and cause someone to underestimate the critical nature of the situation [
42,
44,
46]. Drawing on the authors’ previous research [
42], the model in this study calculates perceived risk levels by second using the equations given below:
where
is agent i’s level of perceived risk at time period t,
is i’s level of perceived risk during previous time period
t−1, and
is the change in perceived risk level at time
t caused by observing emergency cues [
42]. On the basis of agent i’s current behavioral state,
is calculated as follows [
42]:
where
if agent i’s behavior is normal;
if agent i’s behavior is investigating;
if agent i’s behavior is evacuating at walking speed if agent i’s behavior is evacuating at accelerated speed.
,
,
, and
stand for the impact of other agents in a normal state (
), investigating state (
), state of evacuating at walking speed (
), and state of evacuating at accelerated speed (
), with these agents being observed by agent
I at time
t [
42].
In the equations above, the impact of other agents in a different state (i.e., normal (
), investigating (
), evacuating at walking speed (
), or evacuating at accelerated speed (
)), all of whom are observed by agent
I at time
t, is as follows [
42]:
where
is agent i’s interpretation of the level of perceived risk surrounding agent
j when agent
j exhibits normal behavior between the values of 0 to 1,
is agent i’s interpretation of the level of perceived risk surrounding agent
j when agent
j exhibits investigating behavior between the values of 1 to 2,
is agent i’s interpretation of the level of perceived risk surrounding agent
j when agent
j exhibits evacuating at walking speed behavior between the values of 2 to 3,
is agent i’s interpretation of the level of perceived risk surrounding agent
j when agent
j exhibits evacuating at accelerated speed behavior between the values of 3 to 4, and
is the level of perceived risk surrounding agent
I at previous point in time
t−1 [
42].
On the other hand, perceiving and interpreting definite and credible signs of a fire (e.g., flame or smoke) triggers the most active response so that the individual in question will exit the danger zone as quickly as possible. In this scenario, perceived risk value is immediately elevated to the highest range of 3 to 4. If the level of perceived risk exceeds or is less than the threshold of its current behavioral state, an agent will make the decision to trigger a behavioral transition to the next active or passive response stage [
44]. The specific equations, model structure, and verification/validation processes for assessing the perceived risk of an individual agent can be found in Choi et al. 2018.
The second critical element, wayfinding ability, is likewise affected by an individual’s cognitive capabilities. In order to follow an egress path out of a possibly dangerous environment, an agent should be able to correctly identify his or her current location in the building, assess alternative escape routes based on prior knowledge of the building layout, and make a decision as to the route and exit toward which he or she should move. Wayfinding ability would be restricted if the agent had a cognitive disability that impeded access to factors such as familiarity with the building layout and effective use of informative building signage (e.g., evacuation plans, exit signs). The model for this study accordingly includes the additional variables denoted in
Table 4 to account for attributes of perception, interpretation, and decision-making which affect an agent’s risk perception and wayfinding abilities. These attributes comprise certain innate characteristics hindering an agent’s processes of perception, interpretation, and decision-making while establishing perceived risk and conducting wayfinding procedure. An agent with a value of 0.5 in perception ability, for instance, has only half the capacity to accurately perceive his or her surrounding agents and current location compared to an agent with a perception value of 1.0.
As shown in
Table 5, the last critical element, evacuation velocity, is determined by an agent’s current behavioral state. The model presumes that an agent in a normal state will be stationary at a fixed position without any velocity. When investigating or evacuating at walking speed, the agent’s velocity will be assigned the average walking speed of an adult moving inside a building, which amounts to a value between 0.6 to 0.8 m/s [
55]. During the most active response to an emergency situation, the agent will run toward an exit at a velocity of 2.3 to 2.5 m/s [
42,
56]. However, as vulnerable building occupants are often unable to move as quickly as the emergency situation demands, the model sets evacuation velocity at a variable mobility range between 0 and 1. With full mobility, an agent will move at a walking speed of 0.8 m/s; velocity decreases to 0.4 m/s with a mobility value of 0.5.
On the basis of the survey results on the emergency response abilities, these values including perception, interpretation, decision-making, and mobility abilities are pre-assigned as an agent’s fixed characteristics.