Spatial-size scaling of pedestrian groups under growing density conditions

Social aspects of collision avoidance: a detailed analysis of two-person groups and individual pedestrians

Pedestrian groups are commonly found in crowds but research on their social aspects is comparatively lacking. To fill that void in literature, we study the dynamics of collision avoidance between pedestrian groups (in particular dyads) and individual pedestrians in an ecological environment, focusing in particular on (i) how such avoidance depends on the group's social relation (e.g. colleagues, couples, friends or families) and (ii) its intensity of social interaction (indicated by conversation, gaze exchange, gestures etc). By analyzing relative collision avoidance in the "center of mass" frame, we were able to quantify how much groups and individuals avoid each other with respect to the aforementioned properties of the group. A mathematical representation using a potential energy function is proposed to model avoidance and it is shown to provide a fair approximation to the empirical observations. We also studied the probability that the individuals disrupt the group by "passing through it" (termed as intrusion). We analyzed the dependence of the parameters of the avoidance model and of the probability of intrusion on groups' social relation and intensity of interaction. We confirmed that the stronger social bonding or interaction intensity is, the more prominent collision avoidance turns out. We also confirmed that the probability of intrusion is a decreasing function of interaction intensity and strength of social bonding. Our results suggest that such variability should be accounted for in models and crowd management in general. Namely, public spaces with strongly bonded groups (e.g. a family-oriented amusement park) may require a different approach compared to public spaces with loosely bonded groups (e.g. a business-oriented trade fair).

Identification of social groups and waiting pedestrians at railway platforms using trajectory data

To investigate the impact of social groups on waiting behaviour of passengers at railway platforms a method to identify social groups through the monitoring of distances between pedestrians and the stability of those distances over time is introduced. The method allows the recognition of groups using trajectories only and thus opens up the possibility of studying crowds in public places without constrains caused by privacy protection issues. Trajectories from a railway platform in Switzerland were used to analyse the waiting behaviour of passengers in dependence of waiting time as well as the size of social groups. The analysis of the trajectories shows that the portion of passengers travelling in groups reaches up to 10% during the week and increases to 20% on the weekends. 60% of the groups were pairs, larger groups were less frequent. With increasing group size, the mean speed of the members decreases. Individuals and pairs often choose waiting spots at the sides of the stairs and in vicinity of obstacles, while larger groups wait close to the platform entries. The results indicate that passengers choose waiting places according to the following criteria and ranking: shortest ways, direction of the next intended action, undisturbed places and ensured communication. While individual passengers often wait in places where they are undisturbed and do not hinder others, the dominating comfort criterion for groups is to ensure communication. The results regarding space requirements of waiting passengers could be used for different applications. E.g. to enhance the level of service concept assessing the comfort of different types of users, to avoid temporary bottlenecks to improve the boarding and alighting process or to increase the robustness of the performance of railway platforms during peak loads by optimising the pedestrian distribution.

Intrinsic group behaviour II: On the dependence of triad spatial dynamics on social and personal features; and on the effect of social interaction on small group dynamics

In a follow-up to our work on the dependence of walking dyad dynamics on intrinsic properties of the group, we now analyse how these properties affect groups of three people (triads), taking also in consideration the effect of social interaction on the dynamical properties of the group. We show that there is a strong parallel between triads and dyads. Work-oriented groups are faster and walk at a larger distance between them than leisure-oriented ones, while the latter move in a less ordered way. Such differences are present also when colleagues are contrasted with friends and families; nevertheless the similarity between friend and colleague behaviour is greater than the one between family and colleague behaviour. Male triads walk faster than triads including females, males keep a larger distance than females, and same gender groups are more ordered than mixed ones. Groups including tall people walk faster, while those with elderly or children walk at a slower pace. Groups including children move in a less ordered fashion. Results concerning relation and gender are particularly strong, and we investigated whether they hold also when other properties are kept fixed. While this is clearly true for relation, patterns relating gender often resulted to be diminished. For instance, the velocity difference due to gender is reduced if we compare only triads in the colleague relation. The effects on group dynamics due to intrinsic properties are present regardless of social interaction, but socially interacting groups are found to walk in a more ordered way. This has an opposite effect on the space occupied by non-interacting dyads and triads, since loss of structure makes dyads larger, but causes triads to lose their characteristic V formation and walk in a line (i.e., occupying more space in the direction of movement but less space in the orthogonal one).

Identification of social relation within pedestrian dyads

This study focuses on social pedestrian groups in public spaces and makes an effort to identify the type of social relation between the group members. As a first step for this identification problem, we focus on dyads (i.e. 2 people groups). Moreover, as a mutually exclusive categorization of social relations, we consider the domain-based approach of Bugental, which precisely corresponds to social relations of colleagues, couples, friends and families, and identify each dyad with one of those relations. For this purpose, we use anonymized trajectory data and derive a set of observables thereof, namely, inter-personal distance, group velocity, velocity difference and height difference. Subsequently, we use the probability density functions (pdf) of these observables as a tool to understand the nature of the relation between pedestrians. To that end, we propose different ways of using the pdfs. Namely, we introduce a probabilistic Bayesian approach and contrast it to a functional metric one and evaluate the performance of both methods with appropriate assessment measures. This study stands out as the first attempt to automatically recognize social relation between pedestrian groups. Additionally, in doing that it uses completely anonymous data and proves that social relation is still possible to recognize with a good accuracy without invading privacy. In particular, our findings indicate that significant recognition rates can be attained for certain categories and with certain methods. Specifically, we show that a very good recognition rate is achieved in distinguishing colleagues from leisure-oriented dyads (families, couples and friends), whereas the distinction between the leisure-oriented dyads results to be inherently harder, but still possible at reasonable rates, in particular if families are restricted to parent-child groups. In general, we establish that the Bayesian method outperforms the functional metric one due, probably, to the difficulty of the latter to learn observable pdfs from individual trajectories.

Effect of form of obstacle on speed of crowd evacuation

This paper investigates the effect of the form of an obstacle on the time that a crowd takes to evacuate a room, using a toy model. Pedestrians are modeled as active soft matter moving toward a point with intended velocities. An obstacle is placed in front of the exit, and it has one of four shapes: a cylindrical column, a triangular prism, a quadratic prism, or a diamond prism. Numerical results indicate that the evacuation-completion time depends on the shape of the obstacle. Obstacles with a circular cylinder (C.C.) shape yield the shortest evacuation-completion time in the proposed model.

Intrinsic group behaviour: Dependence of pedestrian dyad dynamics on principal social and personal features

Being determined by human social behaviour, pedestrian group dynamics may depend on “intrinsic properties” such as the purpose of the pedestrians, their personal relation, gender, age, and body size. In this work we investigate the dynamical properties of pedestrian dyads (distance, spatial formation and velocity) by analysing a large data set of automatically tracked pedestrian trajectories in an unconstrained “ecological” setting (a shopping mall), whose apparent physical and social group properties have been analysed by three different human coders. We observed that females walk slower and closer than males, that workers walk faster, at a larger distance and more abreast than leisure oriented people, and that inter-group relation has a strong effect on group structure, with couples walking very close and abreast, colleagues walking at a larger distance, and friends walking more abreast than family members. Pedestrian height (obtained automatically through our tracking system) influences velocity and abreast distance, both growing functions of the average group height. Results regarding pedestrian age show that elderly people walk slowly, while active age adults walk at the maximum velocity. Groups with children have a strong tendency to walk in a non-abreast formation, with a large distance (despite a low abreast distance). A cross-analysis of the interplay between these intrinsic features, taking in account also the effect of an “extrinsic property” such as crowd density, confirms these major results but reveals also a richer structure. An interesting and unexpected result, for example, is that the velocity of groups with children increases with density, at least in the low-medium density range found under normal conditions in shopping malls. Children also appear to behave differently according to the gender of the parent.

Velocity correlations and spatial dependencies between neighbors in a unidirectional flow of pedestrians

The aim of the paper is an analysis of self-organization patterns observed in the unidirectional flow of pedestrians. On the basis of experimental data from Zhang et al. [J. Zhang et al., J. Stat. Mech. (2011) P0600410.1088/1742-5468/2011/06/P06004], we analyze the mutual positions and velocity correlations between pedestrians when walking along a corridor. The angular and spatial dependencies of the mutual positions reveal a spatial structure that remains stable during the crowd motion. This structure differs depending on the value of n, for the consecutive nth-nearest-neighbor position set. The preferred position for the first-nearest neighbor is on the side of the pedestrian, while for further neighbors, this preference shifts to the axis of movement. The velocity correlations vary with the angle formed by the pair of neighboring pedestrians and the direction of motion and with the time delay between pedestrians' movements. The delay dependence of the correlations shows characteristic oscillations, produced by the velocity oscillations when striding; however, a filtering of the main frequency of individual striding out reduces the oscillations only partially. We conclude that pedestrians select their path directions so as to evade the necessity of continuously adjusting their speed to their neighbors'. They try to keep a given distance, but follow the person in front of them, as well as accepting and observing pedestrians on their sides. Additionally, we show an empirical example that illustrates the shape of a pedestrian's personal space during movement.