Modeling crowd turbulence by many-particle simulations

Modelling physical contacts to evaluate the individual risk in a dense crowd

Tumble and stampede in a dense crowd may be caused by irrational behaviours of individuals and always troubles the safety management of crowd activities. Risk evaluation based on pedestrian dynamical models can be regarded as an effective method of preventing crowd disasters. Here, a method depending on a combination of collision impulses and pushing forces was used to model the physical contacts between individuals in a dense crowd, by which the acceleration error during physical contacts caused by a traditional dynamical equation can be avoided. The human domino effect in a dense crowd could be successfully reproduced, and the crushing and trampling risk of a microscopic individual in a crowd could be quantitatively evaluated separately. This method provides a more reliable and integral data foundation for evaluating individual risk that shows better portability and repeatability than macroscopic crowd risk evaluation methods and will also be conducive to preventing crowd disasters.

Agent-based modeling of mass shooting case with the counterforce of policemen

Mass shooting cases have caused large casualties worldwide. The counterforce, such as the policemen, is of great significance to reducing casualties, which is the core issue of social safety governance. Therefore, we model both the killing force and counterforce, to explore the crowd dynamics under the shooting. Taking the “Borderline” shooting in 2018 as the target case, the agent-based modeling is applied to back-calculate this dynamic process and explore key behavior rules of individuals. The real death tolls of three classes of agents (civilians, policemen, & killers) are as the real function, based on which we calculate the gaps between real target case and simulations. Eventually, we obtain three optimal solutions, which achieve the least gap or highest matching degree. Besides, we make counterfactual inferences under the optimal solutions, to explore the strategic interactions between policemen and killers. For strategies of killers, we explore different sizes, positions, and moving patterns of the killers. The optimal size of policemen is four to five, for each one killer. For strategies of policemen, we explore the size, locations, and the response time. It indicates that optimal response time of policemen is thirty to forty shots of the killer, and the death of civilians and policemen can be minimized, and the death probability of the killer can be maximized. These findings help to improve public safety governance for our cities. To effectively deal with sudden shooting terrorist cases, patrol routes, reasonable settings, and swift dispatches of the police (stations) should be considered.

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.

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.

Beyond the faster-is-slower effect

The "faster-is-slower" effect arises when crowded people push each other to escape through an exit during an emergency situation. As individuals push harder, a statistical slowing down in the evacuation time can be achieved. The slowing down is caused by the presence of small groups of pedestrians (say, a small human cluster) that temporarily block the way out when trying to leave the room. The pressure on the pedestrians belonging to this blocking cluster increases for increasing anxiety levels and/or a larger number of individuals trying to leave the room through the same door. Our investigation shows, however, that very high pressures alter the dynamics in the blocking cluster and, thus, change the statistics of the time delays along the escaping process. A reduction in the long lasting delays can be acknowledged, while the overall evacuation performance improves. We present results on this phenomenon taking place beyond the faster-is-slower regime.

Pedestrian collective motion in competitive room evacuation

When a sizable number of people evacuate a room, if the door is not large enough, an accumulation of pedestrians in front of the exit may take place. This is the cause of emerging collective phenomena where the density is believed to be the key variable determining the pedestrian dynamics. Here, we show that when sustained contact among the individuals exists, density is not enough to describe the evacuation, and propose that at least another variable –such as the kinetic stress– is required. We recorded evacuation drills with different degrees of competitiveness where the individuals are allowed to moderately push each other in their way out. We obtain the density, velocity and kinetic stress fields over time, showing that competitiveness strongly affects them and evidencing patterns which have been never observed in previous (low pressure) evacuation experiments. For the highest competitiveness scenario, we detect the development of sudden collective motions. These movements are related to a notable increase of the kinetic stress and a reduction of the velocity towards the door, but do not depend on the density.

Jamming transitions induced by an attraction in pedestrian flow

We numerically study jamming transitions in pedestrian flow interacting with an attraction, mostly based on the social force model for pedestrians who can join the attraction. We formulate the joining probability as a function of social influence from others, reflecting that individual choice behavior is likely influenced by others. By controlling pedestrian influx and the social influence parameter, we identify various pedestrian flow patterns. For the bidirectional flow scenario, we observe a transition from the free flow phase to the freezing phase, in which oppositely walking pedestrians reach a complete stop and block each other. On the other hand, a different transition behavior appears in the unidirectional flow scenario, i.e., from the free flow phase to the localized jam phase and then to the extended jam phase. It is also observed that the extended jam phase can end up in freezing phenomena with a certain probability when pedestrian flux is high with strong social influence. This study highlights that attractive interactions between pedestrians and an attraction can trigger jamming transitions by increasing the number of conflicts among pedestrians near the attraction. In order to avoid excessive pedestrian jams, we suggest suppressing the number of conflicts under a certain level by moderating pedestrian influx especially when the social influence is strong.

Crowd Simulations and Determining the Critical Density Point of Emergency Situations

OBJECTIVE

In modern societies, crowds and mass gatherings are recurrent. A combination of inadequate facilities and inefficient population management can lead to injury and death. Simulating people's behavior in crowds and mass gatherings can assist in the planning and management of gatherings, especially in emergency situations.

METHODS

We aimed to determine the crowd pattern and the critical density point in the grand bazaar of Kerman in Iran. We collected data by use of a census method with a questionnaire. To determine the critical density point, height and weight data were placed in the equation $\,s\,{\equals}\,\sqrt {{{L{\vskip -1.5pt \,\,\asterisk\,\,}M} \over {3600}}} $ and the outer body surface of all the individuals in the bazaar was calculated. The crowd was simulated by use of flow-based modeling. Flow rate was determined by using the equation (flow rate=density * speed). By use of SketchUp Pro software (version 8; Trimble, Sunnyvale, CA), the movement of each person and the general flow rate were simulated in the three-dimensional environment of Kerman bazaar.

RESULTS

Our findings showed that the population critical density point in Kerman bazaar would be 6112 people. In an accident, the critical density point in Kerman bazaar would be created in about 1 minute 10 seconds after the event.

CONCLUSION

It seems necessary to identify and provide solutions for reducing the risk of disasters caused by overcrowding in Kerman bazaar. It is suggested that researchers conduct studies to design safe and secure emergency evacuation of Kerman bazaar as well as proper planning for better and faster access of aid squads to this location. (Disaster Med Public Health Preparedness. 2017;11:674-680).

Deffuant model on a ring with repelling mechanism and circular opinions

We investigate a Deffuant model on a ring by introducing two modifications: the repelling mechanism and the circular opinions. The repelling mechanism drives the opinions of two individuals away from each other and the circular opinions are defined on a circle. We find that the repelling mechanism tends to polarize the opinions of adjacent individuals and the circular opinions bring up a spatiotemporal pattern in which all individuals take different opinions but the opinion difference between two neighboring individuals tends to zero in the limit of the population size. In the Deffuant model with both repelling mechanism and the circular opinions, opinion dynamics depends on both the bounded confidence and the convergence rate. The interplay between the repelling mechanism and the circular opinion may give rise to time-dependent opinion dynamics.

Evacuation of Pedestrians with Two Motion Modes for Panic System

In this paper, we have captured an underlying mechanism of emergence of collective panic in pedestrian evacuations by using a modification of the lattice-gas model. We classify the motion of pedestrians into two modes according to their moods. One is gentle (mode I), the other is flustered (mode II). First, to research the cause for crowd, we fix the motion modes of pedestrians and increase the proportion of pedestrians with motion mode II (ρ_II). The simulation results show that the pedestrians with motion mode II are lack of evacuation efficiency and cause more casualties. Further, we use the SIS (susceptible-infective-susceptible) model to describe the spreading of the panic mood. The system can be in the high-mix state when the infection probability λ is greater than a fuzzy threshold. In addition, the distances S from wounded people to the exit are researched, the number of wounded people gets maximum at the internal S = 5 ∼ 10, which is independent of ρ_II and λ. This research can help us to understand and prevent the emergence of collective panic and reduce wounds in the real evacuation.

Experimental proof of faster-is-slower in systems of frictional particles flowing through constrictions

The "faster-is-slower" (FIS) effect was first predicted by computer simulations of the egress of pedestrians through a narrow exit [D. Helbing, I. J. Farkas, and T. Vicsek, Nature (London) 407, 487 (2000)]. FIS refers to the finding that, under certain conditions, an excess of the individuals' vigor in the attempt to exit causes a decrease in the flow rate. In general, this effect is identified by the appearance of a minimum when plotting the total evacuation time of a crowd as a function of the pedestrian desired velocity. Here, we experimentally show that the FIS effect indeed occurs in three different systems of discrete particles flowing through a constriction: (a) humans evacuating a room, (b) a herd of sheep entering a barn, and (c) grains flowing out a 2D hopper over a vibrated incline. This finding suggests that FIS is a universal phenomenon for active matter passing through a narrowing.

From Mindless Masses to Small Groups: Conceptualizing Collective Behavior in Crowd Modeling

Computer simulations are increasingly used to monitor and predict behavior at large crowd events, such as mass gatherings, festivals and evacuations. We critically examine the crowd modeling literature and call for future simulations of crowd behavior to be based more closely on findings from current social psychological research. A systematic review was conducted on the crowd modeling literature (N = 140 articles) to identify the assumptions about crowd behavior that modelers use in their simulations. Articles were coded according to the way in which crowd structure was modeled. It was found that 2 broad types are used: mass approaches and small group approaches. However, neither the mass nor the small group approaches can accurately simulate the large collective behavior that has been found in extensive empirical research on crowd events. We argue that to model crowd behavior realistically, simulations must use methods which allow crowd members to identify with each other, as suggested by self-categorization theory.

Effects of Switching Behavior for the Attraction on Pedestrian Dynamics

Walking is a fundamental activity of our daily life not only for moving to other places but also for interacting with surrounding environment. While walking on the streets, pedestrians can be aware of attractions like shopping windows. They can be influenced by the attractions and some of them might shift their attention towards the attractions, namely switching behavior. As a first step to incorporate the switching behavior, this study investigates collective effects of switching behavior for an attraction by developing a behavioral model. Numerical simulations exhibit different patterns of pedestrian behavior depending on the strength of the social influence and the average length of stay. When the social influence is strong along with a long length of stay, a saturated phase can be defined at which all the pedestrians have visited the attraction. If the social influence is not strong enough, an unsaturated phase appears where one can observe that some pedestrians head for the attraction while others walk in their desired direction. These collective patterns of pedestrian behavior are summarized in a phase diagram by comparing the number of pedestrians who visited the attraction to the number of passersby near the attraction. Measuring the marginal benefits with respect to the strength of the social influence and the average length of stay enables us to identify under what conditions enhancing these variables would be more effective. The findings from this study can be understood in the context of the pedestrian facility management, for instance, for retail stores.

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.

Continuum modeling of crowd turbulence

With the growth in world population, the density of crowds in public places has been increasing steadily, leading to a higher incidence of crowd disasters at high densities. Recent research suggests that emergent chaotic behavior at high densities-known collectively as crowd turbulence-is to blame. Thus, a deeper understanding of crowd turbulence is needed to facilitate efforts to prevent and plan for chaotic conditions in high-density crowds. However, it has been noted that existing algorithms modeling collision avoidance cannot faithfully simulate crowd turbulence. We hypothesize that simulation of crowd turbulence requires modeling of both collision avoidance and frictional forces arising from pedestrian interactions. Accordingly, we propose a model for turbulent crowd simulation, which incorporates a model for interpersonal stress and acceleration constraints similar to real-world pedestrians. Our simulated results demonstrate a close correspondence with observed metrics for crowd turbulence as measured in known crowd disasters.

Extreme power law in a driven many-particle system without threshold dynamics

We study a one-dimensional system of spatially extended particles, which are attached to regularly spaced locations by means of elastic springs. The particles are assumed to be driven by Gaussian noise and to have dissipative, energy-conserving, or antidissipative (pinball-like) interactions, when the particle density exceeds a critical threshold. While each particle in separation shows a well-behaved behavior characterized by a Gaussian velocity distribution, the interaction of particles at high densities can cause an avalanchelike momentum and energy transfer, which can generate extreme (steep) power laws without a well-defined variance and mean value. Specifically, the velocity variance increases dramatically towards the free boundaries of the driven many-particle system. The model might also have some relevance for better understanding of crowd disasters. Our results suggest that these are most likely caused by passive momentum transfers, not by active pushing.

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.

Predicting pedestrian flow: a methodology and a proof of concept based on real-life data

Building a reliable predictive model of pedestrian motion is very challenging: Ideally, such models should be based on observations made in both controlled experiments and in real-world environments. De facto, models are rarely based on real-world observations due to the lack of available data; instead, they are largely based on intuition and, at best, literature values and laboratory experiments. Such an approach is insufficient for reliable simulations of complex real-life scenarios: For instance, our analysis of pedestrian motion under natural conditions at a major German railway station reveals that the values for free-flow velocities and the flow-density relationship differ significantly from widely used literature values. It is thus necessary to calibrate and validate the model against relevant real-life data to make it capable of reproducing and predicting real-life scenarios. In this work we aim at constructing such realistic pedestrian stream simulation. Based on the analysis of real-life data, we present a methodology that identifies key parameters and interdependencies that enable us to properly calibrate the model. The success of the approach is demonstrated for a benchmark model, a cellular automaton. We show that the proposed approach significantly improves the reliability of the simulation and hence the potential prediction accuracy. The simulation is validated by comparing the local density evolution of the measured data to that of the simulated data. We find that for our model the most sensitive parameters are: the source-target distribution of the pedestrian trajectories, the schedule of pedestrian appearances in the scenario and the mean free-flow velocity. Our results emphasize the need for real-life data extraction and analysis to enable predictive simulations.

Collective dynamics of pedestrians interacting with attractions

In order to investigate collective effects of interactions between pedestrians and attractions, this study extends the social force model. Such interactions lead pedestrians to form stable clusters around attractions, or even to rush into attractions if the interaction becomes stronger. It is also found that for high pedestrian density and intermediate interaction strength, some pedestrians rush into attractions while others move to neighboring attractions. These collective patterns of pedestrian movements or phases and transitions between them are systematically presented in a phase diagram. The results suggest that safe and efficient use of pedestrian areas can be achieved by moderating the pedestrian density and the strength of attractive interaction, for example, in order to avoid situations involving extreme desire for limited resources.

Efficient egress of escaping ants stressed with temperature

In the present work we investigate the egress times of a group of Argentine ants (Linepithema humile) stressed with different heating speeds. We found that the higher the temperature ramp is, the faster ants evacuate showing, in this sense, a group-efficient evacuation strategy. It is important to note that even when the life of ants was in danger, jamming and clogging was not observed near the exit, in accordance with other experiments reported in the literature using citronella as aversive stimuli. Because of this clear difference between ants and humans, we recommend the use of some other animal models for studying competitive egress dynamics as a more accurate approach to understanding competitive egress in human systems.

Least-effort trajectories lead to emergent crowd behaviors

Pedestrian crowds often have been modeled as many-particle systems, usually using computer models known as multiagent simulations. The key challenge in modeling crowds is to develop rules that guide how the particles or agents interact with each other in a way that faithfully reproduces paths and behaviors commonly seen in real human crowds. Here, we propose a simple and intuitive formulation of these rules based on biomechanical measurements and the principle of least effort. We present a constrained optimization method to compute collision-free paths of minimum caloric energy for each agent, from which collective crowd behaviors can be reproduced. We show that our method reproduces common crowd phenomena, such as arching and self-organization into lanes. We also validate the flow rates and paths produced by our method and compare them to those of real-world crowd trajectories.

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.

The walking behaviour of pedestrian social groups and its impact on crowd dynamics

Human crowd motion is mainly driven by self-organized processes based on local interactions among pedestrians. While most studies of crowd behaviour consider only interactions among isolated individuals, it turns out that up to 70% of people in a crowd are actually moving in groups, such as friends, couples, or families walking together. These groups constitute medium-scale aggregated structures and their impact on crowd dynamics is still largely unknown. In this work, we analyze the motion of approximately 1500 pedestrian groups under natural condition, and show that social interactions among group members generate typical group walking patterns that influence crowd dynamics. At low density, group members tend to walk side by side, forming a line perpendicular to the walking direction. As the density increases, however, the linear walking formation is bent forward, turning it into a V-like pattern. These spatial patterns can be well described by a model based on social communication between group members. We show that the V-like walking pattern facilitates social interactions within the group, but reduces the flow because of its “non-aerodynamic” shape. Therefore, when crowd density increases, the group organization results from a trade-off between walking faster and facilitating social exchange. These insights demonstrate that crowd dynamics is not only determined by physical constraints induced by other pedestrians and the environment, but also significantly by communicative, social interactions among individuals.

Axelrod models of social influence with cultural repulsion

Since both attractive and repulsive effects among agents are important in social systems, we present simulations of two models based on Axelrod's homogenization mechanism that includes repulsion. These models are the repulsive model, where all individuals can repel, and the partially repulsive model where only a fraction of repelling agents are considered. In these two models, attractive dynamics is implemented for agents with the ability to repel each other only if the number of features shared by them is greater than a threshold parameter. Otherwise, repelling dynamics is used. In the repulsive model, the transition from a monocultural state to a fragmented one often occurs abruptly from one cultural-variability value to the next one and a second transition emerges. For the partially repulsive model, there are also two different transitions present: the initial one being as abrupt as the one found for the repulsive model, whereas the second one follows a less abrupt behavior and resembles that of the original Axelrod model. However, the second transition for this model occurrs from a partially fragmented state and not from a monocultural one.

Experimental study of the behavioural mechanisms underlying self-organization in human crowds

In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared with bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.

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

We show that keeping a constant lower limit on the net-time headway is the key mechanism behind the dynamics of pedestrian streams. There is a large variety in flow and speed as functions of density for empirical data of pedestrian streams obtained from studies in different countries. The net-time headway, however, stays approximately constant over all these different data sets. By using this fact, we demonstrate how the underlying dynamics of pedestrian crowds, naturally follows from local interactions. This means that there is no need to come up with an arbitrary fit function (with arbitrary fit parameters) as has traditionally been done. Further, by using not only the average density values but the variance as well, we show how the recently reported stop-and-go waves [Helbing, Phys. Rev. E 75, 046109 (2007)] emerge when local density variations take values exceeding a certain maximum global (average) density, which makes pedestrians stop.