Congestion-Based Earthquake Emergency Evacuation Simulation Model for Underground Structure

Abstract

Herein, the Dijkstra algorithm was used to develop a model that considers evacuee congestion and derives an optimal evacuation route in underground structures in the event of an earthquake. The ground conditions and seismic intensities were varied, and the evacuation route was analyzed for four cases. The damage index for each underground structure due to an earthquake was determined considering the ground conditions and structure depth, and the evacuation speed reduction was evaluated as a function of the damage index. A congestion coefficient was applied when the evacuation capacity exceeded the threshold to reflect the evacuation speed reduction due to increased congestion in the same evacuation route. The evacuation route in some sections changed when congestion was considered, and the final evacuation time increased significantly when the congestion coefficient was applied. When the evacuation capacity at each node exceeded the threshold, the 1/3 value was applied as the congestion coefficient to evacuation velocity. When the original evacuation route was used after applying the congestion coefficient, the evacuation time increased by up to 220%. However, the evacuation time can be reduced by applying an alternative route that considers congestion. When an alternative route derived from considering congestion was used, the evacuation time decreased by up to 45% compared to that when the original route was used, and the time required decreased by up to 840 s. Hence, the reduction in evacuation speed due to evacuee congestion must be considered to derive alternative, optimal evacuation routes in the event of a disaster. In addition, evacuation routes should account for the location of evacuees using technologies such as real-time indoor positioning to consider the congestion level of evacuees.

1. Introduction

Large-scale seismic activities have been recorded worldwide in recent years, including the 7.8-magnitude earthquake in Turkey in 2023 and the 7.2-magnitude earthquake in Taiwan in 2024. The development of underground spaces is widespread around the world, and the assessment of the underground structure’s safety during an earthquake is an important topic. In Korea, the 5.8-magnitude Gyeongju earthquake in 2016 and the 5.4-magnitude Pohang earthquake in 2017 also occurred, and these large-scale earthquakes have increased social anxiety against earthquakes. Moreover, the demand for seismic preparedness, response technology, and deep underground facilities, such as the GTX (Great Train eXpress), has been increasing. In this context, various analytical studies have been conducted on underground structures [1]. Identifying evacuation routes in the event of an earthquake becomes challenging because of the damage to underground structures, stampedes or secondary accidents, and obstruction of view. Moreover, rescue is difficult in the event of human casualties [2,3]. As such, the Ministry of Land, Infrastructure, and Transport design guidelines [4] specify that the platform must be evacuated within four minutes and the station within six minutes in the event of a subway disaster. The Seoul Metropolitan Government guidelines for municipal administration and major work plans indicate that the golden time for a subway disaster is three minutes. However, according to the 2016 Seoul Metropolitan Government survey, the emergency evacuation time exceeded four minutes for 51% (74 places) of the 145 stations on Seoul Subway Lines 5 to 8 [2,5]. The Gangnam Station, one of the busiest stations in the Seoul subway system, caters to approximately 300,000 passengers every hour during commute hours [6]. A disaster during peak hours can prolong the evacuation time further, owing to the congestion of evacuation routes. The evacuation time for stations is expected to increase further because of the recent increase in deep station facilities, such as the GTX. Therefore, optimal evacuation route guidance technology is necessary to ensure rapid evacuation in the event of a seismic disaster and minimize human casualties.

In this context, the evacuation of building occupants during earthquakes has been extensively investigated. Zhou et al. [7] quantified user evacuation responses according to seismic intensity using evacuation simulation. Chu et al. [8] analyzed the effects of diverse non-structural damage that may occur indoors upon evacuation in the event of an earthquake. The earthquake evacuation route prediction models considered in these studies were focused on buildings that are highly vulnerable to damage due to earthquakes. Liu and Zou [9] and Chen et al. [10] examined evacuation route derivation models for underground station structures with a focus on fire disasters. Underground structures have been recognized as relatively earthquake-safe structures compared to buildings [11]. However, cut-and-cover structures, such as underground station structures, are prone to damage due to ground displacement [12]. In the event of seismic damage to underground structures, evacuation is expected to be extremely difficult. However, evacuation models against earthquakes in underground station structures have not been extensively investigated, and optimal evacuation route systems for earthquakes have not been proposed. In addition, research on identifying alternative evacuation routes that consider congestion has not yet been conducted. Therefore, user evacuation models for earthquakes that consider congestion must be examined.

The Dijkstra algorithm has been widely used across the world to obtain optimal evacuation routes in the event of a disaster. Hong et al. [13] searched for routes on a single layer using the Dijkstra algorithm and presented two or more Dijkstra algorithm linkage methods for multiple layers. They also proposed variable evacuation routes depending on the disaster. Kim et al. [14] examined methods to derive the shortest distance by obtaining situational information using a wireless sensor network and actively utilizing the Dijkstra algorithm. Jung et al. [15] developed an algorithm that accounted for fast-changing urban traffic conditions in real time and derived the optimal route based on the Dijkstra algorithm.

Efficient implementations of the Dijkstra algorithm have also been investigated. Mun et al. [16] proposed a Dijkstra* algorithm that reduces the computational time of the Dijkstra algorithm. Park et al. [17] used a deep learning model to find the evacuation routes of a ship. However, these studies do not fully reflect the characteristics of subway station structures in Korea and the disaster characteristics. Hence, studies on optimal evacuation routes for underground station structures are necessary. Jeong et al. [3] simulated fire in subway stations and confirmed that the distribution of betweenness centrality is concentrated in specific zones. However, there has been a lack of studies on the increase in evacuation time caused by congested evacuation routes and the resulting route re-derivation.

Therefore, in this study, an algorithm based on the Dijkstra algorithm was developed to derive the optimal evacuation route while accounting for the disaster situation. In addition, the effect of the evacuation speed decreasing after a certain level of congestion was reflected, and based on this, an algorithm to derive an alternative route that can evacuate in the minimum time was developed. The placement of passengers under the same disaster situation varied, and the concentration of passengers overtime during the evacuation was examined. Subsequently, an algorithm was developed to derive the optimal evacuation route that accounts for congestion and redistributes passengers.

2. Evacuation Simulation Model Using Dijkstra Algorithm

2.1. Evacuation Model Using the Dijkstra Algorithm

The Dijkstra algorithm employs nodes and edges that correlate the nodes. It is a blind search algorithm that finds the shortest route by deriving the minimum value from the start node (i0) to the destination node. The main feature of the Dijkstra algorithm is that it is a blind search algorithm that considers the number of all cases, and as a result, it has the advantage of finding an evacuation path in the least amount of time. Since the evacuation model is directly related to the casualties, it is most desirable to apply a blind search algorithm to find the minimum time. Figure 1 shows a schematic of Dijkstra’s algorithm.

Dijkstra’s algorithm involves the following steps. First, the source node is assigned a value of zero (0), and the remaining nodes are assigned a value of infinity (INF). Calculation begins from the start node, and the value that is added to the start node and the edge value is compared with the adjacent node (i1). If the value that is added to the start node and the edge value is smaller than the adjacent node, the adjacent node is updated with the value. Through repeated comparisons and calculations, the minimum value of the distance is derived considering all cases. By backtracking the calculation route that results in the minimum value, the corresponding route can be defined as the shortest route from the start node to the destination node. Because the minimum value is obtained after considering all possible cases, the shortest route derived using the Dijkstra algorithm corresponds to the optimal route.

The Python programming language was used to develop an algorithm that outputs an optimal evacuation route according to the evacuee congestion in a station. Four functions—described below—were defined and used.

The first function (Fun 1) implements the Dijkstra algorithm and outputs the shortest route between the source and destination nodes.

The second function (Fun 2) backtracks the shortest route and generates a set by start node to aggregate the number of people per node over time (seconds). For betweenness centrality analysis, it derives the number of people per node over time by aggregating the number of people over time.

The third function (Fun 3) applies weights to edges adjacent to nodes that exceed the threshold of the number of people per node. In the event of an earthquake in a station, evacuation via the optimal route may lead to crowding in certain spaces. Consequently, the evacuation speed decreases, and secondary accidents, such as stampede, may occur. This function, which assigns appropriate weights to edges to ensure evacuation without crowding at the station, reflects the rate of reduction in the evacuation speed.

The fourth function (Fun 4) updates the graph by applying weights to the edges adjacent to crowded nodes. After Fun 4, the code restarts, and the edges adjacent to the updated nodes are no longer updated.

The algorithm, formulated using the aforementioned functions, works as follows. After deriving the optimal evacuation route using the Dijkstra algorithm, the number of people per node is calculated every second. The number of people per node is stored in a set. If the number of people per node exceeds the set threshold, a preset weight is assigned to the edges adjacent to the node, and the calculation is restarted. The node, updated once, is not re-updated even if it exceeds the threshold again. This procedure ensures an even distribution of the evacuees by decreasing the evacuation speed in crowded spaces. The flowchart of the Dijkstra algorithm is shown in Figure 2.

2.2. Input Parameters for the Underground Station Evacuation Model

2.2.1. Geometry of the Underground Structure

In this study, a seismic disaster situation in an underground station structure was assumed, and the evacuation of all people at the station was simulated, considering the reduction in evacuation speed and congestion due to the disaster. A representative cross-section of a Korean subway station was used in the simulation. A typical underground station in Korea has three basement floors. Train platforms are located on the third basement floor, and ticket gates are located on the first. The second basement floor is used as a passageway between the platforms and the ticket gates. A simplified model of the underground station space was used in the evacuation simulation. Figure 3 shows a geometric model of the station. Each floor was divided into four sections, and two exits were positioned at both ends of the first basement floor. Subway stations in Korea are typically 200 m long and accommodate ten 20 m cars; hence, the distance between the horizontal spaces was set to 50 m. The vertical distance between the spaces was set to 5 m in accordance with the floor height specified in the Subway Key Design Criteria [4] published by the Urban Infrastructure Headquarters of the Seoul Metropolitan Government.

The station space was divided into nodes; the Dijkstra algorithm was applied to the simplified underground station cross-section, and an evacuation was simulated. A node and cross-section diagram of the underground station is shown in Figure 4. For the horizontal space, the evacuation distance was calculated to be 50 m under the assumption of movement between the middle of each space. The vertical evacuation distance was set to 7 m by assuming a staircase slope of 45° in accordance with the Subway Key Design Criteria [18] for a floor height of 5 m. Stairs are vertical movement elements, and congestion on the stairs may increase. Accordingly, the stair node was set in the middle of the stairs, and the distance between the vertical movement elements was determined to be 3.5 m. For the evacuation section from the first basement floor to the ground, the total horizontal evacuation distance was set to 14 m, considering the longer height to the ground; the distance between the vertical nodes was set to 7 m.

2.2.2. Number of Evacuees and Evacuation Time

The number of evacuees in a disaster situation was set based on Gangnam Station Line 2, which is the busiest subway station. According to the Seoul Metropolitan Government [6], the average number of users at the Gangnam Station from 17:00 to 19:00 was approximately 600,000 as of 2023. Thus, the number of users per minute can be assumed to be 5000. Accordingly, during peak hours, the number of people waiting at the platforms, in addition to boarding and alighting passengers, was assumed to be 5000; this number was used in the evacuation route derivation model. The underground station comprises subway platforms on the third basement floor and ticket gates on the first basement floor. The maximum congestion situation corresponds to the maximum number of passengers per car. The maximum number of passengers per train vehicle is 240, and a subway train with ten cars carries 2400 passengers. Accordingly, 2400 people out of a total floating population of 5000 were set to be located on the third basement floor. The number of people on the first basement floor with ticket gates was assumed to be higher than that on the second basement floor; 1600 people (almost 60% of 2600) were placed on the first basement floor, and 1400 people (almost 40% of 2600) on the second.

Table 1. Personnel allocation table.

Basement 1	Basement 2	Basement 3	Total (People)
1600	1400	2400	5000

summarizes the final personnel allocation by floor. The horizontal evacuation speed of passengers in the station was set to 60 m/min, and the vertical evacuation speed was set to 15 m/min in accordance with the design guidelines for subway stations and transit amenities [4] (

Table 2. Evacuation speed by evacuation factor. [4].

Evacuation Factor	Evacuation Speed
Horizontal transportation (platform, concourse, corridor)	60 m/min
Vertical transportation (stairs, stationary, escalator)	15 m/min
Escalator	36 m/min

). It was assumed that escalators do not operate during a disaster.

2.3. Seismic Risk Analysis for the Underground Station

The seismic risk for each station zone was evaluated to simulate the evacuation route in the event of an earthquake in the underground station. Kwon et al. [19] proposed a damage index based on the depth of the underground station and ground type. The suggested damage index in the previous research was applied to evaluate the seismic risk of each zone of the station with three basement floors. Results of previous studies have shown that the ground type has a significant impact on the seismic risk [19]. The evacuation route simulation results were evaluated based on the differences in the risk for each zone. According to the ground classification in seismic design standards, the left side of the underground station was assumed to be ground with a shear wave speed of 360 m/s, which corresponds to an S_D ground in soil classification for seismic design [20], and the right side was assumed to be ground with a shear wave speed of 150 m/s which corresponds to an S_E ground in soil classification for seismic design [20]. In addition, the variation in the evacuation risk and evacuation route due to changes in the ground conditions were examined by varying the area of the soft ground layer (which has a relatively high risk). The earthquake scenario was selected using Korean seismic design standards [20]. The Korean seismic design standards specify that the earthquake magnitudes for preventing collapse are approximately 0.2 g and 0.3 g, corresponding to return periods of 2400 and 4800 years, respectively. The seismic risk analysis cases are shown in

Table 3. Seismic risk analysis cases.

Case No.	Ground Condition	Input Acceleration (g)
1	Left side 100 m vs. = 360 m/s Right side 100 m vs. = 150 m/s	0.3
2	Left side 50 m vs. = 360 m/s Right side 150 m vs. = 150 m/s	0.3
3	Left side 100 m vs. = 360 m/s Right side 100 m vs. = 150 m/s	0.2
4	Left side 50 m vs. = 360 m/s Right side 150 m vs. = 150 m/s	0.2

. The damage state criteria proposed by Park et al. [21] were used. The damage state of the station structure was classified into four states: no damage (ds1), minor damage (ds2), moderate damage (ds3), and extensive damage (ds4). The damage status is calculated based on the damage index, which is derived as the ratio of the moment in the structure to the yielding moment of the structure [20]. The damage index values according to the damage states are listed in

Table 4. Damage state by damage index [21].

Damage Index (DI)	Damage State
0 < DI < 1	No damage (ds1)
1 < DI < 1.4	Minor damage (ds2)
1.4 < DI < 2.3	Moderate damage (ds3)
2.3 < DI	Extensive damage (ds4)

. Figure 5 shows the results of the seismic risk analysis for the node and cross-section diagram of the underground station. The value between each node is the damage index obtained from the seismic risk analysis. The damage state was defined on the basis of the damage index (Table 4), and different colors correspond to different damage states. The damage index value (and the level of the damage state) increases with increasingly softer ground and increasingly deeper structures. The seismic risk analysis results indicated that the damage index at a higher depth was higher than that at a lower depth. This was attributed to the shear force caused by the boundary conditions at the bedrock.

2.4. Determination of the Evacuation Speed

2.4.1. Speed Reduction Due to Seismic Risk

An earthquake in an underground station structure adversely affects the evacuation route because of the damage to the structure and falling rocks, thereby leading to a reduction in the evacuation speed. A disaster has a significant impact on the evacuation speed of the passengers. Rikito Mizuno and Nihei [22] showed that hydraulic variables, such as the water depth and flow velocity, reduce the evacuation speed by 30–50% in the event of a flood disaster. Hassanopour et al. [23] reported that in the event of a seismic disaster in buildings, the evacuation speed decreases by 10% in the case of minor damage, by up to 60% in the case of extensive damage, and by up to 90% if injuries occur. Wang and Zhang [24] examined the accessibility to underground structures and the possibility of traversing damaged structures. They suggested that minor damage involves small falling rocks and non-structural damage that do not significantly interfere with access and passage. Moderate damage involves groundwater leaks and rocks on passages, wherein access and traversal are possible only upon moderate repair. Extensive damage involves large-scale fractures and the inflow of groundwater, making evaluation and traversal impossible. They proposed an evacuation speed reduction function according to the damage state and damage index. The effect of minor damage on the overall evacuation speed was small. Therefore, as proposed by Hassanopour et al. [23], it was deduced that the evacuation speed decreased by up to 10%. In the case of extensive damage, basic traffic is expected to be almost impossible, and only minimal movement for evacuation is expected to be possible. An evacuation speed reduction rate of 90% in the case of injury was applied, considering that evacuation in the event of a disaster is more difficult in underground structures than in buildings. In the case of moderate damage, the evacuation speed was assumed to decrease linearly between minor damage and extensive damage, depending on the damage index. Figure 6 shows the evacuation speed reduction function used in this study. A number of evacuation speed reduction effects were considered, and the evacuation speed ratio, compared with the normal state (white background) and evacuation time (gray background) between nodes, was derived, as shown in Figure 7.

2.4.2. Evacuation Speed Reduction Due to Evacuee Congestion

In the event of a disaster in a station during peak hours, passengers attempt to evacuate by the shortest route, thereby leading to crowding in certain spaces. Evacuation can be difficult when a large number of people are concentrated in one space, which may lead to secondary damage, such as a stampede. In this study, the congestion coefficient was used to account for the evacuation speed reduction due to congestion. The evacuation capacity of each zone was calculated with respect to the maximum evacuation capacity specified in the subway station and transit amenity design guidelines (

Table 5. Evacuation capacity per meter for different evacuation factors [18].

Evacuation Factor	Evacuation Capacity
Horizontal transportation (platform, concourse, corridor)	80 persons/m × min
Vertical transportation (stairs, stationary, escalator)	60 persons/m × min
Escalator	120 persons/m × min
Turnstile	60 persons/min

). The Subway Key Design Criteria [18] recommends a minimum platform width of 8 m and the maximum number of evacuees per meter is 80. Accordingly, for horizontal sections, it was assumed that the evacuation capacity was beyond the threshold, and the evacuation speed was reduced when more than 640 people were concentrated. Similarly, for the vertical section, the maximum evacuation capacity was set to 360 people; this capacity was obtained by multiplying the minimum width of 6 m by 60 people, which is the maximum number of evacuees per meter. The congestion coefficient was applied when the evacuation capacity at each node exceeded the threshold. Zhou et al. [25] suggested that the evacuation speed decreases to 1/3 of the original speed when the density per square meter exceeds three people during an earthquake evacuation. As the density per square meter exceeds three people in this study, 1/3 was used as the congestion coefficient.

3. Evacuation Simulation Results and Discussion

The evacuation simulation model described above primarily reduces the evacuation speed of evacuees according to the seismic risk due to a disaster, and the evacuation occurs at the reduced evacuation speed. The model reduces the evacuation speed further if congestion increases when the concentration of people exceeds the evacuation capacity at a particular node. The evacuation time required when the route was derived while considering the level of congestion was compared with the evacuation time required when the optimal route was chosen without considering the level of congestion.

Table 6. Evacuation routes and evacuation times without the congestion coefficient.

Start Node	Evacuation Route									Exit Node	Evacuation Time (s)
0	0	14	4	18	8	22	12			12	108.5
1	1	15	5	19	9	8	22	12		12	159.6
2	2	16	6	5	19	9	8	22	12	12	536.6
3	3	17	7	21	11	23	13			13	417.4
4	4	18	8	22	12					12	72.32
5	5	19	9	8	22	12				12	123.47
6	6	5	19	9	8	22	12			12	256.47
7	7	21	11	23	13					13	137.40
8	8	22	12							12	42.32
9	9	8	22	12						12	93.47
10	10	11	23	13						13	187.11
11	11	23	13							13	62.8
Maximum evacuation time											536.6

,

Table 7. Evacuation routes and evacuation times applying alternative routes with the congestion coefficient.

Start Node	Evacuation Route									Exit Node	Evacuation Time (s)
0	0	14	4	18	8	22	12			12	325.6
1	1	0	14	4	18	8	22	12		12	390.0
2	2	1	0	14	4	18	8	22	12	12	890.0
3	3	17	7	21	11	23	13			13	1252.2
4	4	18	8	22	12					12	217.0
5	5	19	9	8	22	12				12	370.4
6	6	7	21	11	23	13				13	545.3
7	7	21	11	23	13					13	412.2
8	8	22	12							12	127.0
9	9	8	22	12						12	280.4
10	10	11	23	13						13	561.3
11	11	23	13							13	188.4
Maximum evacuation time											890.0

and

Table 8. Evacuation routes and evacuation times applying the original route with the congestion coefficient.

Start Node	Evacuation Route									Exit Node	Evacuation Time (s)
0	0	14	4	18	8	22	12			12	325.6
1	1	15	5	19	9	8	22	12		12	479.0
2	2	16	6	5	19	9	8	22	12	12	1609.8
3	3	17	7	21	11	23	13			13	1252.2
4	4	18	8	22	12					12	217.0
5	5	19	9	8	22	12				12	370.4
6	6	5	19	9	8	22	12			12	769.8
7	7	21	11	23	13					13	412.2
8	8	22	12							12	127.0
9	9	8	22	12						12	280.4
10	10	11	23	13						13	561.3
11	11	23	13							13	188.4
Maximum evacuation time											1609.8

show the results derived via optimal evacuation route analysis at each start node for case 1. Table 6 shows the results when the evacuation speed reduction weights according to evacuee congestion were not applied. The results show that evacuation occurred at exit 12 for nodes 2, 6, and 10, although exit 13 was closer. The left section with relatively hard ground suffered a lower degree of damage than the right section with soft ground, leading to a difference in evacuation speed reduction. Therefore, the evacuation route was determined to be along the direction with a lower degree of damage rather than the adjacent exit. Table 7 shows the evacuation route results for different start nodes when congestion was considered. When the evacuation capacity exceeded the threshold for each horizontal and vertical node, the congestion coefficient, which reduces the evacuation speed to 1/3 of the original, was applied. Consequently, the evacuation routes for start nodes 1, 2, and 6 changed (yellow background), and the maximum evacuation time increased significantly from 536.6 to 890 s. In the case of node 6, in particular, the optimal evacuation route when evacuee congestion was not considered was [5,6,8,9,12,19,22], whereas the optimal route when evacuee congestion was considered was [6,7,11,13,21,23]; that is, the evacuation route changed from the left exit to the right exit. This change may be attributed to the concentration of evacuees in the relatively less damaged left passage, which leads to a reduction in the evacuation speed and, consequently, an alternative route.

Table 8 shows the results of evacuation along the original route derived in Table 6 when the congestion coefficient is applied. Compared to the results shown in Table 7, the evacuation time increased significantly (blue background) for start nodes 1, 2, and 6, which have an alternative route, and the maximum evacuation time increased to 1609 s. Figure 8 shows the evacuation route of node 2, which has the longest evacuation time, for the case of applying the alternative route and the case of applying the original route. As shown in the figure, the alternative route avoids Floor 5, Stair 19, which is expected to be highly congested, and the actual evacuation time is significantly reduced. These results demonstrate that, in areas where an increase in evacuation time is expected due to evacuee congestion, alternative routes must be derived while accounting for congestion to ensure the evacuation of all people within the shortest time period.

The same analysis was conducted for cases 2 to 4, and the results are summarized in

Table 9. Maximum evacuation time for the original and alternative routes.

Case No.	Without Congestion Coefficient	With Congestion Coefficient—Original Route	With Congestion Coefficient—Alternative Route
Case 1	536.6	1609.8	890.0
Case 2	576.5	1729.6	1368.5
Case 3	809.1	1867.2	1514.9
Case 4	1138.2	2771.5	1931.4

. The final evacuation time increased significantly when the congestion coefficient was applied. Evacuation along the original route after applying the congestion coefficient required 130–220% more evacuation time. In particular, the final evacuation time increased to 1633 s in case 4. That is, the evacuation of all people during a disaster takes more than 15 min, which may lead to a large number of human casualties. When an alternative route was derived after applying the congestion coefficient, the increase in the evacuation time was much smaller. Compared to the case wherein the original route was used, the evacuation time decreased by 19–45% when an alternative route that accounted for congestion was used, and the evacuation time was in the range of 350–840 s. These results indicate that an increase in the evacuation time due to congestion is inevitable in the event of a disaster. Hence, in sections where an increase in evacuation time is expected, real-time alternative routes must be calculated by considering congestion to ensure the evacuation of all people within a safe time period. Although this study was conducted for an earthquake scenario, the congestion-based evacuation route simulation model can be applied to other disaster scenarios such as fires, terrorist attacks, and floods. However, when applied to other disasters, the speed reduction effect and route restriction of certain areas for each disaster scenario should be quantitatively evaluated. For example, in the case of a fire, evacuation routes are restricted in the direction of smoke spread, which may increase congestion in other areas and should be quantitatively evaluated. The human casualties in a disaster are closely related to how many evacuees can escape to safety within a safe time. The results of this study show that evacuation routes that do not fully account for congestion can significantly increase escape times, which can lead to an increase in casualties. Therefore, it is essential that congestion-related factors be considered in evacuation guidelines and standards, and further research should continue to be conducted.

4. Conclusions

In this study, a model that can derive the optimal evacuation route considering evacuee congestion was developed using the Dijkstra algorithm to ensure rapid and safe evacuation of passengers in an underground station in the event of a seismic disaster.

• A model to derive the optimal evacuation route in the event of an earthquake was developed considering evacuee congestion using a simplified representation of a Korean subway station cross-section with three basement floors. Results of previous studies, wherein the risk according to the ground type and depth was assessed, were used in the seismic risk analysis, and the evacuation speed reduction due to the seismic damage to the structure was evaluated. The evacuation speed reduction due to evacuee congestion was defined using the evacuation capacity of the subway station. The evacuation speed was reduced to 1/3 of the original speed when the number of people exceeded the evacuation capacity. The effects of seismic damage and crowding beyond the evacuation capacity on evacuation time were analyzed using the Dijkstra algorithm;
• When the evacuation speed reduction due to congestion was not considered, the evacuation route was focused on the left exit (which was relatively less damaged) than the right exit (which was subject to severe seismic damage). This demonstrated the reduction in the evacuation speed due to seismic damage; the resulting concentration of evacuees in certain sections could increase congestion;
• When the evacuation route was derived considering the reduction in the evacuation speed due to congestion, the Dijkstra algorithm searched for alternative routes to account for the evacuation speed reduction. In particular, in some sections, the optimal evacuation route, which was the relatively less damaged left passage when evacuee congestion was not considered, changed to the right passage when an alternative route was derived considering congestion. This change may be attributed to the reduction in the evacuation speed due to the concentration of evacuees in the relatively less damaged left passage and the consequent derivation of an alternative route by the algorithm;
• When the original route was chosen for evacuation, despite the reduction in evacuation speed due to congestion, the evacuation time increased significantly due to increased congestion and reduced evacuation speed. When an alternative route derived by considering congestion was used, the evacuation time decreased by up to 45% compared to that when the original route was used, and the time required decreased by up to 840 s. Hence, alternative routes must be derived according to evacuee congestion when the optimal evacuation route is calculated. Apart from considering real-time congestion, evacuation routes should account for the location of evacuees using technologies such as real-time indoor positioning;
• The limitations of this study are as follows: First, a single seismic scenario was considered and applied to a simplified two-dimensional structure with three basement floors. Second, variables that can lead to a reduction in the evacuation speed of evacuees, such as the mental state, obstructed vision, and obstacles, were not considered. Third, the personal characteristics of evacuees, such as children or people with a disability, were not considered. Fourth, this study only focuses on the effect of congestion on the evacuation time of all users during an earthquake and cannot consider the phenomenon of congestion level changes and the subsequent slowdown and recovery of evacuation speed. Finally, this study was conducted only for earthquake scenarios, which could limit the generalization of evacuation routes for other disasters such as fire and flood;
• In future research, it is necessary to apply the proposed congestion-based earthquake emergency evacuation simulation model to complex historical structures in three dimensions and to consider various variables, such as the evacuee’s state, the presence of obstacles, and a disaster-disadvantaged person, which can have an effect on evacuation speed. Also, the real-time congestion changes and the subsequent slowdown and recovery of evacuation speed should be considered in further study. After developing an advanced congestion-based evacuation model, the verification of the evacuation model should be conducted based on experimental data. It is also necessary to create an evacuation simulation model applying other algorithms, such as the A* algorithm and the genetic algorithm, and perform a performance comparison. Also, since the analysis was performed only for earthquake scenarios, further studies, such as quantification of speed reduction effect and route restriction, are needed to apply it to fires, terrorist attacks, and other disasters. The combination of congestion-based evacuation route models and real-time indoor positioning technologies can provide efficient and safe routing for evacuees within an integrated disaster management system, which could be a game-changer in reducing casualties in disasters.