Patient and impatient pedestrians in a spatial game for egress congestion

Pedestrians in static crowds are not grains, but game players

The local navigation of pedestrians is assumed to involve no anticipation beyond the most imminent collisions, in most models. These typically fail to reproduce some key features experimentally evidenced in dense crowds crossed by an intruder, namely, transverse displacements toward regions of higher density due to the anticipation of the intruder's crossing. We introduce a minimal model based on mean-field games, emulating agents planning out a global strategy that minimizes their overall discomfort. By solving the problem in the permanent regime thanks to an elegant analogy with the nonlinear Schrödinger's equation, we are able to identify the two main variables governing the model's behavior and to exhaustively investigate its phase diagram. We find that, compared to some prominent microscopic approaches, the model is remarkably successful in replicating the experimental observations associated with the intruder experiment. In addition, the model can capture other daily-life situations such as partial metro boarding.

Measuring Dynamics in Evacuation Behaviour with Deep Learning

Bounded rationality is one crucial component in human behaviours. It plays a key role in the typical collective behaviour of evacuation, in which heterogeneous information can lead to deviations from optimal choices. In this study, we propose a framework of deep learning to extract a key dynamical parameter that drives crowd evacuation behaviour in a cellular automaton (CA) model. On simulation data sets of a replica dynamic CA model, trained deep convolution neural networks (CNNs) can accurately predict dynamics from multiple frames of images. The dynamical parameter could be regarded as a factor describing the optimality of path-choosing decisions in evacuation behaviour. In addition, it should be noted that the performance of this method is robust to incomplete images, in which the information loss caused by cutting images does not hinder the feasibility of the method. Moreover, this framework provides us with a platform to quantitatively measure the optimal strategy in evacuation, and this approach can be extended to other well-designed crowd behaviour experiments.

Twofold effect of self-interest in pedestrian room evacuation

Evacuation dynamics of pedestrians in a square room with one exit is studied. The movement of the pedestrians is guided by the static floor field model. Whenever multiple pedestrians are trying to move to the same target position, a game theoretical framework is introduced to address the conflict. Depending on the payoff matrix, the game that the pedestrians are involved in may be either hawk-dove or prisoner's dilemma, from which the reaped payoffs determine the capacities, or probabilities, of the pedestrians occupying the preferred vacant sites. The pedestrians are allowed to adjust their strategies when competing with others, and a parameter κ is utilized to characterize the extent of their self-interest. It is found that self-interest may induce either positive or negative impacts on the evacuation dynamics depending on whether it can facilitate the formation of collective cooperation in the population or not. Particularly, a resonance-like performance of evacuation is realized in the regime of prisoner's dilemma. The effects of placing an obstacle in front of the exit and the diversity of responses of the pedestrians to the space competition on the evacuation dynamics are also discussed.

Modeling Helping Behavior in Emergency Evacuations Using Volunteer’s Dilemma Game

People often help others who are in trouble, especially in emergency evacuation situations. For instance, during the 2005 London bombings, it was reported that evacuees helped injured persons to escape the place of danger. In terms of game theory, it can be understood that such helping behavior provides a collective good while it is a costly behavior because the volunteers spend extra time to assist the injured persons in case of emergency evacuations. In order to study the collective effects of helping behavior in emergency evacuations, we have performed numerical simulations of helping behavior among evacuees in a room evacuation scenario. Our simulation model is based on the volunteer’s dilemma game reflecting volunteering cost. The game theoretic model is coupled with a social force model to understand the relationship between the spatial and social dynamics of evacuation scenarios. By systematically changing the cost parameter of helping behavior, we observed different patterns of collective helping behaviors and these collective patterns are summarized with a phase diagram.

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.

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.

Statistical fluctuations in pedestrian evacuation times and the effect of social contagion

Mathematical models of pedestrian evacuation and the associated simulation software have become essential tools for the assessment of the safety of public facilities and buildings. While a variety of models is now available, their calibration and test against empirical data are generally restricted to global averaged quantities; the statistics compiled from the time series of individual escapes ("microscopic" statistics) measured in recent experiments are thus overlooked. In the same spirit, much research has primarily focused on the average global evacuation time, whereas the whole distribution of evacuation times over some set of realizations should matter. In the present paper we propose and discuss the validity of a simple relation between this distribution and the microscopic statistics, which is theoretically valid in the absence of correlations. To this purpose, we develop a minimal cellular automaton, with features that afford a semiquantitative reproduction of the experimental microscopic statistics. We then introduce a process of social contagion of impatient behavior in the model and show that the simple relation under test may dramatically fail at high contagion strengths, the latter being responsible for the emergence of strong correlations in the system. We conclude with comments on the potential practical relevance for safety science of calculations based on microscopic statistics.

Spatial game in cellular automaton evacuation model

For numerical simulations of crowd dynamics in an evacuation we need a computationally light environment, such as the cellular automaton model (CA). By choosing the right model parameters, different types of crowd behavior and collective effects can be produced. But the CA does not answer why, when, and how these different behaviors and collective effects occur. In this article, we present a model, where we couple a spatial evacuation game to the CA. In the game, an agent chooses its strategy by observing its neighbors' strategies. The game matrix changes with the distance to the exit as the evacuation conditions develop. In the resulting model, an agent's strategy choice alters the parameters that govern its behavior in the CA. Thus, with our model, we are able to simulate how evacuation conditions affect the behavior of the crowd. Also, we show that some of the collective effects observed in evacuations are a result of the simple game the agents play.

Simulation of counterflow pedestrian dynamics using spheropolygons

Pedestrian dynamic models are typically designed for comfortable walking or slightly congested conditions and typically use a single disk or combination of three disks for the shape of a pedestrian. Under crowd conditions, a more accurate pedestrian shape has advantages over the traditional single or three-disks model. We developed a method for simulating pedestrian dynamics in a large dense crowd of spheropolygons adapted to the cross section of the chest and arms of a pedestrian. Our numerical model calculates pedestrian motion from Newton's second law, taking into account viscoelastic contact forces, contact friction, and ground-reaction forces. Ground-reaction torque was taken to arise solely from the pedestrians' orientation toward their preferred destination. Simulations of counterflow pedestrians dynamics in corridors were used to gain insight into a tragic incident at the Madrid Arena pavilion in Spain, where five girls were crushed to death. The incident took place at a Halloween Celebration in 2012, in a long, densely crowded hallway used as entrance and exit at the same time. Our simulations reconstruct the mechanism of clogging in the hallway. The hypothetical case of a total evacuation order was also investigated. The results highlights the importance of the pedestrians' density and the effect of counterflow in the onset of avalanches and clogging and provides an estimation of the number of injuries based on a calculation of the contact-force network between the pedestrians.

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.

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.