Centrifugal force model for pedestrian dynamics

Polarised crowd in motion: insights into statistical and dynamical behavior

The collection of active agents often exhibits intriguing statistical and dynamical properties, particularly when considering human crowds. In this study, we have developed a computational model to simulate the recent experiment on real marathon races by Bain et al. (Science 363:46-49, 2019). Our primary goal is to investigate the impact of race staff on crowd dynamics. By comparing simulated races with and without the presence of race staff, our study reveals that the local velocity and density of participants display a wave pattern akin to real races for both the cases. The observed traveling wave in the crowd consistently propagates at a constant speed, regardless of the system size under consideration. The participants' dynamics in the longitudinal direction primarily contribute to velocity fluctuations, while fluctuations in the transverse direction are suppressed. In the absence of race staff, density and velocity fluctuations weaken without significantly affecting other statistical and dynamic characteristics of the crowd. Through this research, we aim to deepen our understanding of crowd motion, providing insights that can inform the development of effective crowd management strategies and contribute to the successful control of such events.

Relative rate of expansion controls speed in one-dimensional pedestrian following

Patterns of crowd behavior are believed to result from local interactions between pedestrians. Many studies have investigated the local rules of interaction, such as steering, avoiding, and alignment, but how pedestrians control their walking speed when following another remains unsettled. Most pedestrian models assume the physical speed and distance of others as input. The present study compares such "omniscient" models with "visual" models based on optical variables. We experimentally tested eight speed control models from the pedestrian- and car-following literature. Walking participants were asked to follow a leader (a moving pole) in a virtual environment, while the leader's speed was perturbed during the trial. In Experiment 1, the leader's initial distance was varied. Each model was fit to the data and compared. The results showed that visual models based on optical expansion (\(\dot{\theta }\)) had the smallest root mean square error in speed across conditions, whereas other models exhibited increased error at longer distances. In Experiment 2, the leader's size (pole diameter) was varied. A model based on the relative rate of expansion (\(\dot{\theta }/\theta \)) performed better than the expansion rate model (\(\dot{\theta }\)), because it is less sensitive to leader size. Together, the results imply that pedestrians directly control their walking speed in one-dimensional following using relative rate of expansion, rather than the distal speed and distance of the leader.

How do classroom-turnover times depend on lecture-hall size?

Academic spaces in colleges and universities span classrooms for 10 students to lecture halls that hold over 600 people. During the break between consecutive classes, students from the first class must leave and the new class must find their desks, regardless of whether the room holds 10 or 600 people. Here we address the question of how the size of large lecture halls affects classroom-turnover times, focusing on non-emergency settings. By adapting the established social-force model, we treat students as individuals who interact and move through classrooms to reach their destinations. We find that social interactions and the separation time between consecutive classes strongly influence how long it takes entering students to reach their desks, and that these effects are more pronounced in larger lecture halls. While the median time that individual students must travel increases with decreased separation time, we find that shorter separation times lead to shorter classroom-turnover times overall. This suggests that the effects of scheduling gaps and lecture-hall size on classroom dynamics depends on the perspective-individual student or whole class-that one chooses to take.

An Exploration of the Multiplicative Effect of "Other People" and Other Environmental Effects on Violence in the Night-Time Environment

BACKGROUND

The characteristics of night-time environments (NTEs) in which alcohol is consumed and that contribute to violence are poorly described. We explore competing explanations for violence in the NTE, with a particular focus on the number of patrons and its association with assault-related visits to a hospital emergency department. Other environmental features including the weather and notable events were also considered. The primary aim was to stimulate debate around the causal mechanisms responsible for violence.

METHODS

Assault-related ED visits occurring between 8 pm and 4 am were recorded at the University Hospital of Wales, the single Emergency Department (ED) serving Cardiff, Wales, United Kingdom. Footfall was derived from the total number of unique MAC addresses recorded per hour collected from ten wireless fidelity monitoring tools located in the city centre. A narrative review of the literature concerning alcohol and violence informed exploratory analyses into the association between night-time footfall, sporting events, the weather, and other potential predictors of assault-related visits to the ED. We developed analytic methods from formal accounts of queueing.

RESULTS

International rugby matches at home, the weather (temperature), national holidays, the day of the week, and number of patrons in the NTE predicted assault-related injury (R² = 0.70), with footfall yielding a positive non-linear exponential association consistent with predictions derived from mathematical models of queueing.

DISCUSSION

Assault-related visits to the ED have a non-linear association with the number of people socialising in the night-time environment and are further influenced by the weather and notable events. Opportunities for further research that might inform policy and interventions aimed at better managing NTEs are discussed.

Questioning the Anisotropy of Pedestrian Dynamics: An Empirical Analysis with Artificial Neural Networks

Identifying the factors that control the dynamics of pedestrians is a crucial step towards modeling and building various pedestrian-oriented simulation systems. In this article, we empirically explore the influential factors that control the single-file movement of pedestrians and their impact. Our goal in this context is to apply feed-forward neural networks to predict and understand the individual speeds for different densities of pedestrians. With artificial neural networks, we can approximate the fitting function that describes pedestrians’ movement without having modeling bias. Our analysis is focused on the distances and range of interactions across neighboring pedestrians. As indicated by previous research, we find that the speed of pedestrians depends on the distance to the predecessor. Yet, in contrast to classical purely anisotropic approaches—which are based on vision fields and assume that the interaction mainly depends on the distance in front—our results demonstrate that the distance to the follower also significantly influences movement. Using the distance to the follower combined with the subject pedestrian’s headway distance to predict the speed improves the estimation by 18% compared to the prediction using the space in front alone.

Real-Time Evacuation Strategy Based on Cell-Inspired Simulation Model

During the evacuation process in an emergency, the route conditions usually change instantaneously, which makes routing selection a challenging work. To describe dynamic changes in the evacuation environment, this work proposes a real-time evacuation strategy based on a comprehensive route constraint in the framework of a cell-inspired simulation model, intelligence decision P system (IDPS). In our model, the comprehensive route constraint is formed to describe more complex road condition information including the total distance, congestion state, and unreliability of the route. Meanwhile, the IDPS model has been further improved in both the knowledge base description and the decision-making ability. Experiments are conducted to simulate five different scenarios in a fire evacuation. The results show that the evacuation strategy with a comprehensive route constraint has a significant improvement in the evacuation efficiency and has higher robustness. Which kind of route condition should be emphasized more in different evacuation scenarios is also analyzed.

A microscopic approach to study the onset of a highly infectious disease spreading

We combine a pedestrian dynamics model with a contact tracking method to simulate the initial spreading of a highly infectious airborne disease in a confined environment. We focus on a medium size population (up to 1000 people) with a small number of infectious people (1 or 2) and the rest of the people are divided between immune and susceptible. We adopt a space-continuous model that represents pedestrian dynamics by the forces acting on them, i.e. a microscopic force-based model. Once discretized, the model results in a high-dimensional system of second order ordinary differential equations. Before adding the contact tracking to the pedestrian dynamics model, we calibrate the model parameters, compare the model results against empirical data, and show that pedestrian self-organization into lanes can be captured. We consider an explicit approach for contact tracking by introducing a sickness domain around a sick person. A healthy but susceptible person who remains in the sickness domain for a certain amount of time may get infected (with a prescribed probability) and become a so-called secondary contact. As a concrete setting to simulate the onset of disease spreading, we consider terminals in two US airports: Hobby Airport in Houston and the Atlanta International Airport. We consider different scenarios and we quantify the increase in average number of secondary contacts as a given terminal becomes more densely populated, the percentage of immune people decreases, the number of primary contacts increases, and areas of high density (such as the boarding buses) are present.

General scaling in bidirectional flows of self-avoiding agents

The analysis of the classical radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. A formal extension of this approach has revealed recently the existence of a universal scaling in the collective spatial patterns of pedestrians, characterized by an effective potential of interaction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V(\tau )$$\end{document}V(τ) conveniently defined in the space of the times-to-collision \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\boldsymbol{\tau }}$$\end{document}τ between the individuals. Here we significantly extend and clarify this idea by exploring numerically the emergence of that scaling for different scenarios. In particular, we compare the results of bidirectional flows when completely different rules of self-avoidance between individuals are assumed (from physical-like repulsive potentials to standard heuristic rules commonly used to reproduce pedestrians dynamics). We prove that all the situations lead to a common scaling in the t-space both in the disordered phase (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V(\tau ) \sim {\tau }^{-2}$$\end{document}V(τ)~τ−2) and in the lane-formation regime (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$V(\tau ) \sim {\tau }^{-1}$$\end{document}V(τ)~τ−1), independent of the nature of the interactions considered. Our results thus suggest that these scalings cannot be interpreted as a proxy for how interactions between pedestrians actually occur, but they rather represent a common feature for bidirectional flows of self-avoiding agents.

Simulation of Passenger Evacuation Process in Cruise Ships Based on A Multi-Grid Model

The evacuation of the cruise ship is directly related to the safety of passengers during accidents. The method for avoiding and reducing casualties in accidents has become a research frontier of maritime safety. This paper presents the simulation of a passenger evacuation process using a multi-grid model. In the model, directions of passengers’ movement are extended and the relationship between passengers’ orientation and the walking speed under the inclining condition is also analyzed in detail. Considering the space layout, the attraction of the mainstream crowd and exclusion between individuals, the probability of passengers’ transfer between grids is established. The deck of the cruise ship is taken as the evacuation scenario and four parameters are defined for the scenario according to International Maritime Organization (IMO) guidelines. The process of evacuation in the cruise ship is simulated under upright and inclining conditions. Through the analysis of simulation results, evacuation bottleneck data and the relation between inclined angles and evacuation time are obtained. This work may provide a reference for formulating emergency evacuation plans for cruise ships.

Social forces for team coordination in ball possession game

Team coordination is a basic human behavioral trait observed in many real-life communities. To promote teamwork, it is important to cultivate social skills that elicit team coordination. In the present work, we consider which social skills are indispensable for individuals performing a ball possession game in soccer. We develop a simple social force model that describes the synchronized motion of offensive players. Comparing the simulation results with experimental observations, we uncovered that the cooperative social force, a measure of perception skill, has the most important role in reproducing the harmonized collective motion of experienced players in the task. We further developed an experimental tool that facilitates real players' perceptions of interpersonal distance, revealing that the tool improves novice players' motions as if the cooperative social force were imposed.

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.

Walking Ahead: The Headed Social Force Model

Human motion models are finding an increasing number of novel applications in many different fields, such as building design, computer graphics and robot motion planning. The Social Force Model is one of the most popular alternatives to describe the motion of pedestrians. By resorting to a physical analogy, individuals are assimilated to point-wise particles subject to social forces which drive their dynamics. Such a model implicitly assumes that humans move isotropically. On the contrary, empirical evidence shows that people do have a preferred direction of motion, walking forward most of the time. Lateral motions are observed only in specific circumstances, such as when navigating in overcrowded environments or avoiding unexpected obstacles. In this paper, the Headed Social Force Model is introduced in order to improve the realism of the trajectories generated by the classical Social Force Model. The key feature of the proposed approach is the inclusion of the pedestrians’ heading into the dynamic model used to describe the motion of each individual. The force and torque representing the model inputs are computed as suitable functions of the force terms resulting from the traditional Social Force Model. Moreover, a new force contribution is introduced in order to model the behavior of people walking together as a single group. The proposed model features high versatility, being able to reproduce both the unicycle-like trajectories typical of people moving in open spaces and the point-wise motion patterns occurring in high density scenarios. Extensive numerical simulations show an increased regularity of the resulting trajectories and confirm a general improvement of the model realism.

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.

Panic escape polyethism in worker and soldier Coptotermes formosanus (Isoptera: Rhinotermitidae)

Termites were the first animal to form societies. Two hundred million years of evolution provide for a multitude of innate social behaviors that can be experimentally dissected. These fine-tuned patterns of behavior are especially interesting when observing group decision making in the panic mode. In this study, we examined behavioral patterns of termites under panic conditions to gain insight into how an escape flow self-organizes. One hundred worker and 10 soldier Coptotermes formosanus were released into agar plates. After a disturbance was created most workers followed each other and ran along the wall of dishes, thus forming a unidirectional escape flow, whereas soldiers showed a significantly higher frequency of moving to the center of the arena or on periphery of the escape flow as compared to workers. Agonistic behavior was usually observed as soldiers moved to center or periphery. This is the first report on the behavioral repertoire of termites when panicked, with details on the behavioral polymorphism of workers and soldiers during an escape.

Jamming transitions in force-based models for pedestrian dynamics

Force-based models describe pedestrian dynamics in analogy to classical mechanics by a system of second order ordinary differential equations. By investigating the linear stability of two main classes of forces, parameter regions with unstable homogeneous states are identified. In this unstable regime it is then checked whether phase transitions or stop-and-go waves occur. Results based on numerical simulations show, however, that the investigated models lead to unrealistic behavior in the form of backwards moving pedestrians and overlapping. This is one reason why stop-and-go waves have not been observed in these models. The unrealistic behavior is not related to the numerical treatment of the dynamic equations but rather indicates an intrinsic problem of this model class. Identifying the underlying generic problems gives indications how to define models that do not show such unrealistic behavior. As an example we introduce a force-based model which produces realistic jam dynamics without the appearance of unrealistic negative speeds for empirical desired walking speeds.

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.

Obstacle optimization for panic flow--reducing the tangential momentum increases the escape speed

A disastrous form of pedestrian behavior is a stampede occurring in an event involving a large crowd in a panic situation. To deal with such stampedes, the possibility to increase the outflow by suitably placing a pillar or some other shaped obstacles in front of the exit has been demonstrated. We present a social force based genetic algorithm to optimize the best design of architectural entities to deal with large crowds. Unlike existing literature, our simulation results indicate that appropriately placing two pillars on both sides but not in front of the door can maximize the escape efficiency. Human experiments using 80 participants correspond well with the simulations. We observed a peculiar property named tangential momentum, the escape speed and the tangential momentum are found to be negatively correlated. The idea to reduce the tangential momentum has practical implications in crowd architectural design.

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.

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.

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.

Navigation and steering for autonomous virtual humans

The ever-increasing applicability of interactive virtual worlds in industry and academia has given rise to the need for robust, versatile autonomous virtual humans to inject life into these environments. There are two fundamental problems that must be addressed to produce functional, purposeful autonomous populaces: (1)Navigation: finding a collision-free global path from an agent's start position to its target in large complex environments, and (2) Steering: moving an agent along the path while avoiding static and dynamic threats such as other agents. In this review, we survey the large body of contributions in steering and navigation for autonomous agents in dynamic virtual worlds. We describe the benefits and limitations of different proposed solutions and identify potential future research directions to meet the needs for the next generation of interactive virtual world applications. WIREs Cogn Sci 2013, 4:263-272. doi: 10.1002/wcs.1223 For further resources related to this article, please visit the WIREs website.

Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here, we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, either empirically or theoretically. As basis for a quantitative analysis, we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows us to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore, an anticipation mechanism is introduced which reduces the jamming probability.

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.

Continuous-space automaton model for pedestrian dynamics

An off-lattice automaton for modeling pedestrian dynamics is presented. Pedestrians are represented by disks with variable radius that evolve following predefined rules. The key feature of our approach is that although positions and velocities are continuous, forces do not need to be calculated. This has the advantage that it allows using a larger time step than in force-based models. The room evacuation problem and circular racetrack simulations quantitatively reproduce the available experimental data, both for the specific flow rate and for the fundamental diagram of pedestrian traffic with an outstanding performance. In this last case, the variation of two free parameters (r(min) and r(max)) of the model accounts for the great variety of experimental fundamental diagrams reported in the literature. Moreover, this variety can be interpreted in terms of these model parameters.

Generalized centrifugal-force model for pedestrian dynamics

A spatially continuous force-based model for simulating pedestrian dynamics is introduced which includes an elliptical volume exclusion of pedestrians. We discuss the phenomena of oscillations and overlapping which occur for certain choices of the forces. The main intention of this work is the quantitative description of pedestrian movement in several geometries. Measurements of the fundamental diagram in narrow and wide corridors are performed. The results of the proposed model show good agreement with empirical data obtained in controlled experiments.

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.

Analysis of pedestrian dynamics in counter flow via an extended lattice gas model

The modeling of human behavior is an important approach to reproduce realistic phenomena for pedestrian flow. In this paper, an extended lattice gas model is proposed to simulate pedestrian counter flow under the open boundary conditions by considering the human subconscious behavior and different maximum velocities. The simulation results show that the presented model can capture some essential features of pedestrian counter flows, such as lane formation, segregation effect, and phase separation at higher densities. In particular, an interesting feature that the faster walkers overtake the slower ones and then form a narrow-sparse walkway near the central partition line is discovered. The phase diagram comparison and analysis show that the subconscious behavior plays a key role in reducing the occurrence of jam cluster. The effects of the symmetrical and asymmetrical injection rate, different partition lines, and different combinations of maximum velocities on pedestrian flow are investigated. An important conclusion is that it is needless to separate faster and slower pedestrians in the same direction by a partition line. Furthermore, the increase of the number of faster walkers does not always benefit the counter flow in all situations. It depends on the magnitude and asymmetry of injection rate. And at larger maximum velocity, the obtained critical transition point corresponding to the maximum flow rate of the fundamental diagram is in good agreement with the empirical results.

Modeling crowd turbulence by many-particle simulations

A recent study [D. Helbing, A. Johansson, and H. Z. Al-Abideen, Phys. Rev. E 75, 046109 (2007)] has revealed a "turbulent" state of pedestrian flows, which is characterized by sudden displacements and causes the falling and trampling of people. However, turbulent crowd motion is not reproduced well by current many-particle models due to their insufficient representation of the local interactions in areas of extreme densities. In this contribution, we extend the repulsive force term of the social force model to reproduce crowd turbulence. We perform numerical simulations of pedestrians moving through a bottleneck area with this model. The transitions from laminar to stop-and-go and turbulent flows are observed. The empirical features characterizing crowd turbulence, such as the structure function and the probability density function of velocity increments, are reproduced well; i.e., they are well compatible with an analysis of video data during the annual Muslim pilgrimage.

Dynamics of crowd disasters: an empirical study

Many observations of the dynamics of pedestrian crowds, including various self-organization phenomena, have been successfully described by simple many-particle models. For ethical reasons, however, there is a serious lack of experimental data regarding crowd panic. Therefore, we have analyzed video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006. They reveal two subsequent, sudden transitions from laminar to stop-and-go and "turbulent" flows, which question many previous simulation models. While the transition from laminar to stop-and-go flows supports a recent model of bottleneck flows [D. Helbing, Phys. Rev. Lett. 97, 168001 (2006)], the subsequent transition to turbulent flow is not yet well understood. It is responsible for sudden eruptions of pressure release comparable to earthquakes, which cause sudden displacements and the falling and trampling of people. The insights of this study into the reasons for critical crowd conditions are important for the organization of safer mass events. In particular, they allow one to understand where and when crowd accidents tend to occur. They have also led to organizational changes, which have ensured a safe Hajj in 1427H.

Analytical approach to continuous and intermittent bottleneck flows

We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an asymptotic stationary solution. If the inflow is above this value, we observe queue formation, which can be described by a shock wave equation. We also address the experimental observation of intermittent outflows, taking into account the lack of space in the merging zone by a minimum function and coordination problems by a stochastic variable. This results in avalanches of different sizes even if friction, force networks, inelastic collapse, or delay-induced stop-and-go waves are not assumed. Our intermittent flows result from a random alternation between particle propagation and gap propagation. Erratic flows in congested merging zones of vehicle traffic may be explained in a similar way.