Emergency exits as bottlenecks in escape routes are important for designing traffic facilities. Particularly, the capacity estimation is a crucial performance criterion for assessment of pedestrians’ safety in built environments. For this reason, several studies were performed during the last decades which focus on the quantification of movement through corridors and bottlenecks. These studies were usually conducted with populations of homogeneous characteristics to reduce influencing variables and for reasons of practicability. Studies which consider heterogeneous characteristics in performance parameters are rarely available. In response and to reduce this lack of data a series of well-controlled large-scale movement studies considering pedestrians using different types of wheelchairs was carried out. As a result it is shown that the empirical relations
Experimental investigations of pedestrian movements and dynamics have been widely improved during the last decades. Many studies under laboratory or field conditions have been performed to address movement characteristics, improve tracking methods, or investigate behavioural insights [
The findings of this research were recently collected and comparatively prepared by extended reviews focussing on different flow types and geometries [
Until now, only a few studies considered a more heterogeneous characterisation of participants. This challenge is addressed by a review of Geoerg et al. [
Concluding, little is known about the influence of heterogeneity on pedestrian movement characteristics which calls into the question of transferability for existing data to heterogeneous population settings. Therefore, this work is developed to analyse a series of well-controlled movement studies with focus on characteristics of pedestrians’ movement and assessment of performance of a facility. The structure is organised as follows: in Section
The movement studies were conducted as a part of the interdisciplinary research project SiME (SiME is an acronym for the German meaning of “safety for all people” and is funded by the German Ministry of Education and Research) on two days in an industrial hall in Wermelskirchen-Dabringhausen (Germany) in June 2017. Twelve studies with more than 145 single runs and overall 252 participants with populations composed of people with and without disabilities were performed. In addition studies without any people with disabilities have been conducted.
Non-disabled participants (NDP) were recruited by public call while participants with disabilities (PWD) were recruited from a sheltered workshop. For defining the type of disability and to consider and select participants with disabilities, we used the Score RNA-approach, which is a method to weight potentially critical indicators for egress (for details we refer to [
The consideration of an appropriate proportion of people with disabilities in the overall population is oriented towards the prevalence of disability (approximately 10 % in Germany [
We differentiate the population of a study into two subpopulations: on the one hand the participants with disabilities (disabled subpopulation) and on the other hand the participants without any disabilities (non-disabled subpopulation). In accordance with the reported ratio of inhabitants with disabilities, it has been tried to configure the populations in a similar ratio. In addition, we did reference studies for all geometrical settings with a reference population without any disabilities. The mean age of the disabled participants was
Participation was absolutely voluntary for everybody and a cancellation of participation without any negative consequences was possible at any time. All participants have been paid 25 € per half a day of participation. Only anonymous data were used for the studies and the methodological design, data storage process, and the access authorisation for data were approved by the ethics committee of the Bergische Universität Wuppertal. No ethical concerns were mentioned.
The aim of the studies was to investigate the impact of presence of wheelchair users on performance criteria for movement in built environments under laboratory conditions. Following the classification of complex movements by Shi et al. [
Controlled boundary conditions and characteristic of each run. Note that some participants have to rest after a run due to their disability and that volunteers without tasks participated run-wise.
Bot_whe | Run | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 |
Width | 0.9 m | 1.0 m | 1.1 m | 1.2 m | |||||
N (non-disabled) | 81 | 81 | 80 | 80 | 83 | 83 | 85 | 83 | |
N (disabled) | 7 | ||||||||
| |||||||||
Bot_ref | Run | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 |
Width | 0.9 m | 1.0 m | 1.1 m | 1.2 m | |||||
N (non-disabled) | 67 | 67 | 66 | 66 | 69 | 69 | 69 | 69 | |
N (disabled) | – | ||||||||
| |||||||||
Cor_whe | Run | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 |
Width | 0.9 m | 1.0 m | 1.1 m | 1.2 m | |||||
N (non-disabled) | 85 | 83 | 85 | 85 | 84 | 83 | 85 | 86 | |
N (disabled) | 7 | ||||||||
| |||||||||
Cor_ref | Run | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 |
Width | 0.9 m | 1.0 m | 1.1 m | 1.2 m | |||||
N (non-disabled) | 68 | 68 | 69 | 69 | 70 | 69 | 68 | 69 | |
N (disabled) | – |
Sketch of the study setup. The width
Sketch of the bottleneck study
Sketch of the corridor study
Snapshot of the bottleneck study
Snapshot of the corridor study
Individual trajectories of movement through a bottleneck and a corridor with a width of 0.9 m considering participants using a wheelchair (left) and without participants with disabilities (right). Participants using a wheelchair are coloured in orange. Black rectangles represent the measurement surface (coordinates are given in the legend).
Every experimental design is characterized by research pragmatic decisions, priorities, and a focus on complexity reduction. The authors are aware that this results in limitations for transferability to real scenarios. In particular, such narrow and long corridors are rarely found in real geometries. The decision for the geometric boundary conditions was made against the background of investigating the transition from single-file movement to group movement (corridor). On the other hand, bottlenecks are defined by their temporal and/or local limitation. The influence of the output from the bottleneck and the empirically observed capacity-increasing effect of very short bottlenecks [
The passageway through the study setting was captured by nine high-definition cameras attached to the ceiling of the hall (height
Calculation of characteristics is separated into different approaches: (a) values of a fixed time interval (space-time-mean, according to [
The mean movement speed
The specific flow
The unimpeded (free) movement speed
Unimpeded movement speeds in
Study | N (PWD) | | N (NDP) | |
---|---|---|---|---|
Elderly | 4 | 1.30 | 81 | 1.42 |
Cognition | 9 | 1.20 | 88 | 1.47 |
Wheelchair | 7 | 0.96 | 77 | 1.45 |
Walk | 5 | 1.28 | 70 | 1.44 |
Mixed | 5 | 0.71 | 74 | 1.43 |
Hetero | 12 | 1.33 | 71 | 1.47 |
Reference | 68 | 1.47 |
Overall, the observed unimpeded movement speeds of nondisabled participants are comparable with literature findings (see [
In general, a fundamental diagram describes the relation between density and movement speed or density and flow. It indicates the importance for calculation methods for dimensioning pedestrian facilities [ a free-flow branch at low density, where the flow increases with density and the movement speeds are similar to the desired (unimpeded) movement speeds a branch where interactions between pedestrians occur with needs for changes of velocity and directions but still a stable flow a congested branch at higher densities where the flow decreases with increasing density due to the distance to neighbours and which in consequence leads to the formation of jams
Schematic representation of the fundamental diagram
Time-space plots of movement through a bottleneck with different widths considering participants using a wheelchair (left) and without participants with disabilities (right). Black rectangle: measurement surface in space and time (steady states). The threshold for visualisation was defined by
The obtained trajectory data enable analysing the movement through the geometries in relation of space and time. Figure
It can be seen that the movement through the bottleneck for the reference population is uniform and homogeneous for all widths. All participants overcame the same distances by a similar time and without overtaking and clogging effects. The overall passage time decreases with increasing bottleneck width (from top to down). In contrast, the data for a population with wheelchair users are presented on the left side in Figure
We focus on the fundamental diagrams to analyse the characteristics of movement depending on population characteristics (Figures
To determine the fundamental diagram only data from stable conditions are used (see the grey coloured area in Figure
Time series of
Time development with wheelchair subpopulation (Bot_whe_01)
Time development with reference population (Bot_ref_01)
Fundamental diagrams for bottleneck studies. The mean values are presented as scattered bins in density intervals of 0.1
Fundamental diagrams for corridor studies. The mean values are presented as scattered bins in density intervals of 0.1
In result the shape of the measurement surface depends on space and time. In constant space-dimension we took the measurement in a rectangular area in a distance of 4 m to the bottleneck entrance (Figures
The steady state for the configuration with wheelchair users takes the significant fluctuations and multiple local maxima in density and flow (caused by the inhomogeneous movement in space and time) into account. For the bottleneck configuration the density increases within 25 s from initial density up to a local maximum for bottleneck and remains steady (but fluctuating) for
Because of the limited number of participants, a polite and considerate behaviour, and the motivation of the participants, we only observed mean density values between 1.0
It is noticeable that the observed mean movement speed is remarkably slow and—in case of the bottleneck situation—independent of the density (Figure
A dependency of the (hydrodynamic) flow on density was observed for both geometries and is independent of the population configuration. In both presented studies, the capacity
The individual time gap for the passage of a line between a participant and the person moving ahead of him (preceding person) is analysed to quantify the individual distance headway. The headway of a pedestrian is used to maintain the distance of an individual to a predecessor because of additional space to adopt movement speed, avoid collisions, or take a step [
The mean time gaps for the disabled and nondisabled subpopulations and the reference population in the bottleneck and a corridor situation of different widths are presented in Table
Individual passage time gap (mean + standard deviation) in
Run | width / m | Time gap | ||
---|---|---|---|---|
disabled population | non-disabled population | |||
Bot_whe | 01 | 0.9 | 2.51 | 0.93 |
02 | 0.9 | 2.83 | 0.97 | |
| ||||
Bot_whe | 03 | 1.0 | 2.69 | 0.84 |
04 | 1.0 | 2.38 | 0.74 | |
| ||||
Bot_whe | 05 | 1.1 | 2.45 | 0.74 |
06 | 1.1 | 2.75 | 0.68 | |
| ||||
Bot_whe | 07 | 1.2 | 1.39 | 0.77 |
08 | 1.2 | 2.23 | 0.62 | |
| ||||
Bot_ref | 01 | 0.9 | – | 0.77 |
02 | 0.9 | – | 0.76 | |
| ||||
Bot_ref | 03 | 1.0 | – | 0.69 |
04 | 1.0 | – | 0.67 | |
| ||||
Bot_ref | 05 | 1.1 | – | 0.61 |
06 | 1.1 | – | 0.62 | |
| ||||
Bot_ref | 07 | 1.2 | – | 0.56 |
08 | 1.2 | – | 0.54 | |
| ||||
Cor_whe | 01 | 0.9 | 5.21 | 1.07 |
02 | 0.9 | 3.03 | 0.99 | |
| ||||
Cor_whe | 03 | 1.0 | 4.47 | 0.91 |
04 | 1.0 | 3.76 | 0.87 | |
| ||||
Cor_whe | 05 | 1.1 | 3.27 | 0.79 |
06 | 1.1 | 3.00 | 0.79 | |
| ||||
Cor_whe | 07 | 1.2 | 3.51 | 0.77 |
08 | 1.2 | 3.10 | 0.76 | |
| ||||
Cor_ref | 01 | 0.9 | – | 0.95 |
02 | 0.9 | – | 0.87 | |
| ||||
Cor_ref | 03 | 1.0 | – | 0.75 |
04 | 1.0 | – | 0.72 | |
| ||||
Cor_ref | 05 | 1.1 | – | 0.72 |
06 | 1.1 | – | 0.69 | |
| ||||
Cor_ref | 07 | 1.2 | – | 0.63 |
08 | 1.2 | – | 0.59 |
Comparison of passage time gaps for bottleneck studies (width
Individual time gaps for run Bot_whe_01 with
Individual time gaps for run Bot_ref_01 without participants using wheelchairs
In case of a bottleneck situation, an increased interaction and communication between participants in wheelchairs and nondisabled participants was noticed. Even if a wheelchair user reaches the entrance to the bottleneck, their neighbours anticipate individual movement speed and stop passing. They interact and solve priority of movement by communication. Social norms, individual behaviour, and degrees of freedom in movement and the influence of technical assistance devices and accompanying persons may affect the passageway [
One of the most important questions while assessing the performance of a facility is to quantify the capacity of a bottleneck and how the capacity increases with the width [
Comparison of specific flows for bottleneck studies considering different subpopulations in a bottleneck. Reference data is obtained from [
Specific flow for study Bot_whe with
Specific flow for study Bot_ref without participants using wheelchairs
Comparison of specific flows for studies considering different subpopulations in a corridor. Reference data is obtained from [
Specific flow for study Cor_whe with
Specific flow for study Cor_ref without participants using wheelchairs
It is generally assumed that the specific flow is a linear (e.g., [
A series of well-controlled studies on movement through a bottleneck and a corridor was performed. We compared the influence of different populations (with and without wheelchair users) on movement characteristics. Individual trajectories of
Unimpeded movement speed of all participants was measured and analysed with respect to the individual abilities. Expected unimpeded movement speeds (
Further on, the speed-density and flow-density relation (fundamental diagram) was studied. It was found that the basic shape of the flow-density relation is similar to previous research, but the shape of the speed-density relation is different in case of the bottleneck configuration. Because of a polite and considerate (social) behaviour, participants anticipate their movement speed to the slower wheelchair users and renounced overtaking actions. This results in density regions of the fundamental diagram of 3.0
It is found that the participants using wheelchairs keep larger distances to their predecessors, which is caused by the slower movement speeds in corridors and as a consequence of communication process in front of the bottleneck. Furthermore, additional space in case of larger widths has no effects on the time gaps of wheelchair users because the additional space is to leak for overtaking or passing the line simultaneously.
As a consequence, the specific flow concept is only approved for the reference study without disabled participants. Because of significantly lower specific flow for disabled subpopulations, the cumulative specific flow of heterogeneous group is constant and depend not on the width. It is worth mentioning that the number of data for the wheelchair users is limited and that usage of larger steps of additional widths (e.g., a multiple of a wheelchair width) may have an impact on the flow.
As a first step, the presented results may be used to improve the capacity calculations for different configurations of populations in design and planning process of facilities. Further research, especially on the comparison between different process in movement and different ratios of populations, is required.
Measurement surface /
Bottleneck
Corridor
Effective length of the covered distance during the sampling interval
Flow rate /
Specific flow /
Capacity of a facility /
Length of the bottleneck /
Measurement area
Numbers of participants
Unique identification number of a participant
Study with a reference population without any disabled participants
Safety for pedestrians with disabilities
Time /
Lower and upper limit of the time interval /
Movement speed /
Unimpeded (free) movement speed /
Propagation speed of a congestion /
Voronoi movement speed /
Mean movement speed /
Width /
Study with a subpopulation using a wheelchair
Horizontal axis in the Cartesian coordinate system /
Vertical axis in the Cartesian coordinate system /
Mean value
Sampling interval /
Density where the flow reaches the maximum /
Voronoi density /
Mean density /
Density, where the velocity is close to zero due to overcrowding /
Standard deviation
Trajectory data will be published with DOI at the Juelich database about data in pedestrian dynamics (http://ped.fz-juelich.de/db/) with the latest six months after publication of this research article.
The authors declare that they have no conflicts of interest.
Paul Geoerg, Jette Schumann, Stefan Holl, and Anja Hofmann carried out the problem identification and developed the method for the selection and evaluation of relevant material for the contribution. Paul Geoerg, Jette Schumann, and Stefan Holl carried out the movement studies. Paul Geoerg and Jette Schumann carried out the analysis and drafted the manuscript. Stefan Holl and Anja Hofmann suggested modifications in the manuscript critically revising its content. All authors read and approved the final manuscript.
We thank the team and employees of the Lebenshilfe Bergisches Land and the anonymous participants for the committed and patient support during planning and conduction of the movement studies. Part of this work has been performed within the research program safety for people with physical, mental, or age-related disabilities (SiME) funded by the German Federal Ministry of Education and Research-BMBF (grant numbers 13N13946 and 13N13950). Paul Geoerg thanks the SFPE Foundation for financial support with Dr. Guylène Proulx, OC Scholarship.
This section contains supplementary data for the fundamental diagrams