The Collection and Compilation of Small Group Data for Scenario Setting of Simulations and Experiments

Abstract

The influence of small groups in evacuation cannot be ignored. However, the current simulations and experimental studies have oversimplified the settings of small groups and evacuation scenarios. A significant disparity exists between the findings of existing studies and real-world scenarios. This paper compiled data on the number and size of small groups and the location of small group members in built environments. Subsequently, a scenario with intricate functions and shapes was established, and finally, these data was employed in agent-based simulations. The data encompassed 50 small groups comprising a total of 111 members. These groups, ranging from 2 to 4 members each, exhibited spatial separations between members spanning from 1 m to 23 m. Simulation outcomes indicated a detrimental effect of small groups on overall evacuation. A significant and positive correlation was observed between the distance separating small group members and the escalation in evacuation time, total jam time, and evacuation distance. The data provides a foundation for configuring initial scenarios in small group evacuation experiments and simulations. The simulation results can provide a basis for hospital safety evacuation management.

1. Introduction

1.1. Background

Within the past year, the China Fire and Rescue Force alone responded to 825,000 fires, with 2053 deaths, 2122 injuries, and 7.16 billion yuan in direct property damage [1]. In the event of an emergency, close family members and friends may form small groups and evacuate together [2,3,4]. Existing safety evacuation designs often only focus on individual evacuations, lacking consideration for small group evacuations. Research on small group evacuations is needed to deepen the human-centered safety evacuation design and reduce casualties and property losses.

1.2. Research Objectives and Work Aims

1.2.1. Research Objectives

Hoogendoorn et al. classified the decision-making behavior of purposeful pedestrians into three levels: strategic, tactical, and operational [5]. As for the decision-making behavior of small group members in evacuation, studies have been conducted to provide basic data at the tactical and operational levels, including small group path choice [6], and small group members’ evacuation speed [7]. Junxue Zhou et al. developed a wide range of indoor earthquake evacuation scenario databases for evacuation models by analyzing evacuation videos in various types of buildings [8]. Unfortunately, their study lacked data at the strategic level, which includes composition and spatial distribution of small group members, hindering the application of the database for verifying the accuracy of small group evacuation models. Data at the strategic level, including the number and size of small groups, the number of small group members, and the spatial distribution of them, are still lacking. This gap makes research on small group evacuation challenging (Figure 1).

The context of evacuation scenario settings has garnered considerable attention. However, there remain two primary research challenges in this area. Firstly, real-life evacuation scenarios often involve diverse small groups composed of occupants with varying mobility capabilities, such as elderly individuals accompanied by adults in commercial complexes, and teenagers and children accompanied by adults in gymnasiums. Current research seldom incorporates heterogeneous small groups with differing walking abilities into simulated scenarios. Secondly, evacuation of building spaces characterized by intricate functions and shapes presents heightened complexities. Existing studies predominantly focus on analyzing evacuation dynamics within singular functional spaces like pedestrian zones, classrooms and offices, and gymnasiums, typically characterized by simpler spatial layouts such as rectangular, L-shaped, or circular designs. Consequently, there is a dearth of research on evacuation in buildings featuring complex functions and shapes, thereby posing novel challenges and opportunities for small group evacuation studies.

Due to the lack of strategic level data and the simplification of simulation scenarios, the impact of small groups on evacuation remains an open question.

Therefore, our research objectives are as follows: (1) to collect strategic level data to enhance the realism of evacuation experiments and simulations; (2) to set more intricate simulation scenario; and (3) to assess the influence of small groups on evacuation.

1.2.2. Work Aims

To achieve our research objectives, we have established the following work aims: (1) collecting data on numerous small groups characterized by varying distances among members; (2) employing appropriate data collection methods to ensure accuracy; (3) setting evacuation scenarios involving small groups comprising occupants with diverse walking abilities; (4) creating a spatial environment that integrates passage, waiting, and usage functionalities, characterized by complex geometric shapes; and (5) assessing the positive and negative impacts of small groups on both overall and occupants’ evacuation processes.

We selected the outpatient department of a large general hospital in China for data collection and simulation. This choice was primarily motivated by the following reasons: (1) the outpatient department hosts numerous small groups comprising patients and their accompanying persons, the accompanying persons need to help patients handle various procedures, the distribution of small group members and their distances are diverse; (2) comprehensive surveillance coverage allows for accurate data acquisition through video observation; (3) small groups within the hospital exhibit diverse walking abilities and strong group cohesion; (4) hospitals encompass multifunctional spaces such as waiting areas and exam rooms, resulting in a complex spatial layout; and (5) simulation outcomes in hospital settings are crucial for ensuring the safety and well-being of all occupants.

1.3. Literature Review

Existing research has conducted evacuation experiments in real scenarios using hypothetical strategic level small group data [9], or computer evacuation simulations in hypothetical scenarios [10,11,12,13,14,15,16,17,18,19] (

Table 1. Typical studies pertinent to our research objectives.

Strategic Level Data	Scenario Setting		Simulation Results	Attitude	Ref.
Hypothetical strategic level small group data	Evacuation experiments in hypothetical scenarios	Rectangular room	Slow down initiate movement	Negative	[6]
			Decrease evacuation speed and increase evacuation time		[7]
			Decrease evacuation time	Positive	[22]
		Rectangular pedestrian zone	Increase the average evacuation time	Negative	[20]
	Evacuation experiments in real scenarios	Rectangular room and stair	Depend on the competition mechanism of occupants	Both positive and negative	[9]
	Evacuation modeling and simulating in hypothetical scenarios	Rectangular room	Reduce evacuation efficiency	Negative	[10]
			Increase evacuation time		[12]
					[13]
					[15]
					[19]
			Decrease evacuation time	Positive	[14]
			Increase evacuation efficiency		[17]
		Rectangular pedestrian zone	Increase evacuation time and decrease average speed	Negative	[11]
			Increase total evacuation time		[16]
		T-shaped pedestrian zone	Depend on the density of occupants	Both positive and negative	[18]
	Evacuation modeling and simulating in real scenarios	Rectangular pedestrian zone	Increase total evacuation time	Negative	[21]

). However, in both experiments and simulations, the scenario settings were typically simplistic. Researchers made assumptions about the number of small group members and their proportion to the total number of occupants, the number and size of small groups, the location of small group members, and the distance between members (Figure 2). The building spaces in experiments and simulations predominantly featured spatial functions such as rooms [6,7,9,10,12,13,14,15,17,19] and pedestrian zones [11,16,18,20,21]. The spatial layouts mainly consisted of rectangular shapes [6,7,9,10,11,12,13,14,15,16,17,20,21,22] and T-shaped configurations [18]. The outcomes derived from experiments and simulations in hypothetical data and simple scenarios were different. One group of researchers believed that small group evacuation behaviors reduced the overall evacuation efficiency [6,7,10,11,12,15,16,19,20,21], another group of researchers believed that they could increase the evacuation efficiency [14,17,22], and yet another group of researchers believed that the positive or negative effect of small groups on overall evacuation depended on the competition mechanism within the small groups [9] as well as the density of occupants [18].

This paper described the methods of the study, followed by an introduction to small group data. The effect of small groups on evacuation was then analyzed through simulation. Comparison between the present study and existing studies was carried out, and directions for further research were explored. Finally, the key findings and implications of the study are summarized.

2. Materials and Methods

2.1. Overview

The research process is shown in Figure 3. We conducted a case study to obtain data and used the data in the Section 2.4.1. Finally, we analyzed the obtained data and the simulation results.

2.2. Case Study

In recent years, the outpatient areas of China’s large general hospitals have implemented an advanced specialist outpatient center system. Except for diagnosis and treatment areas, the exam areas are located next to their required support areas to form a specialist outpatient center, with a hospital street linking multiple specialist outpatient centers. The layout of each specialist outpatient center is the same. Nanjing R large general hospital adopts a specialist outpatient center system. The number of occupants in the endocrinology outpatient center is close to the average number of occupants in all centers in R hospital, and the numbers of men and women within are similar, almost all the occupants are adults, and most can walk normally. Therefore, this paper took the endocrinology outpatient center of Nanjing R hospital as an example.

The endocrinology outpatient center contains a primary waiting area, a secondary waiting area, an exam area, a support area, and an office area, as well as patient corridors, staff corridors, and two evacuation stairs (Figure 4). Upon arrival, patients and their accompanying persons check in and wait in the primary waiting area before proceeding to the secondary waiting area upon being called. They then leave the center after consultation, examination, or treatment. For the purpose of our study, we delimited the analysis area (AA) to the region delineated by the purple line in Figure 4. This area encompasses all waiting small group data and provides ample scope for investigating the impact of small groups on evacuation.

Fires are most dangerous at the time of peak occupants. According to Chinese practice, the number of occupants in the outpatient areas on Mondays is the highest during the week. So, we obtained surveillance videos of AA from 07:00 to 18:00 on Monday, 23 December 2019. The positions and perspectives of four cameras are illustrated in Figure 4. Meanwhile, we conducted a questionnaire interview on 23 December 2019, from 10:00 AM to 11:00 AM in AA. We randomly selected and interviewed 5 healthcare staff members and 50 patients along with their accompanying persons. To respect personal privacy, we recorded respondents’ gender and approximate age based on observation. The interview question was are you familiar with the locations of the stairs on the east and west sides? During questioning, we indicated the general directions of the east and west staircases. These responses were recorded as input data for Pathfinder to model occupants’ behavior settings.

2.3. Data Collection

2.3.1. Total Number of Occupants

We imported the collected videos into BORIS version 7.8 (Behavioral Observation Research Interactive Software) and recorded the behavior of occupants’ entering and exiting the AA, along with the respective timestamps of entry and exit. Subsequently, we processed the data to analyze the fluctuation in the number of occupants in the AA over time, identifying the peak occupancy moment. Furthermore, we conducted a total count of occupants present at this peak moment. For details about the BORIS software, see reference [23].

2.3.2. Small Group Data at a Strategic Level

Small group data at a strategic level includes the number of small group members and their proportion to the total number of occupants, the number and size of small groups, and the distance between members within the same small group.

We observed the surveillance videos and numbered all occupants in the AA at the time of peak occupants and recorded the physical characteristics (gender, age, role, clothing, hairstyle) of all numbered occupants. We recorded the location of all numbered occupants in CAD (Figure 5). Based on the above characteristics, they were identified in the surveillance videos from 07:00 to 18:00, and their dynamic behaviors were observed, and their dynamic characteristics (walking ability and walking posture) were recorded (Figure 5). We determined whether the numbered occupants belonged to the same small group based on whether they moved together for a long period of time and whether communication occurred. We identified the leader of the small group as the occupant among the accompanying persons who took the initiative to check in, find seats, and observe the call screen. Some small group members left the AA alone to go to the toilet, cashier, before the time of peak occupants. They were assumed to be outside (located on the hospital street), and when the evacuation simulation started, they would come back to meet the other members of the same small group in the AA. We recorded small group information for all numbered occupants (Figure 5). All occupants in the AA at the time of peak occupants were named as all members in AA (AMsAA), including members that we assumed were located on the hospital street. An occupant belonging to a small group was designated as a member in a group (MIG).

According to the statistics provided in Figure 5, the number of MIGs, the number and size of small groups, and the location of MIGs can be obtained. The proportion of MIGs to the total number of occupants was calculated. Furthermore, the distance between MIGs within the same small group was measured using CAD. We defined the distance between the two MIGs within the same small group as the geometric shortest path distance between the centers of these two MIGs on the building plane (Figure 6). ‘Adjacent’ indicated that two MIGs were not separated from each other and the distance was less than 1 m.

2.4. Modeling and Simulation

The average daily number of outpatient visits exceeds 10,000, with high density and below-average mobility of occupants. Given the unfamiliarity of occupants with the built environment in outpatient areas, unannounced fire drills can induce panic and worsen the psychological and physical distress of patients. Advance notice fire drills differ significantly from real emergencies, and conducting extensive fire drills in hospitals is often deemed impractical due to various logistical constraints. Computer simulations have emerged as effective tools for studying the evacuation behaviors of small groups in outpatient areas. The agent-based model can represent individual attributes such as gender, height, and shoulder width. Pathfinder software, equipped with an agent-based model, facilitates simulation of small group evacuation behaviors and assisted evacuation behaviors [24]. It has demonstrated utility in hospital evacuation modeling [25,26,27,28,29,30,31,32]. Therefore, we used Pathfinder version 2019 to simulate the evacuation of small groups. The moment when there are the most occupants in AA was used as the starting moment for the simulation.

2.4.1. Modeling

The model of the endocrinology outpatient center of R hospital was established using Pathfinder (Figure 7).

According to Figure 5, the location of occupants and occupant profiles (adult men, adult women, elderly men, elderly women, and in wheelchairs) were set in Pathfinder. Also, the shoulder width, height, and speed of different profiles were set (

Table 2. Base data used in the simulation.

Type	Shoulder Width (cm) (Maximum Shoulder Width Plus Clothing Thickness) [33,34]	Speed (m/s) [35]	Speed-Density Model [24]	Height (m) (Net Height Plus the Thickness of Footwear) [33,34]
Adult men	49.4	1.30	SFPE	1.715
Adult women	45.7	1.24	SFPE	1.625
Elderly men	49.3	1.04	SFPE	1.685
Elderly women	45.9		SFPE	1.565

). Shoulder width was determined as the median of the maximum width observed among Chinese adult men and women, as well as Chinese elderly men and women [33,34]. An additional 50 mm was added to account for their heavy clothing, following the literature guidelines. Height encompassed the median height of Chinese adult men and women, as well as Chinese elderly individuals [33,34]. To accommodate footwear, heights for adult men, elderly men, and elderly women were increased by 25 mm, and by 45 mm for adult women, as recommended in the literature. Occupant speed in this study, following Pathfinder guidelines for expected maximum speeds [24], utilized data from Long Shi et al. [35], where speeds represent averages specific to each occupant type. Pathfinder’s built-in speed-density model [24] was employed for simulations. Figure 8 presents dimensions of wheelchairs and wheelchair seats [34], speed data for wheelchair patients [35], and details of the speed-density model used in simulations [24]. Small groups of occupants were combined, with one designated leader per group, MIGs followed their leaders during evacuation.

According to the interviews conducted, patients and their accompany persons were instructed to evacuate through Exit 1 or Exit 2 of the west evacuation stair in Pathfinder. In contrast, healthcare staff members were directed to utilize Exit 1, Exit 2, or Exit 3 of either the west or east evacuation stairs (Figure 4). The determination of specific evacuation exits for occupants in the simulation was guided by Pathfinder’s cost calculations [24]. The evacuation procedures were configured within Pathfinder, as illustrated in Figure 9.

To illustrate the effect of small groups on the evacuation, control group scenario 1.0 and scenario 2.0 were set. Scenario 1.0 did not set up small groups, and each occupant evacuated separately. In scenario 2.0, small groups were set up and followers needed to find the leader first and then follow the leader to evacuate. To avoid the effects of fire location, and smoke on evacuation, we assumed that the fire was not inside the AA, and there was no smoke.

2.4.2. Simulation

Simulations were performed using Pathfinder’s steering mode to output evacuation indicators such as evacuation time, evacuation distance, evacuation speed, and jam time of all occupants in scenarios 1.0 and 2.0 (

Table 3. Main evacuation indicators.

Index	Description
TET	Total evacuation time: Time required from the start of the evacuation simulation to the last occupant entering the exit.
OET	Occupant evacuation time: Time required for an occupant to enter the exit from the start of the evacuation simulation.
OTJT	Occupant total jam time: Total time for an occupant to move at a speed of less than 0.25 m/s throughout the evacuation.
OED	Occupant evacuation distance: Total distance traveled by an occupant during evacuation.
OES	Occupant evacuation speed: Average speed of movement of an occupant during evacuation.

For details about the Pathfinder software, see reference [29].

). By observing the Pathfinder dynamic simulation, the assembling time of MIGs in scenario 2.0 was counted.

2.5. Data Analysis

We used Excel to tabulate the output indicators of the simulation and analyzed the impact of small groups on the overall evacuation by examining changes in the indicators across scenarios 1.0 and 2.0. We computed total and average values of various simulation-derived indicators to characterize the overall evacuation process. Additionally, to address significant behavioral outliers, we analyzed indicator distributions at the median [36], 5th percentile, and 95th percentile levels [37] in the simulated output.

In SPSS26.0, scatter plots were generated for pairs of variables, including the distance between members, the assembling time, OET, OTJT, OED, and OES. We applied linear, quadratic, cubic, growth, logarithmic, exponential, logistic, and power functions for curve estimation for each pair of variables. Based on the significance level, R², and correlation coefficient of different models, we determined the correlation between variables and the degree of correlation. In cases where multiple functions showed significant correlation and the differences in R² were minimal, we selected the simplest function to summarize the relationship between the two variables.

3. Results

3.1. Interview

The interview results are as follows: (1) out of the 50 patients and their accompanying persons interviewed, there were 28 females and 22 males. Among them, 2 occupants were elderly, and the remaining 48 were middle-aged and young. The five healthcare staff members interviewed consisted of three females and two males, all of whom were middle-aged and young; (2) the 50 patients and their accompanying persons were unaware of the location of the east evacuation stair exit. Consequently, they indicated their intention to use only Exit 1 and Exit 2 of the west evacuation stair (Figure 4); and (3) healthcare staff members were familiar with the locations of both evacuation stairs and had the option to choose between Exits 1, 2, and 3 (Figure 4).

3.2. Simulation Starting Time and Total Number of Occupants

The change in the number of occupants counted by BORIS over time is depicted in Figure 10. The time of peak occupants was recorded at 14:37:54, with a total of 169 occupants in the AA. Healthcare staff members, such as doctors, accessed the exam rooms from staff corridors, which were not visible in the surveillance videos (Figure 4). We assumed one doctor per exam room, with 12 doctors in 12 exam rooms. In total, 6 of the 12 doctors were assumed to be male, 6 were assumed to be female, and the male and female doctors were distributed in the exam room at intervals. This made a total of 181 in the AA. Based on dynamic observations, one occupant from each of the three small groups exited the ESA through Door 1 before 14:37:54, and the other members were waiting in the primary waiting area south. The total number of evacuees was 184.

3.3. Small Group Data at a Strategic Level

3.3.1. Number and Size of Small Groups, Number of MIGs, and Their Proportion to the Total Number of Occupants

Since there was no video of exam rooms, we observed occupants entering and leaving each exam room in CCTV3 and CCTV4 during the period before and after 14:37:54, counted their numbers and recorded their small group information. The specific information is shown in

Table 4. Information of patients and their accompanying persons in exam rooms at 14:37:54.

Exam Room	Information	Number of Small Groups	Number of MIGs	Walking Ability
1	1 Adult man, 1 adult woman	1	2	Walking independently
2	1 Adult man, 2 adult women	1	3	Walking independently
3	1 Adult woman	0	0	Walking independently
4	1 Adult man, 1 elderly man	1	2	Walking independently
5	/	0	0	/
6	2 Adult men, 3 adult women	2 (Each included 1 adult man and 1 adult woman)	4	Walking independently
7	1 Adult man, 1 adult woman	1	2	Walking independently
8	2 Adult women	1	2	Walking independently
9	1 Adult woman	0	0	Walking independently
10	1 Adult man	0	0	Walking independently
11	/	0	0	/
12	2 Adult men, 1 adult woman	1	3	Walking independently

.

Combined with Figure 5, a total of 50 small groups consisting of 111 occupants were identified, with MIGs accounting for 60.33% of the total number of occupants. The size and number of small groups are detailed in

Table 5. Size and number of small groups.

The Size of Small Groups	Number of Small Groups	Number of MIGs	The Proportion of MIGs to the Total Number of Occupants (%)
2 occupants	40	80	43.48
3 occupants	9	27	14.67
4 occupants	1	4	2.17
total	50	111	60.33

. Notably, there were no small groups comprised of five occupants or more.

3.3.2. Initial Location and Distance between MIGs

We assumed that the patients in the exam rooms were all seated, while accompanying persons stood next to them. The initial location of the occupants in the AA is depicted in Figure 11a.

In Figure 11b, MIGs in the same small group are depicted with the same color. Most of the MIGs were in close proximity to each other. The seats separated the MIGs, and some of them were standing near the call screens for fear of missing the call, while others were located elsewhere in the primary waiting area.

Details of the distances between MIGs are shown in Figure 12 and

Table A1. Maximum distances between MIGs.

Maximum Distance (m)	Number of Groups (Cumulative)	Details	Number of MIGs (Cumulative)	Proportion to the Total Number of MIGs (%)
Adjacent	23	1 small group of 3 occupants, 22 small groups of 2 occupants, a total of 47 occupants	47	42.34
1–2	36	6 small groups of 3 occupants, 7 small groups of 2 occupants, a total of 32 occupants	79	71.17
2–3	39	2 small groups of 2 occupants, 1 small group of 4 occupants, a total of 8 occupants	87	78.38
4–5	40	1 small group of 3 occupants, a total of 3 occupants	90	81.08
5–6	42	2 small groups of 2 occupants, a total of 4 occupants	94	84.68
6–7	44	1 small group of 2 occupants, 1 small group of 3 occupants, a total of 5 occupants	99	89.19
8–9	45	1 small group of 2 occupants, a total of 2 occupants	101	90.99
12–13	46	1 small group of 2 occupants, a total of 2 occupants	103	92.79
16–17	47	1 small group of 2 occupants, a total of 2 occupants	105	94.59
17–18	48	1 small group of 2 occupants, a total of 2 occupants	107	96.40
21–22	49	1 small group of 2 occupants, a total of 2 occupants	109	98.20
22–23	50	1 small group of 2 occupants, a total of 2 occupants	111	100

. The maximum distance between MIGs within the same small group ranged from 1 m to 23 m.

3.4. Modeling and Simulation Results

3.4.1. The Effect of Small Groups on Overall Evacuation

As shown in Figure 13a, the TET of scenario 2.0 increased compared to that of scenario 1.0, and the evacuation efficiency of scenario 2.0 is lower than that of scenario 1.0. As shown in

Table 6. Effect of small groups on overall evacuation.

Occupant	Index	Scenario 1.0				Scenario 2.0				Average Value Increase Compared with Scenario 1.0
		P 5	P 50	P 95	Average	P 5	P 50	P 95	Average
AMsAA	TET (s)	57.26				140.26				83	144.95%
	OET (s)	5.47	27.00	52.09	27.91	6.73	31.69	85.80	35.53	7.62	27.30%
	OTJT (s)	0.23	1.28	29.25	4.65	0.23	4.56	54.56	11.85	7.20	154.84%
	OED (m)	3.67	20.73	41.42	20.67	3.36	19.23	38.27	19.28	−1.39	−6.72%
	OES (m/s)	0.19	0.83	1.10	0.78	0.16	0.61	1.05	0.61	−0.17	−21.79%
MIG	TET (s)	57.05				140.26				83.21	145.85%
	OET (s)	7.31	31.72	53.05	30.70	9.40	39.00	87.99	41.09	10.39	33.84%
	OTJT (s)	0.22	1.36	31.49	5.05	1.08	7.31	65.26	14.77	9.72	192.48%
	OED (m)	5.45	23.51	45.41	22.64	5.69	21.40	38.95	20.77	−1.87	−8.26%
	OES (m/s)	0.20	0.84	1.07	0.78	0.17	0.58	0.84	0.56	−0.22	−28.21%

P: The sign for the percentile. Like P 5, it means that 5% of the values are equal to and less than it, and 95% of the values are greater than it.

, compared with scenario 1.0, the TET, average OET, and average OTJT of scenario 2.0 increase by 144.95%, 27.30%, and 154.84%, respectively, and the average OED and average OES decrease by 6.72% and 21.79%, respectively. As shown in

Table 7. Effect of small groups on occupants.

Index	Changes in Scenario 2.0 Compared to Scenario 1.0	AMsAA	Proportion (%)	MIG	Proportion (%)
OET	Shorten	44	23.91	20	18.02
	Longer	107	58.15	70	63.06
	Invariant	33	17.93	21	18.92
OED	Shorten	104	56.53	76	68.47
	Longer	37	35.58	22	19.82
	Invariant	43	41.35	13	11.71
OES	Faster	25	13.59	11	9.91
	Slower	138	75.00	98	88.29
	Invariant	21	11.41	2	1.80
OTJT	Shorten	33	17.93	13	11.71
	Longer	133	72.28	91	81.98
	Invariant	18	9.78	7	6.31

Shorten or slower indicates a decrease of 5% or more in data, Longer or Faster indicates an increase of 5% or more, and Invariant indicates a change of less than 5% in data.

, 72.28% of occupants’ OTJT and 58.15% of occupants’ OET, 56.53% of occupants’ OED, and 75.00% of occupants’ OES decrease.

The Pathfinder dynamic simulation revealed that MIGs within the same small group needed to gather and evacuate together. In crowd evacuation, it was difficult for MIGs walking behind the crowd to find other members in front of the crowd by speeding up the pace. Instead, they had to progress forward with the crowd, searching for other members as they evacuated. MIGs at the front of the line either waited in the crowd for other members walking behind the crowd or attempted to move against the main evacuation flow to find them. In either case, these MIGs became an obstacle to the evacuation of others and created congestion, leading to an increase in TET, a slowdown in OES, and an increase in OTJT. In the common evacuation phase, the leader would slow down to wait for other MIGs, and MIGs with faster OES would reduce speed to accommodate those with slower OES, which also led to increased TET and slower OES.

Figure 14 illustrates that the curvature of the evacuation path in scenario 1.0 is higher than that in scenario 2.0. Individuals may have more trajectory changes than groups [38]. When occupants evacuated individually, they were subject to forces of varying magnitudes and directions from surrounding occupants. As a result, their movement paths tended to be more curved as they adjusted to these forces. Occupants in the same small group tended to act as a cohesive unit, even under the force of other surrounding occupants, their path changes were less significant, resulting in straighter evacuation paths and shorter evacuation distances.

As shown in Table 7, the OET and OTJT of fewer MIGs decrease, and the OED and OES increase. The reasons were as follows: (1) at the beginning of the evacuation, occupants in Scenario 1.0 lined up and formed congestion at the seats near Exit 2 (Figure A1), and a subsequent portion of occupants did not choose Exit 2. However, in Scenario 2.0, assembling behavior resulted in scattered congestion points, Exit 2 was not congested, and more occupants chose Exit 2 (

Table 8. Number of occupants arriving at each exit.

Exit	Scenario 1.0	Scenario 2.0
Exit 1	90	75
Exit 2	86	102
Exit 3	8	7

). Their OET and OTJT decreased, and their OES increased; (2) a portion of MIGs evacuated from Exit 2 in scenario 1.0, while they followed the leader to evacuate from Exit 1 instead in scenario 2.0, which reduced congestion, improved OES, and shortened OET, although the OED became longer.

3.4.2. The Effect of Small Groups on Evacuation of MIGs

As shown in Table 6, compared with scenario 1.0, the scenario 2.0 TET, average OET, and average OTJT of MIGs increase by 145.85%, 33.84%, and 192.48%; average OED and average OES decrease by 8.26% and 28.21%, respectively. As shown in Table 7, the OET of 63.06% of MIGs and the OTJT of 81.98% of MIGs increase, and the OED of 68.47% of MIGs and OES of 88.29% of MIGs decrease.

The distance between MIGs in the same small group affected their assembling behavior and then affected the overall evacuation. Given the limited number of small groups consisting of three and four occupants, our analysis primarily focused on examining the effect of the distance between MIGs within small groups of two occupants on evacuation.

Among the 18 small groups of two occupants with non-adjacent members, two failed to gather, because the leader would not be able to stop and wait for followers in such a high-density crowd but would be pushed forward by the crowd. The assembling time of the remaining 16 small groups is shown in

Table 9. Assembling time of 16 small groups.

Small Group Number	Distance between MIGs (m)	Assembling Time (s)	Small Group Number	Distance between MIGs (m)	Assembling Time (s)
1	12.15	0.9	9	81.13	10.8
2	10.57	0.9	10	124.51	17.3
3	12.24	1	11	50.26	18.5
4	18.88	1.4	12	61.07	18.9
5	13.48	1.7	13	173.83	21.9
6	19.64	2	14	168.56	22.2
7	19.32	2.6	15	223.50	37.7
8	28.18	3.2	16	214.19	120.1

. As shown in Figure 15, the assembling time of MIGs is divided into three stages. From 0 s to 11 s, 9 small groups completed aggregation; 11 s to 38 s, 6 small groups completed the aggregation, the TET of small groups that have completed aggregation within 11 s to 18 s is relatively long, which may because the maximum density of occupants occurred between the two rows of waiting seats in the primary waiting area south (Figure A1(f2)); and the last small group gathered for 121 s.

According to the scatter plots generated in SPSS (Figure S1), we carried out curve estimation analysis (Table S1). The results of the curve estimation analysis are presented in

Table 10. Variable correlation.

Dependent Variable Independent Variable	Distance between MIGs	Assembling Time	Increase in OET	Increase in OTJT	Increase in OED	Increase in OES
Distance between MIGs	1 **	0.740 **	0.538 **	0.412 *	0.569 **	Irrelevant
Assembling time	/	1 **	0.683 **	0.589 **	0.499 **	Irrelevant
Increase in OET	/	/	1 **	0.916 **	0.602 **	Irrelevant
Increase in OTJT	/	/	0.916 **	1 **	Irrelevant	−0.520 **
Increase in OED	/	/	0.602 **	Irrelevant	1 **	0.388 *
Increase in OES	/	/	134.308X2 + 21.823X + 9.581 **	−0.520 **	48.302X2 + 40.690X + 3.963 **	1 **

**: p < 0.01, *: 0.01 < p < 0.05.

, where the spacing of MIGs negatively affect the evacuation of MIGs. Specifically, when the increase in OES served as an independent variable, it exhibited a quadratic correlation with the increase in OET and OED. The other two variables demonstrated linear correlations.

A longer distance between MIGs resulted in extended assembling time and increased values for OTJT, OET, and OED. The correlation analysis revealed that the strongest correlation with the distance between MIGs was assembling time, with a correlation coefficient of 0.740, followed by increase in OED with a correlation coefficient of 0.569. The increase in assembling time directly led to higher values for OET and OTJT, with correlation coefficients of 0.683 and 0.589, respectively.

The increase in OET exhibited the strongest correlation with the increase in OTJT, with a correlation coefficient of 0.916. Additionally, apart from OET, the increase in OTJT showed significant correlation with assembling time, with a correlation coefficient of 0.589. The increase in OES demonstrated its strongest correlation with the increase in OTJT, with a correlation coefficient of −0.520, and it was not correlated with the increases in distance between MIGs, assembling time, or OET.

As indicated in Table 7, compared to scenario 1.0, 18.02% of the MIGs in scenario 2.0 have shorter OET, and 9.91% of the MIGs have faster OES. This suggested that a significant portion of MIGs successfully aggregated after many occupants had already completed their evacuation. Consequently, these MIGs could evacuate swiftly without being impeded by others. This meant that the assembling behavior of MIGs resulted in a sequential order of evacuation of all occupants, which can be proven by the fact that the evacuation order of MIGs in scenario 2.0 was more backward than that in scenario 1.0 (

Table A2. Evacuation order changes for MIGs with reduced evacuation times.

MIGs’ Name	Scenario 1.0	Scenario 2.0	Increase	MIGs’ Name	Scenario 1.0	Scenario 2.0	Increase
6	156	134	−22	69	140	111	−29
16	167	101	−66	75	174	156	−18
17	131	86	−45	106	183	158	−25
27	181	89	−92	86	142	87	−55
34	178	144	−34	124	125	84	−41
157	35	24	−11	137	166	136	−30
165	82	60	−22	140	170	115	−55
169	126	36	−90	117	96	90	−6
46	98	48	−50	145	135	112	−23
44	158	50	−108	111	177	140	−37
48	107	33	−74	112	180	138	−42
49	184	54	−130	195	104	67	−37
50	173	110	−63	67	165	128	−37
176	31	9	−22	175	86	114	28

).

4. Discussion

The main tasks undertaken, and the contributions are summarized as follows: (1) identified 50 small groups ranging from two to four members each, and distances between members spanning from 1 m to 23 m, which can help to set the initial scene for evacuation experiments and simulations. Employed BORIS and video observation methods to collect precise data, which was applicable for data collection in various building types; (2) configured small groups consisting of occupants with diverse walking abilities, including wheelchair patients and the old, and designed spatial environments integrating passage, waiting, and medical treatment spaces. These configurations enhanced the realism of the simulation; and (3) determined that small groups reduced overall evacuation efficiency, with the distance between members exerting the most significant negative impact on evacuation time, which can help emergency response managers to organize and control the evacuation.

4.1. The Data Collection on Small Groups

Despite ongoing efforts, there remains a notable dearth of universal and precise strategic level data.

Existing studies have made assumptions about the initial location of MIGs, specifying their gathering points [7]. Some studies have attempted to reconstruct the initial positions of occupants within small spaces by utilizing fixed seating arrangements [39,40,41,42]. However, these location data are primarily applicable to buildings such as schools, office spaces, and libraries, where fixed seating arrangements are common. They may not accurately reflect the dynamics of large public buildings like exhibition halls, commercial complexes, and hospitals, where occupants’ locations are constantly changing. Consequently, these data lack universality.

Our innovation lies in collecting location data of MIGs in a 450 m² specialist outpatient center, where the occupants’ locations change continuously fluctuate and quantifying it as the distance between MIGs. Unlike fixed location data, the distance between MIGs offers broad utility in setting up experiments and simulations.

Obtaining precise small group data presents significant challenges. Lei You et al. conducted on-site sampling to ascertain the percentage of MIGs and the size of small groups in different types of buildings [10]. Their findings revealed that in hospitals, the percentage of MIGs was 80.4%, while groups consisting of 1–3 occupants comprised 65.2–76.8% of occupants in most public spaces. Groups with more than three occupants accounted for 23.2–34.8%. However, sample surveys are inherently subject to random variation, leading to potential imprecision.

Our innovation involves leveraging surveillance videos capturing daily activities within a specialist outpatient center to gather accurate data on the number and size of small groups, the number of MIGs, and the location distribution of small group members. The percentage of MIGs in our study is 60.33%, which is lower than the statistic of Lei You et al. This is also due to the high sampling error.

4.2. The Scenario Setting on Small Group Evacuation

In the context of occupants’ setting, occupants with diverse mobility capabilities were grouped into small groups where the closeness among members was enhanced by pre-existing familial and friendship ties. Ma, Y. et al. examined evacuation scenarios involving small groups in high-rise buildings in 2017. However, all members of the small groups were undergraduate students aged 18–22, who were instructed to evacuate in pairs [9]. In the realm of space setting, we have integrated circulation, waiting, and medical treatment functionalities, integrated multiple spaces of varying sizes and shapes to create a complex scenario. Haghani, M. et al. investigated the evacuation of small groups in a room measuring 10.6 m multiple 10.6 m, where square obstacles were strategically placed. However, the space function and form were single, and the area was small [6].

Our innovation lies in the fact that through the real composition of small group members, we can more realistically set their attributes and simulate their assembling behavior. At the same time, the complex functions and shapes of building spaces may lead to the complexity of small group evacuation behavior. These made the simulation in this study more reflective of a realistic evacuation situation, and data output from the simulations and conclusions drawn from the analysis were more realistic and credible.

4.3. The Effect of Small Groups on Evacuation

4.3.1. Assembling Behavior

Simulation is used as a very effective and low-cost analysis method to restore evacuation scenarios. This study simulated the assembling behavior of MIGs during evacuation, where MIGs actively searched for other members or remained stationary. Consistent with previous research, this searching behavior led to congestion, thereby increasing the TET [19,38,43]. Additionally, MIGs waiting in place acted as obstacles to others’ evacuation, thereby slowing down the OES [44].

This study examined the assembling time of MIGs during evacuation and observed significant congestion between 11 s and 38 s, particularly in the pathway between two rows of waiting seats near the exit. In a previous study by X. Chen et al. in 2022, an experiment involving 200 occupants in a square site of 961 m² revealed that assembly behavior resulted in heightened confusion between 20 s and 40 s [19]. Compared to the studies of X. Chen, we had fewer small groups with longer distances between members (see ①–④ in

Table 11. Comparison between this study and existing studies.

Building Environment	Author	Initial Site Area (m2)	Perimeter/Area	Initial Density (pp/m2)	Occupant Information	Proportion of MIGs to Total Occupant (%)	Number of Small Group Members	MIG Location	Evacuation Indicators
									Time It Takes MIGs to Assemble	TET		Average OES
										Time (s)	Increase (%)	Speed (m/s)	Decrease (%)
Real and complex building environment	This study	450 ①	0.65 ⑤	0.41 ⑦	Patients, accompanying persons, and doctors	0	2–4	Adjacent and dispersed ②	Most MIGs assembled within 49 s, accounting for about 35% of the total evacuation time	57.26	/	0.78	/
						60.33 ⑲				140.26	144.9	0.61	21.79
Simple experimental environment set up temporarily	J. Ren [7]	150 ⑨	0.333 ⑥	0.4 ⑧	Experiment volunteers	0	2, 4, 6, 8	Random	Accounting for 40–50%of the total evacuation time	/	/	0.82	/
						10 ⑳				About 19	/	0.56	31.7
						20 ⑳				About 22	About 16
						30 ⑳				About 25	About 32
						40 ⑳				About 25	About 32
Simple experimental environment set up temporarily	Milad Haghani [6]	112.36 ⑩	0.377	0.57	Experiment volunteers	0, 100	1	Adjacent ⑭	/	About 14	/	/	/
							2			About 16	About 14
							3			About 16	About 14
							4			About 15	About 7
Hypothetical but simple computer simulation environment	X. Chen [19]	961 ③	0.13	0.21	Agent	0	2	Random ④	The crowd was the most chaotic at 20–40 s, likely due to MIGs assembling	About 100	/	/	/
						20				About 150	About 50
						40				About 350	About 250
						60				About 500	About 400
Hypothetical but simple computer simulation environment	L. You [10]	163.2 ⑪	0.31	3.68	Agent	0	2–3	Adjacent ⑮	/	About 116	/	/	/
						60				About 120	About 3
						70				About 130	About 12
Hypothetical but simple computer simulation environment	Q. Zhang [11]	1132	0.22	0.53	Agent	0	2	Adjacent ⑯	/	About 140	/	/	/
						20				About 150	About 7
						40				About 140	About 0
						60				About 155	About 10
						80				About 175	About 25
						100				About 140	About 0
Hypothetical but simple computer simulation environment	L. Lu [17]	400 ⑫	0.2	1.88	Agent	40	1	Adjacent ⑰	/	125.3	/	/	/
							2			150.6	20.19
							3			157.2	25.46
Hypothetical but simple computer simulation environment	Yakup Turgut [16]	100 ⑬	0.4	1	Agent	0	2–5	Random	/	About 42	/	/	/
						78				About 49	16.67
Real but simple building environment	Z. Pan [21]	1950	1.54	0.53	Agent	0	2–4	Adjacent ⑱	/	About 2100	/	/	/
						10				About 2200	About 5
						20				About 2300	About 10
						30				About 2400	About 14
						40				About 2300	About 10
						50				About 2400	About 14
						60				About 2350	About 12
						70				About 2300	About 10
						80				About 2350	About 12
						90				About 2400	About 14
						100				About 2500	About 20

①–⑳ are markers for auxiliary reading, making it easy to quickly find relevant data in Table 11 while reading.

), and small groups had less time to complete the aggregation, so the more chaotic time will be further ahead. Since congestion is more likely to occur near exits, increasing the open space near exits is one of the effective measures to improve evacuation efficiency. This can be achieved by minimizing obstacles such as furniture near evacuation exits.

We found that longer distances between MIGs resulted in longer assembling times. In this study, we simulated the assembling behavior of 24 small groups comprising a total of 57 occupants, including groups of 2, 3, or 4 members, within a specialist outpatient center of approximately 450 m². The last small group took 121 s to assemble, accounting for 86.3% of the TET. J. Ren et al. studied experiments with a total of 60 occupants in a rectangular field with an area of 150 m² and concluded that small groups of 2, 3, or 4 occupants consistently found each other in 40–50% of the TET [7]. Our study observed a higher percentage of assembling time compared to J. Ren’s, likely due to the greater complexity of our building spaces (see ⑤ and ⑥ in Table 11), higher occupant density (see ⑦ and ⑧ in Table 11), longer distances between MIGs within the same small groups (see ① and ⑨ in Table 11), and increased cohesion among occupants.

4.3.2. The Effect of Small Groups on Overall Evacuation

Our study supported the conclusion that small groups have a negative effect on overall evacuation [9,10,11,12,16,19,21].

Consistent with existing studies, this study concluded that small groups increased TET, but the increase was 144.95%, higher than most of the existing studies. Existing studies adjusted the number of MIGs in sites of different sizes, and when the proportion of MIGs to the total number of occupants was about 60%, the increase in TET was about 3% [10], 10% [11], 12% [21], 16.67% [16], and 400% [19]. When the number of MIGs in each small group was between two and four, the increase in TET was about 14% [6] and 20% to 30% [12]. In our study, the site area was larger than those in most existing studies (see ① and ⑨–⑬ in Table 11), and the small group members were more dispersed (see ② and ⑭–⑱ in Table 11). Therefore, we believe that the possible reason is that the larger the site area, the more complex the building spaces, or the larger the distance between the MIGs within the same small group, the larger the TET increase, and conversely, the smaller the TET increase.

W. Xie et al. and C. von Krüchten et al. suggested that small group evacuation behaviors reduced the TET when the number of MIGs in each small group was greater than or equal to five [14,22]. Our study was unable to validate this idea because there were no small groups of five or more MIGs in our research.

Consistent with existing studies, this study concluded that small groups decreased OES, but the decrease was 21.79%, lower than that reported in existing studies. Existing studies concluded that small groups reduced OES by 31.7% when the proportion of MIGs to the total number of occupants ranged from 10% to 40% [7]. The OES of MIGs decreased as the number of MIGs increased [45]. Although the number of MIGs in our study was larger (see ⑲ and ⑳ in Table 11), the site area in our study was larger (see ① and ⑨ in Table 11) and the building spaces were more complex (see ⑤ and ⑥ in Table 11) than those in existing studies. We believe that the possible reason is that the larger the site area or the more complex the building spaces, the lower the OES drop.

4.3.3. The Effect of Small Groups on Evacuation of MIGs

Through curve estimation analysis, our study revealed that an increase in the distance between MIGs within the same small group correlates with longer assembling time, OET, OTJT, and OED. So, we believe that reducing the distance between MIGs can improve evacuation efficiency. One such strategy involves the installation of additional call screens to mitigate the dispersed distribution of MIGs. Additionally, optimizing the arrangement of waiting seats to accommodate small groups of two to four occupants, thereby allowing MIGs within the same small group to sit together and shorten the spacing, could be beneficial. Moreover, the development of effective evacuation strategies is paramount. This entails organizing occupants in a logical order for evacuation, supplemented by clear and efficient guidance from healthcare staff members.

Nevertheless, owing to the constraints of the Pathfinder simulation, it is imperative to construct separate simulation models for future research. This approach should meticulously account for the randomization of simulation, as well as the necessity to validate multiple simulation outcomes.

5. Conclusions

In this study, small group data at a strategic level was collected and the effect of small groups on evacuation was investigated through simulation, leading to the following conclusions:

• Small group data at a strategic level was obtained. Small group members accounted for 60.3% of the total number of occupants, and all small groups consisted of two to four occupants. Most members were adjacent to each other, with the maximum distance between MIGs within the same small group varying from 1 m to 23 m. These data can be applied to the setup of evacuation simulation scenarios and experiments in other studies.
• Small groups had a negative impact on overall evacuation. It increased the total evacuation time and total jam time, while decreasing the average evacuation speed of occupants.
• The greater the distance between members, the longer the assembling time, and the greater the increase in evacuation time, total jam time, and evacuation distance. The greater the increase in total congestion time, the greater the decrease in evacuation speed.

In terms of limitations, we set the speed of occupants in Pathfinder as the free movement speed of healthy people rather than the emergency evacuation speed of patients. Although it did not affect our research results, the speed of patients should be low in the actual evacuation process and needs further study. Meanwhile, we did not provide comparison between experimental results and the simulation process. Therefore, in future studies, we can extract the movement speeds of occupants with various walking abilities from the surveillance videos to refine the evacuation study and conduct field experiments to further validate the model. At the same time, future research can also focus on collecting small group data from other types of buildings, and further exploration is necessary to assess how the distance between members of small groups consisting of three or more occupants influences evacuation dynamics.