The influence of individual impairments in crowd dynamics

The importance of empirical relations to quantify the movement of pedestrians through a facility has increased during the last decades since performance‐based design methods became more common. Bottlenecks are of special interest because of their importance for egress routes and as they result in a reduced capacity. The empirical relations as the density‐dependent movement speed or flow rate were derived by studies under laboratory conditions, which were usually conducted with populations of homogeneous characteristics for better control of influencing variables. If individual characteristics of a crowd become more heterogeneous, individuals were forced to adapt their individual movement and control individual manoeuvring. These unintended interactions lead to a different shape of the fundamental empirical relations. Here, we present results from a movement study under well‐controlled boundary conditions in which participants with and without different characteristics of disabilities participated. To consider the effect of different heterogeneities on the capacity of a facility, fundamental diagrams are generated using the Voronoi method. If participants with visible disabilities (such as using assistive devices) are part of a crowd, significant differences relating to the shape of the empirical relations and the capacities are found. This indicates that the heterogeneity of a population leads to an increased interpersonal interaction which results in influenced movement characteristics.


INTRODUCTION
Pedestrian dynamics are important for consideration in any fire safety engineering design. Current regulations referenced on datasets, which are typically based on uniform (homogeneous) population settings, that have been published in the last decades. 1,2 At the same time, enormous efforts have been made to clarify the fundamentals of pedestrian movement during the last decades. The need for work in interdisciplinary teams on issues 3 is increasingly being used to focus several point of views (eg, previous studies 4, 5 ).
Gwynne and Boyce published a comprehensive overview on data for engineering quantification of egress. 6 In order to improve the understanding of the context of the data 7 a comprehensive focus was put on documentation of boundary conditions of the data sets. Data collection considering different levels of movement complexity was discussed by Shi et al. 8  These structuring reviewing publications take particularly data of well-abled participants into account. Due to the recognition of three important mega-trends-mobility, urbanisation, and silver societies (demographic changes)-the use of these data based on homogeneous populations may lead to inapplicable functional relationship, nontransferable performance values, and loss of confidence in performance-based design principles. In particular, the results of the demographic transformation process (eg, increasing proportions of elderly or impaired persons) are not considered in functional relationships of movement and may have an effect on the assessment of crowd movement and evaluation of safe egress. 12 However, few studies have considered truly heterogeneous groups or disabled pedestrians as evidenced by the small proportion of datasets presented in Gwynne and Boyce. 6 Geoerg et al had recently published an extended update on engineering egress data considering pedestrians with disabilites. 13 Findings regarding to unimpeded movement speed and empirical relations were discussed. Hashemi et al had published a survey of drill, simulations, and accesibility and provided data on different movement parameters and disabilities. 14 The impact of a reduced visibility or vision loss on movement characteristics were investigated by previous studies. 15 -20 In general, reduced flow rates and strongly effected movement speed of the individuals are reported. The influencing aspect of individuals using assistive devices (eg, wheelchairs) during crowd movement has been adressed by previous works. [21][22][23] Differences in individual movement speeds between wheelchair users and nondisabled participants were reported. A dependency between the ratio of wheelchair users in a population and the width of an opening was observed. Differences in empirical relations for elderly (or younger respectively) populations were reported by previous works. [24][25][26][27][28][29][30][31][32][33] Especially, reduced movement speed and flow rate were highlighted.
While an increased prevalence to die during a disaster for citizens with disability is well reported (eg, previous studies, 34-40 pp. 74-76 41 ), it is debatable whether those data are still representative in terms of transferability to diverse, inhomogeneous, and more realistic populations. 1 This publication addresses this challenge and presents findings from well-controlled large-scale parameter studies on pedestrians movement through a bottleneck. Populations defined by different disabilities were considered. In contrast to a recently published study of the authors, 42 results of four different populations were compared: participants using wheelchairs (whe), with walking disabilities (wal), with mixed single disabilities (mix), and without any The structure is organised as follows: in Section 2, the setting of the movement studies, the data extraction techniques, and the used calculation methods are introduced. The data analysis follows in Section 3. First, we present a comparison of unimpeded (unrestricted, free) movement speed (v 0 ) of different subpopulations (Section 3.1).
Second, the impact of three subpopulations characterised by presence of participants with different types of impairments (participants using a wheelchair, participants with walking disabilities, and participants with mixed disabilities) on stability of movement in a group is discussed (Section 3.2). Especially, the effect on fundamental relationshipsv(̄) andJ(̄) =̄·v is examined in more detail (Section 4). The conclusion is made in the last section (Section 5).

Study setup
The movement studies were conducted as a part of the interdisciplinary research project SiME. SiME is an acronym for the German The geometry consists of two corridors of different widths. The rear, narrower part was varied w (see Figure 2) was varied in increments of 0.1m from 0.9 to 1.2m ( Table 1). The front part was 2.4 m wider than the rear part and was used to canalise the direction of crowd movement. The initial density was about 3.0m −2 , and each configuration was repeated twice (see Table 1). In addition, every participant was walking through the geometry alone at the beginning (Run 00). The

Data extraction method
The movement through the study setting was captured by nine high-resolution cameras attached to the ceiling of the hall. Each participant wore a coloured cap according to their individual body height.
We used the PeTrack-Framework to determine the automatic extrac-  Table 1 for details of the trial 08 indicated by the two-digit number. Participants with disabilities ( Figure 3A: participants using a wheelchair, Figure 3B: participants with walking disabilities, Figure 3C: participants with mixed (single) disabilities, and Figure 3D: without participants with disabilities). A more detailed description on the individual characteristics of the participants with disabilities is provided in Geoerg et al. 52 The maximum error e max of the trajectories resulting from the perspective camera view is approximately 0.092 m for the camera Note. Some participants have to rest after a run due to their disability and that volunteers without tasks participated run-wise. Abbreviations: Bot_mix, participants with different single disabilities; Bot_ref, all participants without disabilities; Bot_wal, participants with walking disabilities; Bot_whe, participants using a wheelchair; N (NDP), number of participants without disabilities; N (PWD), number of participants have disabilities; w, passage width. Trajectory data is available at the pedestrian dynamics data archive and can be accessed with http://ped.fz-juelich.de/da/2017sime.

Measurement
Based on the individual position and the time step, the participants can be represented as a set of points in the metric space, which can be transferred into a Voronoi diagram. 53   Thus, the density and movement speed distribution of the area is and The density within the v (x, y, t, Δx, Δy) = A detailed error estimation for these methods is difficult to make An example for the distribution of Voronoi density and movement speed over space in a bottleneck (at time step 40.08 s which is similar to frame 1002) for a study with and without wheelchair users is presented in Figure 4.    A slight linear dependency ofv(̄) was observed for the reference population ( Figure 11) for movement in groups with disabled subpopulations a nonlinear dependency was observed (Figures 8-10). While considering participants with mixed disabilities and without disabilities, a dependency between movement speed and density is recognisable over the entire density, the averaged movement speed of populations with wheelchair users and walking disabled participants is independent from densities greater than 1.5 m −2 . This is in contrast to the expected behaviour and data from previous studies with homogeneous populations (eg, previous studies 9,57,91 ) and the classic understanding of the fundamental diagram where dependency between movement speed and density is expected.     Table 1). Here, the observed flow rate increase rather linearly. The flow rate here is much less dependent from the width than for population with mixed single disabilities or the reference population (see the spatial distribution, especially in y-direction of similar coloured points in Figures 1 and 2).