Constant-net-time headway as a key mechanism behind pedestrian flow dynamics

Spontaneous behavioral coordination between avoiding pedestrians requires mutual anticipation rather than mutual gaze

Pedestrians threading through a crowd is a striking example of coordinated actions. Mutual anticipation between pedestrians is a candidate mechanism underlying such coordination. To examine this possibility, we experimentally intervened pairs of pedestrians performing simple avoidance tasks. Pedestrians in the baseline condition spontaneously coordinated their walking speed and angle until passing one another. Visually distracting one of the pedestrians decreased the level of behavioral coordination. Importantly, blocking the pedestrians' gaze information alone did not alter their walking. These results indicate that spontaneous coordination requires mutual anticipation. Eye movement analysis showed that the direction of a pedestrian's gaze changed depending on the uncertainty of the oncoming pedestrian's motion, and that pedestrians tended to look ahead toward the ultimate passing direction before they actually walked in that direction. We propose that body motion cues may be sufficient and available for implicit negotiation of potential future motions.

Pedestrian dynamics at the running of the bulls evidence an inaccessible region in the fundamental diagram

We characterize the dynamics of runners in the famous "Running of the Bulls" Festival by computing the individual and global velocities and densities, as well as the crowd pressure. In contrast with all previously studied pedestrian systems, we unveil a unique regime in which speed increases with density that can be understood in terms of a time-dependent desired velocity of the runners. Also, we discover the existence of an inaccessible region in the speed-density state diagram that is explained by falls of runners. With all these ingredients, we propose a generalization of the pedestrian fundamental diagram for a scenario in which people with different desired speeds coexist.

Spontaneous synchronization of motion in pedestrian crowds of different densities

Interacting pedestrians in a crowd spontaneously adjust their footsteps and align their respective stepping phases. This self-organization phenomenon is known as synchronization. However, it is unclear why and how synchronization forms spontaneously under different density conditions, or what functional benefit synchronization offers for the collective motion of humans. Here, we conducted a single-file crowd motion experiment that directly tracked the alternating movement of both legs of interacting pedestrians. We show that synchronization is most likely to be triggered at the same density at which the flow rate of pedestrians reaches a maximum value. We demonstrate that synchronization is established in response to an insufficient safety distance between pedestrians, and that it enables pedestrians to realize efficient collective stepping motion without the occurrence of inter-person collisions. These findings provide insights into the collective motion behaviour of humans and may have implications for understanding pedestrian synchronization-induced wobbling, for example, of bridges.

Mutual anticipation can contribute to self-organization in human crowds

Human crowds provide paradigmatic examples of collective behavior emerging through self-organization. Understanding their dynamics is crucial to help manage mass events and daily pedestrian transportation. Although recent findings emphasized that pedestrians' interactions are fundamentally anticipatory in nature, whether and how individual anticipation functionally benefits the group is not well understood. Here, we show the link between individual anticipation and emergent pattern formation through our experiments of lane formation, where unidirectional lanes are spontaneously formed in bidirectional pedestrian flows. Manipulating the anticipatory abilities of some of the pedestrians by distracting them visually delayed the collective pattern formation. Moreover, both the distracted pedestrians and the nondistracted ones had difficulties avoiding collisions while navigating. These results imply that avoidance maneuvers are normally a cooperative process and that mutual anticipation between pedestrians facilitates efficient pattern formation. Our findings may influence various fields, including traffic management, decision-making research, and swarm dynamics.

Analysing the link between public transport use and airborne transmission: mobility and contagion in the London underground

BACKGROUND

The transmission of infectious diseases is dependent on the amount and nature of contacts between infectious and healthy individuals. Confined and crowded environments that people visit in their day-to-day life (such as town squares, business districts, transport hubs, etc) can act as hot-spots for spreading disease. In this study we explore the link between the use of public transport and the spread of airborne infections in urban environments.

METHODS

We study a large number of journeys on the London Underground, which is known to be particularly crowded at certain times. We use publically available Oyster card data (the electronic ticket used for public transport in Greater London), to infer passengers' routes on the underground network. In order to estimate the spread of a generic airborne disease in each station, we use and extend an analytical microscopic model that was initially designed to study people moving in a corridor.

RESULTS

Comparing our results with influenza-like illnesses (ILI) data collected by Public Health England (PHE) in London boroughs, shows a correlation between the use of public transport and the spread of ILI. Specifically, we show that passengers departing from boroughs with higher ILI rates have higher number of contacts when travelling on the underground. Moreover, by comparing our results with other demographic key factors, we are able to discuss the role that the Underground plays in the spread of airborne infections in the English capital.

CONCLUSIONS

Our study suggests a link between public transport use and infectious diseases transmission and encourages further research into that area. Results could be used to inform the development of non-pharmacological interventions that can act on preventing instead of curing infections and are, potentially, more cost-effective.

How cognitive heuristics can explain social interactions in spatial movement

The movement of pedestrian crowds is a paradigmatic example of collective motion. The precise nature of individual-level behaviours underlying crowd movements has been subject to a lively debate. Here, we propose that pedestrians follow simple heuristics rooted in cognitive psychology, such as 'stop if another step would lead to a collision' or 'follow the person in front'. In other words, our paradigm explicitly models individual-level behaviour as a series of discrete decisions. We show that our cognitive heuristics produce realistic emergent crowd phenomena, such as lane formation and queuing behaviour. Based on our results, we suggest that pedestrians follow different cognitive heuristics that are selected depending on the context. This differs from the widely used approach of capturing changes in behaviour via model parameters and leads to testable hypotheses on changes in crowd behaviour for different motivation levels. For example, we expect that rushed individuals more often evade to the side and thus display distinct emergent queue formations in front of a bottleneck. Our heuristics can be ranked according to the cognitive effort that is required to follow them. Therefore, our model establishes a direct link between behavioural responses and cognitive effort and thus facilitates a novel perspective on collective behaviour.

Evacuation time estimate for total pedestrian evacuation using a queuing network model and volunteered geographic information

Estimating city evacuation time is a nontrivial problem due to the interaction between thousands of individual agents, giving rise to various collective phenomena, such as bottleneck formation, intermittent flow, and stop-and-go waves. We present a mean field approach to draw relationships between road network spatial attributes, the number of evacuees, and the resultant evacuation time estimate (ETE). Using volunteered geographic information, we divide 50 United Kingdom cities into a total of 704 catchment areas (CAs) which we define as an area where all agents share the same nearest exit node. 90% of the agents are within ≈6,847 m of CA exit nodes with ≈13,778 agents/CA. We establish a characteristic flow rate from catchment area attributes (population, distance to exit node, and exit node width) and a mean flow rate in a free-flow regime by simulating total evacuations using an agent based "queuing network" model. We use these variables to determine a relationship between catchment area attributes and resultant ETEs. This relationship could enable emergency planners to make a rapid appraisal of evacuation strategies and help support decisions in the run up to a crisis.

Universal power law governing pedestrian interactions

Human crowds often bear a striking resemblance to interacting particle systems, and this has prompted many researchers to describe pedestrian dynamics in terms of interaction forces and potential energies. The correct quantitative form of this interaction, however, has remained an open question. Here, we introduce a novel statistical-mechanical approach to directly measure the interaction energy between pedestrians. This analysis, when applied to a large collection of human motion data, reveals a simple power-law interaction that is based not on the physical separation between pedestrians but on their projected time to a potential future collision, and is therefore fundamentally anticipatory in nature. Remarkably, this simple law is able to describe human interactions across a wide variety of situations, speeds, and densities. We further show, through simulations, that the interaction law we identify is sufficient to reproduce many known crowd phenomena.

Exact dynamics of stochastic linear delayed systems: application to spatiotemporal coordination of comoving agents

Delayed dynamics result from finite transmission speeds of a signal in the form of energy, mass, or information. In stochastic systems the resulting lagged dynamics challenge our understanding due to the rich behavioral repertoire encompassing monotonic, oscillatory, and unstable evolution. Despite the vast literature, quantifying this rich behavior is limited by a lack of explicit analytic studies of high-dimensional stochastic delay systems. Here we fill this gap for systems governed by a linear Langevin equation of any number of delays and spatial dimensions with additive Gaussian noise. By exploiting Laplace transforms we are able to derive an exact time-dependent analytic solution of the Langevin equation. By using characteristic functionals we are able to construct the full time dependence of the multivariate probability distribution of the stochastic process as a function of the delayed and nondelayed random variables. As an application we consider interactions in animal collective movement that go beyond the traditional assumption of instantaneous alignment. We propose models for coordinated maneuvers of comoving agents applicable to recent empirical findings in pigeons and bats whereby individuals copy the heading of their neighbors with some delay. We highlight possible strategies that individual pairs may adopt to reduce the variance in their velocity difference and/or in their spatial separation. We also show that a minimum in the variance of the spatial separation at long times can be achieved with certain ratios of measurement to reaction delay.

Analytical modelling of the spread of disease in confined and crowded spaces

Since 1927 and until recently, most models describing the spread of disease have been of compartmental type, based on the assumption that populations are homogeneous and well-mixed. Recent models have utilised agent-based models and complex networks to explicitly study heterogeneous interaction patterns, but this leads to an increasing computational complexity. Compartmental models are appealing because of their simplicity, but their parameters, especially the transmission rate, are complex and depend on a number of factors, which makes it hard to predict how a change of a single environmental, demographic, or epidemiological factor will affect the population. Therefore, in this contribution we propose a middle ground, utilising crowd-behaviour research to improve compartmental models in crowded situations. We show how both the rate of infection as well as the walking speed depend on the local crowd density around an infected individual. The combined effect is that the rate of infection at a population scale has an analytically tractable non-linear dependency on crowd density. We model the spread of a hypothetical disease in a corridor and compare our new model with a typical compartmental model, which highlights the regime in which current models may not produce credible results.

Properties of pedestrians walking in line. II. Stepping behavior

In human crowds, interactions among individuals give rise to a variety of self-organized collective motions that help the group to effectively solve the problem of coordination. However, it is still not known exactly how humans adjust their behavior locally, nor what are the direct consequences on the emergent organization. One of the underlying mechanisms of adjusting individual motions is the stepping dynamics. In this paper, we present first quantitative analysis on the stepping behavior in a one-dimensional pedestrian flow studied under controlled laboratory conditions. We find that the step length is proportional to the velocity of the pedestrian, and is directly related to the space available in front of him, while the variations of the step duration are much smaller. This is in contrast with locomotion studies performed on isolated pedestrians and shows that the local density has a direct influence on the stepping characteristics. Furthermore, we study the phenomena of synchronization-walking in lock step-and show its dependence on flow densities. We show that the synchronization of steps is particularly important at high densities, which has direct impact on the studies of optimizing pedestrians' flow in congested situations. However, small synchronization and antisynchronization effects are found also at very low densities, for which no steric constraints exist between successive pedestrians, showing the natural tendency to synchronize according to perceived visual signals.

Properties of pedestrians walking in line: fundamental diagrams

We present experimental results obtained for a one-dimensional pedestrian flow using high precision motion capture. The full pedestrians' trajectories are obtained. In this paper, we focus on the fundamental diagram, and on the relation between the instantaneous velocity and spatial headway (distance to the predecessor). While the latter was found to be linear in previous experiments, we show that it is rather a piecewise linear behavior which is found if larger density ranges are covered. Indeed, our data clearly exhibits three distinct regimes in the behavior of pedestrians that follow each other. The transitions between these regimes occur at spatial headways of about 1.1 and 3 m, respectively. This finding could be useful for future modeling.

Crowd and environmental management during mass gatherings

Crowds are a feature of large cities, occurring not only at mass gatherings but also at routine events such as the journey to work. To address extreme crowding, various computer models for crowd movement have been developed in the past decade, and we review these and show how they can be used to identify health and safety issues. State-of-the-art models that simulate the spread of epidemics operate on a population level, but the collection of fine-scale data might enable the development of models for epidemics that operate on a microscopic scale, similar to models for crowd movement. We provide an example of such simulations, showing how an individual-based crowd model can mirror aggregate susceptible-infected-recovered models that have been the main models for epidemics so far.

How simple rules determine pedestrian behavior and crowd disasters

With the increasing size and frequency of mass events, the study of crowd disasters and the simulation of pedestrian flows have become important research areas. However, even successful modeling approaches such as those inspired by Newtonian force models are still not fully consistent with empirical observations and are sometimes hard to calibrate. Here, a cognitive science approach is proposed, which is based on behavioral heuristics. We suggest that, guided by visual information, namely the distance of obstructions in candidate lines of sight, pedestrians apply two simple cognitive procedures to adapt their walking speeds and directions. Although simpler than previous approaches, this model predicts individual trajectories and collective patterns of motion in good quantitative agreement with a large variety of empirical and experimental data. This model predicts the emergence of self-organization phenomena, such as the spontaneous formation of unidirectional lanes or stop-and-go waves. Moreover, the combination of pedestrian heuristics with body collisions generates crowd turbulence at extreme densities--a phenomenon that has been observed during recent crowd disasters. By proposing an integrated treatment of simultaneous interactions between multiple individuals, our approach overcomes limitations of current physics-inspired pair interaction models. Understanding crowd dynamics through cognitive heuristics is therefore not only crucial for a better preparation of safe mass events. It also clears the way for a more realistic modeling of collective social behaviors, in particular of human crowds and biological swarms. Furthermore, our behavioral heuristics may serve to improve the navigation of autonomous robots.