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Dieser Artikel geht auf den kritischen, aber oft übersehenen Aspekt der Fußgängerdynamik ein: die Auswirkungen von Rollstuhlfahrern auf die Einfahrtszeiten. Aufbauend auf früheren Arbeiten von Rita Fahy und Guylène Proulx führen die Autoren eine systematische Literaturrecherche und Metaanalyse durch, um zu beurteilen, wie die Anwesenheit von Rollstuhlfahrern die Zeit beeinflusst, die Fußgänger brauchen, um Engpässe zu beseitigen. Die Studie unterstreicht die Notwendigkeit einer inklusiveren Forschung, die unterschiedliche Mobilitätsprofile berücksichtigt, da die traditionellen Austrittszeiten, die anhand homogener Stichproben gemessen werden, die realen Szenarien möglicherweise nicht genau wiedergeben. Die Autoren gehen sorgfältig auf methodische Herausforderungen ein, wie etwa die Standardisierung von Daten aus verschiedenen Versuchsaufbauten und die Berücksichtigung von Unterschieden im Studiendesign. Die Ergebnisse zeigen eine signifikante Zunahme der Austrittszeiten, wenn Rollstuhlfahrer anwesend sind, was die Notwendigkeit aufsichtsrechtlicher Dokumente und Simulationswerkzeuge zur Berücksichtigung der Heterogenität der Menge unterstreicht. Der Artikel betont auch die Bedeutung offener Daten für Reproduzierbarkeit und Transparenz in der wissenschaftlichen Forschung und setzt einen Maßstab für zukünftige Studien zur Fußgängerdynamik.
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Diese Zusammenfassung des Fachinhalts wurde mit Hilfe von KI generiert.
Abstract
Egress time, or how long it takes a pedestrian crowd to pass through a bottleneck during egress, is a crucial metric for safety and capacity considerations. It has been suggested that heterogeneity in the composition of pedestrian crowds - such as variability in mobility, age, or the presence of social groups - could affect egress times. However, only a few empirical studies have addressed this issue. To solidify insights from the existing empirical evidence, we present a systematic literature review and meta-analysis to quantify if the presence of wheelchair users in pedestrian crowds increases egress times. We identified nine studies, all based on controlled experiments, that used a comparable layout in which groups of participants had to move through a bottleneck and compared conditions with and without wheelchair users present. The meta-analysis confirmed the findings from the individual studies. The difference in egress time between conditions with wheelchair users present and those without was close to three standard deviations, indicating a strong effect. We found no evidence for publication bias, such as the under-reporting of non-significant findings. Our work presents a quantitative basis for adjusting expected egress times depending on occupant characteristics. It suggests that the behavioural consequences of crowd heterogeneity are safety relevant and require further investigation.
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1 Introduction
The present paper builds upon the previous work of Rita Fahy and Guylène Proulx, who spearheaded the creation of aggregated databases on pedestrian evacuation movement [1]. The field of pedestrian dynamics is concerned with how people move together in groups or even crowds. The expansion and maturation of this field over the last decade have been documented by continuous growth in scientific publications and available datasets (e.g., see [2, 3]). Research in pedestrian dynamics often responds to societal needs, such as the design and management of safe, efficient, and comfortable environments that require large numbers of people to move efficiently and safely.
One of the main quantities of interest in pedestrian dynamics is egress time, which is the time it takes a pedestrian crowd to clear a bottleneck, for example, when leaving a confined space.1 It is used, among other things, to formulate safety requirements for buildings and vehicles [5]. When measured experimentally in representative building blocks of pedestrian facilities, such as corridors [6, 7] or narrow exits (bottlenecks) [8], it can also be used as a proxy for the flow of people, or, by extension, the capacity of facilities. Many pedestrian dynamics experiments measure egress times from fairly homogeneous samples, primarily comprising young adults without any disabilities or mobility impairments [9, 10]. Therefore, these egress times are likely not representative of more heterogeneous populations and may provide unrealistic bench-marking values for egress times. Several factors that increase crowd heterogeneity have been hypothesised to affect egress times. These include social groups (e.g., family or friends moving together) [11‐16], age (e.g., presence of children or older adults) [17‐19], and physical or psychological disabilities of pedestrians [20, 21]. Demographic trends imply that these causes for crowd heterogeneity are relevant and will likely increase in prevalence [22].
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The direct link between research in pedestrian dynamics and real-world applications drives a requirement for robust and generally valid insights from empirical work, including controlled experiments, to inform regulatory documents or computer simulation tools (e.g., [23‐25]). A commonly adopted framework for pooling evidence from a collection of published work is systematic literature reviews combined with meta-analyses. Critically, meta-analyses weigh available empirical evidence based on the robustness of individual study findings [26‐29]. Studies with larger sample sizes and more runs are typically considered more reliable and given more weight than those with less data. This approach separates true effects from fluctuations more likely to occur in individual studies with fewer participants and runs. While meta-analyses have been employed in transportation research to understand the movement of individual pedestrians [30], their first use in pedestrian dynamics is only very recent. Hu and Bode [31] focused on social groups in unidirectional flow and reconciled contradictory findings, concluding that given the present evidence, it was not possible to determine a clear effect of social groups on egress times. Following on from this work, we investigate whether the presence of people with reduced mobility in a crowd impacts egress time. Reduced mobility covers a broad range of mobility profiles, ranging from people with temporary impairments to those who rely on mobility aids such as canes or wheelchairs for locomotion.
Wheelchair users are a group of people with reduced mobility that has been studied extensively within the pedestrian dynamics literature [20, 32‐34]. Wheelchair users differ from pedestrians in a range of parameters, such as typical space requirements [35], movement speed [1], acceleration [36], height [37], and perceived vulnerability [38‐41]. These individual differences may have cascading effects on macroscopic descriptors of pedestrian dynamics, such as the egress time. In addition, wheelchair users constitute an underserved population, particularly in an evacuation context [42‐46]. For example, Fahy and Proulx report on how wheelchair users experienced the evacuation from the World Trade Center during the events of September 11, 2001 [47]. For these reasons, we explore the effects the presence of wheelchair users in pedestrian crowds has on egress times in the absence of ramps or stairs using a meta-analysis.
The challenges of conducting a meta-analysis on experimentally measured aspects of pedestrian dynamics have been discussed previously [31], and they relate to the broader methodological considerations of performing a statistical analysis on pedestrian dynamics data [48]. To contextualise the work in this contribution, it is worthwhile to revisit the key points. While a substantial body of work reports similar quantities from pedestrian crowd experiments, such as egress times or flows, different studies rarely use the same experimental settings. For example, there are often differences between samples (e.g., age and number of participants included), or in the geometry of the study area (e.g., exit or corridor). This means that measured quantities typically cannot be compared directly across studies. Quantities thus need to be standardised to make them usable in a meta-analysis. Another collection of issues arises from the study of quantities that describe the movement of crowds. Logistic challenges and costs mean that assembling large groups of volunteers for scientific experiments is not easy. This has several implications. First, experimental runs are typically not repeated many times under identical conditions leading to small sample sizes (in the sense that only a few data points are generated per condition).2 This implies a higher expected variability in findings and reduces statistical power, thus limiting the reliability with which differences between conditions can be detected. Second, the same group of participants is often re-used to obtain several samples under the same and changed experimental conditions. From a statistical perspective, this raises questions about the independence of observations obtained from such experiments. For example, the effects of run order, learning, or fatigue can potentially influence the results. We refer to the more detailed discussion on this elsewhere [31, 48]. The combination of small sample sizes and difficult-to-compare studies demonstrates the need for meta-analyses that integrate information across studies and can provide statistically more robust insights in pedestrian dynamics research.
In the following sections, we describe our methodology and findings for a systematic literature review and a meta-analysis on the effect wheelchair users have on the egress time of pedestrian crowds. The main goals of our contribution are to provide an up-to-date survey of the literature, to integrate evidence from different studies, and to contribute to the discussion on the extent to which crowd heterogeneity needs to be considered in egress scenarios.
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2 Methods
2.1 Literature Search
Publications to be used as the foundation for the meta-analysis were retrieved based on the authors’ knowledge and a systematic search. A preliminary search was first performed on Google Scholar using the keywords “pedestrian movement wheelchair users” to identify the following relevant recurring keywords in the literature: “pedestrian* movement”, “crowd*” “dynamics”, “wheelchair”, “disabilit*”, “pedestrian”, and “bottleneck”. A search using a combination of these keywords was performed in the following databases and journals: Scopus, Web of Science, Google Scholar, ScienceDirect, Canadian Journal of Disability Studies, Journal of Accessibility and Design for All, Disability and Society, Disability Studies Quarterly, Review of Disability Studies, and Journal of Disability Policy Studies. These journals were included in the search as they cover accessibility research and could contain relevant studies involving wheelchair users. The search in the databases and journals was limited to peer-reviewed journal articles and conference proceedings (i.e., excluded gray literature). In addition, papers covering the following topics were excluded: (1) numerical modeling or simulation (no empirical data), (2) transportation studies (e.g., examining travel costs of wheelchair vs. non-wheelchair users), (3) urban planning (e.g., examining traffic flow on sidewalks, designing smart cities), (4) pedestrian detection in crowds (e.g., for crowd control/crowd safety), and (5) pedestrian-robot coordination (e.g., robotic/automated wheelchairs).
The papers included in the meta-analysis were selected based on the following criteria: (1) original studies with controlled experiments examining the pedestrian movement of wheelchair and non-wheelchair users through a bottleneck published in English in a peer-reviewed journal or conference proceedings, (2) included an experimental condition with wheelchair users, (3) included an internal control condition (individuals without any disabilities) or an equivalent external control condition could be found, (4) considered only one directional movement (no two directional movement), and (5) data were available or could be extracted.
The search was performed on November 28, 2023 and December 1, 2023. The initial search yielded over 60,000 results across all databases and journals. To manage the volume of results, only the first 20 pages of ScienceDirect (over 2000 results) and the first 10 pages of Google Scholar were were considered (over 59,000 results). The titles and abstracts of the retrieved papers were then screened for relevance. The reference lists of the retrieved papers were also consulted for potentially relevant papers. Thirty-three papers were identified during the title and abstract screening. We consulted the full text of these papers and decided whether to include them in the meta-analysis (see criteria above). The meta-analysis included a total of seven publications (see Fig. 1 for a process chart of the literature selection and the supplementary material for a detailed overview of the literature search results).
Fig. 1
Process flow chart of literature search strategy and results. The review of 33 potential publications yielded nine data sets (from seven peer-reviewed publications) for consideration in the meta-analysis. The discrepancy between the records identified as potentially eligible studies and the screened records is due to treating separate studies published within a single publication as two distinct records. Only the first 10 and 20 pages of search results were considered for Google Scholar and Science Direct search results
We extracted data on egress times from the publications meeting our inclusion criteria for further analysis. In the following, we distinguish between studies and publications. A study consists of a collection of experimental runs in which human participants walk through a given physical setup. In most cases, a study could be generated from a single publication. In some cases, however, runs with and without wheelchair users but otherwise comparable conditions were published by the same group of authors across several papers and could be merged into one study. Each study included at least two, typically more, experimental runs for each of the two main experimental conditions of interest: egress in the absence and presence of one or more wheelchair users. In some publications, additional experimental conditions were tested - such as varying the width of exits.
An overview of the data extraction process is shown in Fig. 2. The first consideration before data extraction was determining whether the full trajectory data were available or could be obtained. If the trajectory data were unavailable, curves for the number of participants who had completed egress over time were obtained manually from figures in publications by three independent raters (to reduce errors in reading data from figures manually). The average binned in the x-direction from the three raters was then used for further analysis. Data was extracted from figures using WebPlotDigitizer.3 If trajectories were available, the same curves could be obtained directly by recording the time points when participants exited the experimental setup by crossing a reference line defined in the associated publications.
The second consideration when extracting data was the number of participants in experimental runs, given that these varied within studies (e.g., due to some participants taking a break, or for logistical reasons when dividing a larger participant pool up into smaller groups). To account for this, the egress number over time curves were truncated at the lowest participant number across experimental runs for a given study. Throughout, participants in wheelchairs were included in these counts.
The third aspect requiring consideration when extracting data was to account for transient dynamics at the start and end of experimental runs. For example, in some experiments, the movement behaviour differed substantially at the start and end of experimental runs when individuals sought to pass through an exit as quickly as possible initially, to avoid having to wait, or when they deliberately walked slowly at the end of experiments to avoid standing in a queue. To reduce the effect of such behaviours on the extracted egress times, we calculated the time points when 5% and 95% of participants in the truncated egress number over time curves had left the study area. Subtracting the former from the latter yielded estimates for the egress time that could be compared across experimental runs within a study.
Further details on how studies were defined and how data on egress times were extracted can be found in Sect. 3 and in the supplementary material. The extracted data comprising egress times for each experimental run is also openly available (see data availability statement).
Fig. 2
Left: Workflow of publication selection and data preparation process. Data was either calculated using published trajectories or extracted from figures. Right: Illustration of the data extraction process. To minimise errors, three raters extracted data from figures (i.e., image files) independently. The average of the three raters along the x-axis was used for further calculations. Shaded areas indicate data included in the meta-analysis. Red indicates treatment conditions (i.e., data from conditions with wheelchair users), and blue control conditions (i.e., without wheelchair users)
Data extracted from the studies satisfying the inclusion criteria needed further preparation to ensure meaningful comparison across studies. We closely followed previously established methods for conducting meta-analyses on pedestrian egress times [31]. The two main sources of variability that needed accounting for related to (1) additional experimental conditions and (2) differences across studies. Each of these will now be discussed in turn.
Our investigation was designed to compare the difference in egress time across two experimental conditions: when one or more wheelchairs are or are not present in the egress of pedestrians. Following convention, we refer to these as treatment (i.e., pedestrian groups with wheelchair users present) and control (i.e., without wheelchair users) conditions. However, some of the studies included in our analysis tested additional experimental conditions, e.g., by varying corridor widths, sometimes only recording data for one run for a given combination of experimental conditions. We thus removed the average variability caused by additional experimental conditions to ensure data from all runs could be used. For the example of different corridor widths, the difference in mean egress time across widths was subtracted from each recorded egress time for the narrower corridor. This resulted in the mean egress times being the same for all corridor widths. Differences in egress times due to the presence/absence of wheelchairs were not affected by shifting mean egress times in this way. The data preparation for each study included in our analysis is detailed in supplementary material.
The studies also varied substantially in terms of the physical experimental setup (e.g., corridor versus bottleneck), the number of participants, and how wheelchair users were introduced into the egress scenario. This implied that it was not possible to quantitatively compare egress times across studies. For example, for the same number of participants, egress times through a narrow bottleneck should be higher compared to egress times through a wide corridor of uniform width. Following Hu and Bode [31], we thus used standardised egress times in our statistical analysis. Our standardisation was performed separately for each study by dividing the mean (and standard deviations) of egress times by the average egress time for the control condition when no wheelchairs are present. This meant that in our statistical analysis, the mean egress time for the condition without wheelchairs was equal to one for all studies.
This data preparation approach was necessary to compare results across studies. However, we made assumptions that had implications for how we interpreted the findings. Our approach to dealing with additional experimental conditions assumed that these conditions did not systematically influence egress in the presence of wheelchairs. An extreme case in which this assumption does not hold would be a reduction in exit width up to the point when a wheelchair can no longer (or only with great difficulty) pass through the exit. In this situation, the exit width condition would likely substantially influence the difference in egress times across the conditions with and without wheelchairs present. Based on the physical setup of experiments and the nature of the additional conditions investigated, we deemed our assumption to be reasonable. However, our approach to standardising egress times for studies means that we cannot report the estimated quantitative effect of introducing wheelchairs into pedestrian egress. Instead, we can only report relative differences, namely increases or decreases in aggregated egress times.
2.4 Statistical Analysis
Our statistical analysis followed a previously established methodology for conducting a meta-analysis on pedestrian egress times [31], making use of existing methodological recommendations [26]. We used the R programming environment, version 4.3.1 [49], and the R packages ‘esc’ [50], ‘meta’ [51], ‘metafor’ [52], and ‘dmetar’ [53].
From the standardised mean egress times, we computed Hedges’ g scores as our measure for effect sizes, that is the difference in mean across treatments, divided by the pooled and weighted standard deviation [27]. This required, for each study, the mean and standard deviations of egress times across all replicate experimental runs in each of the two treatments (with and without wheelchairs), as well as the number of experimental runs in each treatment. These scores are particularly suited for meta-analysis with few studies and can be interpreted as the number of standard deviations by which the means of the treatments differ [27]. The information in the Hedges’ g scores from all studies and their associated standard errors was then assimilated using a fixed-effect model for meta-analysis using the generic inverse variance method [29], yielding an estimate and confidence interval for the pooled effect size across all studies [28]. This statistical model only requires the estimation of a single quantity, the mean effect size. Like all statistical models, this fixed-effect model for meta-analysis makes distributional assumptions, and we checked if these held qualitatively by comparing the quantiles for standardized effect estimates against the expected theoretical quantiles (following Ref. [54]). The low number of studies included in our meta-analysis, combined with the low number of replicate experimental runs for some studies, could raise questions about the robustness of our estimates and the validity of the distributional assumptions in our statistical analysis. We acknowledge these limitations and provide all data necessary for repeating this meta-analysis with the inclusion of additional data or using alternative statistical methods.
It is important to check if the distribution of effect sizes across studies can be meaningfully represented using a pooled effect size. In particular, for meta-analyses that include a low number of studies, such as ours, concerns that outliers could influence the overall result needed to be addressed. To do so, we performed a leave-one-out assessment for the pooled effect size by repeating our meta-analysis with one of the included studies in turn removed from the analysis. Quantitative measures for the heterogeneity of effect sizes across studies have been developed, including Cochran’s Q, Higgin’s and Thompson’s \(I^2\), and Tau-squared (\(\tau ^2\)) [26]. However, these measures can be sensitive to the number of studies, and the number of replicates for each study, or can be difficult to interpret [26]. As such, we report the above-mentioned measures for completeness, and for comparison to other meta-analyses, but refrain from discussing their values in detail.
Pooling information from several studies in a meta-analysis also provides an opportunity to investigate if the distribution of reported effect sizes meets our expectations, or if there is evidence for bias in publications. A commonly referred to example in the literature is the possibility of experiments with inconclusive results or those with very small numbers of replicates being under-reported in published work [55]. If such studies with low effect sizes were not accounted for in the meta-analysis, the pooled effect size could be inflated (biased) compared to the true effect size. To explore the possibility of publication bias, we use the commonly adopted funnel plot method, where effect size is plotted against the standard error for the effect in studies. Smaller studies with fewer replicates have larger standard errors, and we thus expect the scatter of observed effect sizes to decrease symmetrically with decreasing standard error (increasing study size) in a funnel-like shape. In the absence of publication bias, reported effect sizes should fall symmetrically within this funnel shape.
3 Results
3.1 Selected Literature
Nine studies were defined for the purpose of the meta-analysis. These studies were extracted from seven publications. In some cases it was necessary to define control conditions from additional publications, for example, when data from test and control conditions were published in different sources. Most studies considered describe controlled experiments that were carried out in the northern hemisphere. Five of the publications originated from the People’s Republic of China and one each from Germany and Canada. These studies are described in more detail below, and Fig. 1 shows how the nine studies were identified (see Sect. 2.1 for more details).
In general, all selected studies focus on understanding pedestrian flow dynamics to improve evacuation strategies and safety. Their shared objective is to analyze the impact of wheelchair users within heterogeneous crowds, consisting of both pedestrians and wheelchair users. Each study employs controlled environments to simulate real-world evacuation scenarios, thereby generating measures such as traffic efficiency (flow rate), density, and speed.
Although all studies were conducted under well-controlled conditions, they exhibit notable differences in experimental design. These differences include variations in bottleneck widths, funnel-shaped angles, corridor designs, and proportion of wheelchair users, among others.
The following paragraphs provide summaries of each study, highlighting their methodologies and findings. Additionally, Table 1 offers a comparative presentation of the most important characteristics, allowing for a clear and concise overview of the key aspects of each study. More information about the transformation from original (raw) data into input data for the meta-analysis is presented in the supplementary material.
Fu et al. [56], referred to as fu2022, aimed to understand the impact of individuals with disabilities on evacuation dynamics. They conducted experiments (in total nine experimental runs) using a bottleneck setup with varying group sizes (total numbers of evacuees of \(n=[20,\, 40,\, 60]\)) and different ratios (0, 5, and 10%) of wheelchair users present. The authors found that the presence of individuals with disabilities significantly slowed down the evacuation process. The study highlighted the need to consider diverse mobility profiles in engineering and safety planning to ensure accurate predictions and effective evacuation strategies.
Geoerg et al. [34, 57‐59] investigated the dynamics of pedestrian movement in the presence of wheelchair users (and other types of disabilities). They focused on the effect of various impairments on crowd movement and evacuation efficiency. We defined two studies from this set of publications, referred to as geoerg2019cor and geoerg2019bot. This distinction was made because the publications reported on two experiments with substantially different physical geometries (bottleneck and corridor). Both geometries varied in width (\(w=[{0.9}, {1.0}, {1.1}, {1.1}]\, {\text {m}}\)) and the experiments were performed with an approximately constant ratio of participants using wheelchairs of different propulsion types (\(n=5\), ca. 6%) and without wheelchair users (\(n=75)\). Each condition was repeated once, resulting in a total of eight experimental runs for each study. Additionally, an internal control study without wheelchair users was conducted with similar characteristics (width, number of repetitions, similar group size). The studies suggest that wheelchair users’ speed affects the overall movement speed and flow rate, even at low-density regimes. It is concluded that different types of impairments, such as reduced mobility or visual impairments, significantly impact egress times and movement patterns.
You et al. [60], referred to as you2023, performed a study on understanding how different impairments influence the evacuation dynamics of crowds. They used a straight corridor setup and varied the width of the entrance and exit to achieve different density regimes. The participant group consisted of 32 individuals without disabilities and six participants using wheelchairs (21%). No repetitions of the experimental runs were conducted, and no internal control study was performed. The authors found that impairments, such as mobility and visual disabilities, significantly affect flow patterns and egress times. The study highlights the necessity of incorporating diverse mobility needs in evacuation planning to ensure efficient and safe evacuations for all individuals. Since an internal control group was not used in this study, another study (Hu et al. [16]) with similar boundary conditions was used as a control group for the comparison. Hu et al. [16] examined how the presence of social groups influences pedestrian dynamics within unidirectional flow conditions. Controlled experiments with different proportions of social groups and individuals, varying the pedestrian density, were conducted. The study found that while social groups slightly affect the speed-density relationship, the effect is minimal and often overshadowed by overall variability. The authors suggest that the effect of social groups may be small when considered at a macroscopic level under non-emergency conditions but could still be important at a more detailed level involving operational behaviours.
Pan et al. [33] investigated how the consideration of wheelchair users affects pedestrian flow through (funnel-shaped) bottlenecks (referred to as pan2020). They performed experiments using symmetric bottleneck setups with different opening angles (\(\alpha = [{0},\, {15},\, {30},\, {45}]^{\circ }\)). Additionally, four experimental runs with varying numbers of wheelchair users (\(n= [0,\, 1,\, 2,\, 3]\)) were conducted for each angle condition, resulting in a total of 16 experimental runs. No repetitions of runs were performed, and an internal control study was conducted. The results showed that the presence of wheelchair users reduced the overall flow rate and increased the time required for all pedestrians to pass through the bottleneck.
Pan et al. [36], referred to as pan021, aimed to create a comprehensive fundamental diagram that incorporates the movement characteristics of both pedestrians without disabilities and wheelchair users in straight corridors (which is a specific form of a bottleneck). They kept the length and width of the corridor constant and controlled the density conditions by varying the entrance and exit widths. For the meta-analysis, four experimental runs (without repetitions) with wheelchair users were considered. Internal control experiments with the same dimensions but without the participation of wheelchair users were also conducted. The findings demonstrated that wheelchair users significantly alter the flow rate and speed dynamics.
He et al. [61], referred to as he2024, examined the movement characteristics of heterogeneous crowds at bottlenecks and included individuals with simulated disabilities in their sample. The study considered three main variables: (1) individual mobility characteristics (individuals without assistive devices, individuals using crutches, and wheelchairs users), (2) bottleneck width (1.2, 1.6, and 2.0 m), and (3) the ratio of individuals with simulated disabilities in the crowd (0, 5, and 10%). Each condition was repeated three times, with participants’ starting positions varying across runs. The authors found that participants using crutches exhibited more frequent detours compared to other groups. Further, an increase in bottleneck width and a decrease in the proportion of individuals with disabilities led to higher flow rates. The study concluded that bottleneck width was the primary factor affecting passing efficiency upstream, whereas the presence and characteristics of individuals with simulated disabilities played a greater role inside and downstream of the bottleneck.
Geoerg et al. [62] conducted laboratory experiments with 25 participants to understand the impact of mobility differences on crowd dynamics at bottlenecks. From this publication, we defined two studies, referred to as geoerg2023base and geoerg2023urgent. This distinction was made because the publication reported on two experiments with substantially different instructions: participants were instructed to complete the task either at a leisurely or at an urgent pace. Participants completed 30 experimental runs in each condition, and an internal control study without the participation of wheelchair users, with a comparable number of repetitions, was conducted. The authors found that individuals using wheelchairs and those carrying luggage required significantly more time to pass through bottlenecks compared to those without additional equipment. This also affected the individuals following them, resulting in slower overall times to clear the bottleneck in both the wheelchair and luggage conditions.
Table 1
Detailed study characteristics
Reference
Type of studya
No. of repetitions
Dependent variablesb
Independent variablesc
Internal control group
Data availabilityd
fu2022
B
0
v, \(\rho\), t, d(t)
N, S, R
Yes
3
geoerg2019bot
B
1
v, \(\rho\), t
w, d
Yes
1
geoerg2019cor
C
1
v, \(\rho\), t
w, d
Yes
1
pan2020
B
0
v, t
\(\alpha\), R
Yes
3
pan2021
B, C
0
v, \(\rho\)
w
Yes
1
you2023
B
0
v, \(\rho\), t
w, d
No
3
geoerg2023base
B
\(>30\)
v, \(\rho\), t
h
Yes
2
geoerg2023urgent
B
\(>30\)
v, \(\rho\), t
h
Yes
2
he2024
B
3
v, \(\rho\), t, d(t)
w, d, R, h
Yes
2
aB: bottleneck, C: corridor
bv: speed, \(\rho\): density, t: time, N: (total) number of evacuees, d(t): distance-time
d1: Raw data published, 2: raw data on request, 3: extracted from plot
3.2 Meta-analysis
The Hedges’ g scores computed from the standardised mean egress times across experimental runs for the two conditions (treatment vs control) took negative values for all studies included in the meta-analysis (see Fig. 3). That is, the mean egress time was faster in the condition without wheelchairs for all studies (see table 2). The 95% confidence intervals for the Hedges’ g scores for all but one study [56] did not overlap with the zero effect line (Hedges’ g equal to zero), suggesting these effects were robust. Pooling effects across studies confirmed that the presence of wheelchairs appears to increase egress times overall, and that we can be confident in this effect, based on the available evidence (effect size, as measured by Hedges’ g: \(-\)2.98, 95% confidence interval: \([-3.39,-2.56]\), testing the null hypothesis of a zero effect: \(z=-14.04\), \(p=9.42\times 10^{-45}\); see also Fig. 3). This suggests that the pooled difference in standardised mean egress times across treatments was 2.98 standard deviations, a large effect. Providing a quantitative estimate for the size of this effect was not possible because the heterogeneity of studies in terms of the experimental setup, number of wheelchairs involved, and number of participants meant we had to standardise egress times. However, considering the raw egress times before standardisation, we can indicate the possible range of increases. The lowest increase in egress time when wheelchairs are present is just over 14% [33], whereas the largest increase is over 100% [60] (see Table 2).
We checked if the distributional assumptions of our statistical model were met and were satisfied that there was no compelling evidence for assumptions being violated (see supplementary material). However, it should be noted that due to the low number of studies in our meta-analysis these findings should be treated with caution.
The forest plot in Fig. 3 shows that studies contributed to the pooled effect differently, depending on the number of experimental runs they included. Studies with higher standard error (typically associated with fewer runs) were given lower weights than those with lower standard error (see Introduction and Refs. [31, 48]). The smallest contribution amounted to less than 1% from You et al. [60], and the largest contribution from one of the two studies obtained from Geoerg et al. [62] amounted to almost a third of the overall weightings. The measures of heterogeneity in our study further corroborate the observation of imbalance across studies (\(Q=20.75\), \(I^2=61.4\%\), and \(\tau ^2=0.71\); where a suggested interpretation is that \(I^2=50\%\) is medium, and \(I^2=75\%\) is substantial heterogeneity across studies). To evaluate whether this imbalance affected the results and to ensure our findings were not disproportionately affected by one study, we conducted a leave-one-out study, omitting one study at a time from our meta-analysis. This suggested that the pooled effect found in our meta-analysis was not substantially skewed by a single study (see supplementary material).
The funnel plot for the studies included in our meta-analysis is symmetrical (Fig. 4). Some studies fell outside of the funnel representing estimated confidence intervals around the pooled effect size. This may indicate somewhat larger variability in effect sizes than expected, but it does not indicate the collection of studies used in our analysis is not representative, given the overall symmetry of the plot. Thus, based on the evidence available, a bias in the data available in the literature is unlikely. Studies with higher and lower standard errors, likely corresponding to studies containing fewer and more experimental runs, respectively, are included in our meta-analysis and the study by You et al. [60] with a total of only six experimental runs presents an outlier in terms of study size. Overall, this suggests an unbiased collection of studies with a reasonable range of experimental runs was included in our analysis.
Table 2
Raw egress times in seconds (mean and standard deviation) for the nine studies included in the meta-analysis, as well as the number of experimental runs per experimental condition (n)
Control
Treatment
N
Mean
S.d.
n
Mean
S.d.
n
fu2022
10.31
0.23
3
19.25
7.72
6
16
geoerg2019bot
31.63
2.90
8
45.63
4.13
8
58
geoerg2019cor
38.20
2.44
8
62.52
9.08
8
60
pan2020
31.23
1.22
4
35.74
2.89
12
73
pan2021
9.75
1.88
4
14.18
1.88
4
49
you2023
12.89
1.71
3
25.94
1.71
3
47
geoerg2023base
12.74
0.91
32
16.48
1.43
31
17
geoerg2023urgent
9.01
0.71
35
12.16
0.86
33
17
he2024
9.01
0.71
3
16.90
4.11
6
53
The number of participants who pass through the experimental setup in a single run is also given (N). Note that the control condition for the study by You et al. [60] is derived from Hu et al. [16]. Egress time data are shown after additional experimental conditions were accounted for, but before standardisation was applied
Fig. 3
Forest plot for the mean difference in standardized egress times for pedestrian crowds with (treatment) and without (control) wheelchair users. Negative values in mean difference indicate an increase in egress times in the presence of wheelchairs. The plot is organised into seven columns. The first column shows the study reference. The second and third columns present the effect size and standard error of the effect size, respectively (Hedges’ g). The remaining three columns show again the effect sizes with their 95% confidence intervals, and the weights of the study within the meta-analysis (weights depend on the standard error of egress times and thus the number of replicates in studies). The overall estimated mean and prediction interval based on a fixed effects model are shown at the bottom. Marker sizes indicate the weight of studies
Funnel plot to visually assess publication bias. The x-axis displays the effect size (Hedges’ g) of individual studies and the y-axis shows the standard error for each study. Generally, studies with larger sample sizes (i.e., more experimental runs) have smaller standard errors and are thus positioned higher up on the y-axis, and vice-versa. The dashed vertical line in the plot represents the average pooled effect size and the dashed funnel the estimated 95% confidence intervals
Here, we present a meta-analysis of the effects of wheelchair users on the egress time of pedestrian crowds moving through a bottleneck. Nine studies (from seven publications) were identified and analysed. Our analysis confirmed the findings from the individual studies, showing that egress times (i.e., the time of the last pedestrian to clear a bottleneck during egress) increase when wheelchair users are introduced into an otherwise homogeneous crowd of pedestrians. Hedges’ g across studies indicated that the difference between treatment and control conditions was around three standard deviations (i.e., an increase of roughly 100%), indicating a strong effect.
This work consolidates the evidence provided by individual studies and further supports the notion that observations from studies relying on homogeneous samples should not be generalized to heterogeneous populations. It is further suggested that tools, such as computational pedestrian evacuation simulations, need to consider differences in individual mobility. A previous meta-analysis found studies were likely to be statistically underpowered to determine if the presence of social groups, another source of crowd heterogeneity, affects egress times [31]. Our findings suggest that for stronger effects, current empirical evidence in pedestrian dynamics experiments is reliable.
The present work relied on data that were either available in public repositories or were extracted from publications. Publicly accessible data are crucial for the reproducibility of science, as it allow other researchers to validate and build upon original findings. When data are openly shared, it enables independent verification of results (such as the present study). This transparency helps to identify errors, biases, or inconsistencies, thereby enhancing the reliability and credibility of scientific research. Encouragingly, neither this meta-analysis nor the previous one [31] found evidence for publication bias, indicating a balanced publication of empirical evidence in pedestrian dynamics research. While it is tempting to call for stronger efforts to standardise experimental research efforts alongside making data openly available to enable comparison and integration of results across studies, it has previously been argued that such tendencies should not come at the expense of important exploratory work [31]. Similarly, a low weighting of studies in our meta-analysis should not be interpreted as an indicator of quality. The studies included here followed different lines of investigation and some fit the framework imposed by our analysis better than others, irrespective of the importance of the work presented in the original publications.
The present work needs to take several limitations into account. First, the present meta-analysis only included studies comparing samples with and without wheelchair users. Consequently, the number of studies considered is relatively low. Future studies are needed to explore and quantify the possible effect of other differences in mobility profiles (e.g., use of luggage or other assistive devices). Second, the present work weighted studies based on how many runs were completed in each condition. This places a stronger emphasis on studies in controlled settings, and introduces a potential bias given the lower ecological validity of laboratory studies compared to field observations. More data are needed from field observations to further validate the observations. Third, some of the studies relied on participants without disabilities using wheelchairs. In addition, different types of wheelchairs (e.g., manual and motorized) were included. While this strengthens the representativeness of these studies, it requires further study to evaluate whether the amount of experience with and the type of assistive devices have an impact. Fourth, we only considered studies from which we were able to confirm effect sizes. That is, it is possible that studies were overlooked in which effect sizes were not reported. Fifth, we only considered egress time. Other parameters (e.g., such as speed over density) were not regarded. Results could vary, depending on the outcome variable considered. For example, there are differences in the required space of a wheelchair compared to a pedestrian and metrics may vary in sensitivity to variations of crowd heterogeneity. Sixth, to conduct a meta-analysis including data from a range of experimental designs, we had to substantially standardise study data. We have already discussed how this limits the interpretation of our findings to a qualitative effect, and how it implies assumptions about the data that may not be met (see Sect. 2.3). Seventh, the studies identified originate from a small number of geographic locations (People’s Republic of China, Germany, Canada). Future work is needed to test whether our findings are generalizable beyond these areas. Finally, we observed a range in effect sizes. While the leave-one-out analysis suggests that none of the included studies had an outsized effect on the overall findings and all observed effects were similar in direction, future work is needed to establish a realistic estimate of this effect size.
5 Conclusion and Outlook
By integrating evidence from the literature, the present study solidified evidence that egress times of pedestrian crowds increase when wheelchair users are present, compared to conditions comprising only pedestrians without wheelchairs. No evidence for publication bias in studies was found. The findings provide potential input for model developers, for example for simulations of pedestrian egress movement. However, future research is needed to quantify the effects of crowd heterogeneity on pedestrian dynamics in more detail.
Acknowledgements
We thank Yanghui Hu and Jun Zhang for providing the raw trajectory data for Refs. [16] and [36]. Paul Geoerg, Maxine Berthiaume, and Max Kinateder acknowledge funding from the National Research Council Canada’s Ideation Fund−New Beginnings Initiative (project number: NBR3-549). Paul Geoerg thanks the German Federal Ministry of Education and Research for financial support (Grant No. 13 N13946) within the research program"Safety for People with Physical, Mental, or Age-Related Disabilities"(SiME). He thanks the SFPE Foundation for financial support through the Guylène Proulx, OC Scholarship in 2017. He expresses gratitude to Karen Boyce for the inspiring discussion and encouragement at a very early stage of this manuscript.
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Note that “egress time” needs to be differentiated from other terms, such as Required Safe Egress Time which refers to the time occupants need to safely evacuate from a building [4].
Note that sample size needs to be differentiated from crowd size; the former refers to the number of data points used in an analysis (e.g., the number of egress times measurements) and the latter to the number of participants completing a single run.
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