Freezing transition in bi-directional CA model for facing pedestrian traffic

We present a bi-directional cellular automaton (CA) model for facing traffic of pedestrians on a wide passage. The excluded-volume effect and bi-directionality of facing traffic are taken into account. The CA model is not stochastic but deterministic. We study the jamming and freezing transitions when pedestrian density increases. We show that the dynamical phase transitions occur at three stages with increasing density. There exist four traffic states: the free traffic, jammed traffic 1, jammed traffic 2, and frozen state. At the frozen state, all pedestrians stop by preventing from going ahead each other. At three transitions, the pedestrian flow changes from the free traffic through the jammed traffic 1 and jammed traffic 2, to the frozen state.     

A new collision avoidance model for pedestrian dynamics

The pedestrians can only avoid collisions passively under the action of forces during simulations using the social force model, which may lead to unnatural behaviors. This paper proposes an optimization-based model for the avoidance of collisions, where the social repulsive force is removed in favor of a search for the quickest path to destination in the pedestrian's vision field. In this way, the behaviors of pedestrians are governed by changing their desired walking direction and desired speed. By combining the critical factors of pedestrian movement, such as positions of the exit and obstacles and velocities of the neighbors, the choice of desired velocity has been rendered to a discrete optimization problem. Therefore,it is the self-driven force that leads pedestrians to a free path rather than the repulsive force, which means the pedestrians can actively avoid collisions. The new model is verified by comparing with the fundamental diagram and actual data. The simulation results of individual avoidance trajectories and crowd avoidance behaviors demonstrate the reasonability of the proposed model.     

Study on evacuation behaviors at a T-shaped intersection by a force-driving cellular automata model

A force-driving cellular automata model considering the social force on cell movement, such as the desirous willing of a pedestrian to exit, the repulsive interaction among pedestrians or between pedestrians and obstacles, was set up to investigate the evacuation behaviors of pedestrians at a T-shaped intersection. And an analogical formulation, taking reference of the magnetic force, was introduced to describe the above repulsive actions. Based on the model, the evacuation behaviors of pedestrians were simulated in terms of different pedestrian density, distribution and corridor width, and then evacuation time was obtained and analyzed. Furthermore, an experiment was conducted to verify the results of the presented model. The results demonstrate that when the density of pedestrians is greater than a certain threshold, pedestrians of a certain direction would be jammed by the repulsion from pedestrians of the counter flow from another direction, and the evacuation time of the former would be longer, even though they are closer to the exit, which would possibly result in a serious casualty in an emergency circumstance. And the phenomenon has been validated by the experiments well. In addition, a corresponding critical corridor width related to different DOPs, beyond which the evacuation time could be decreased rapidly due to a strong degradation of jamming behaviors near the T-shaped intersection, was also discovered and predicted by the proposed model.     

Dynamics of emotional contagion in dense pedestrian crowds

In places with high-density pedestrian movements, irrational emotions can quickly spread out under emergency, which may eventually lead to asphyxiation and crushing. It was noticed that a pedestrian's emotion in crowd would change as a result of the influence from other pedestrians. Thus, to explore the dynamics of emotion contagion process in dense pedestrians, two types of pedestrian emotions, i.e., negative and positive have been identified. Taking into account the emotional transit of a pedestrian, a crowd movement model is established in the present paper. We simulate pedestrian movement in a region with periodic boundary condition to study the dynamics of emotional contagion in dense crowds. Influences of the initial negative pedestrian proportion, pedestrian crowd density, emotion influence radius, and dose factor on the transition of overall crowd emotion state have been investigated. We expect this study could provide theoretical suggestions for crowd management.     

Crowd-induced random vibration of footbridge and vibration control using multiple tuned mass dampers

This paper investigates vibration characteristics of footbridge induced by crowd random walking, and presents the application of multiple tuned mass dampers (MTMD) in suppressing crowd-induced vibration. A single foot force model for the vertical component of walking-induced force is developed, avoiding the phase angle inaccessibility of the continuous walking force. Based on the single foot force model, the crowd-footbridge random vibration model, in which pedestrians are modeled as a crowd flow characterized with the average time headway, is developed to consider the worst vibration state of footbridge. In this random vibration model, an analytic formulation is developed to calculate the acceleration power spectral density in arbitrary position of footbridge with arbitrary span layout. Resonant effect is observed as the footbridge natural frequencies fall within the frequency bandwidth of crowd excitation. To suppress the excessive acceleration for human normal walking comfort, a MTMD system is used to improve the footbridge dynamic characteristics. According to the random vibration model, an optimization procedure, based on the minimization of maximum root-mean-square (rms) acceleration of footbridge, is introduced to determine the optimal design parameters of MTMD system. Numerical analysis shows that the proposed MTMD designed by random optimization procedure, is more effective than traditional MTMD design methodology in reducing dynamic response during crowd-footbridge resonance, and that the proper frequency spacing enlargement will effectively reduce the off-tuning effect of MTMD.     

基于教室人群疏散实验的行人流建模和模拟

基于教室人群疏散实验, 从中归纳出疏散过程中行人的基本运动特征. 将桌椅分别视为不可穿越和可穿越的静态障碍物, 而行人则被当成可移动的障碍物, 这将导致背景场随人群的运动而动态更新, 因此可以更好地反映前方拥挤程度对后面人群路径选择行为的影响. 采用基于动态背景场的元胞自动机模型研究了不同桌椅排列和出口宽度的教室人群疏散过程, 给出了疏散时间的空间分布以及平均和最大疏散时间, 再现了实验中人群疏散的基本特征. 数值模拟结果表明, 疏散时间取决于桌椅的排列方式和教室出口的宽度. 对于同一种排列, 出口越小则疏散时间越长; 对于给定的出口宽度, 通常随着过道数的增加, 疏散时间随之减少; 当过道数增加且过道宽度不足以两人并行, 从两侧进入过道的行人会发生冲突, 使疏散效率有所降低; 靠近出口一侧墙壁设置过道有利于人群的疏散. 文中进一步分析了模拟与实验结果存在差异的原因.     

Experiment and modeling of exit-selecting behaviors during a building evacuation

The evacuation process in a teaching building with two neighboring exits is investigated by means of experiment and modeling. The basic parameters such as flow, density and velocity of pedestrians in the exit area are measured. The exit-selecting phenomenon in the experiment is analyzed, and it is found that pedestrians prefer selecting the closer exit even though the other exit is only a little far. In order to understand the phenomenon, we reproduce the experiment process with a modified biased random walk model, in which the preference of closer exit is achieved using the drift direction and the drift force. Our simulation results afford a calibrated value of the drift force, especially when it is 0.56, there is good agreement between the simulation results and the experimental results on the number of pedestrians selecting the closer exit, the average velocity through the exits, the cumulative distribution of the instantaneous velocity and the fundamental diagram of the flow through exits. According to the further simulation results, it is found that pedestrians tend to select the exit with shorter distance to them, especially when the people density is small or medium. But if the density is large enough, the flow rates of the two exits will become comparable because of the detour behaviors. It reflects the fact that a crowd of people may not be rational to optimize the usage of multi-exits, especially in an emergency.     

Crowd evacuation of pairs of pedestrians

The crowd evacuation of pairs of pedestrians (i.e. pairs consisting of a parent and a child) is numerically investigated. Here, it is assumed that all pedestrians have their own partners, and move randomly inside the bounded domain of the right-hand room as an initial state. All pedestrians start their evacuations after they contact their partners. The evacuations are completed by the transfer of all the pairs from the right-hand room to the left-hand room through an exit. A frozen swarm tends to appear in the right-hand room as the total number of pedestrians increases. The frozen swarm moves without changing its form, unless it is dissolved by a strong collision with a pair of pedestrians that comes back from the left-hand room by accident. Finally, the evacuation speed also depends on the area of the Escape Zone, whereas an obstacle placed in front of an exit also changes the speed of the evacuation in accordance with the type of motion of the children.     

Visualization of crowd synchronization on footbridges

Abstract  

This paper proposes a framework for the visualization of crowd walking synchronization on footbridges. The bridge is modeled as a mass-spring system, which is a weakly damped and driven harmonic oscillator. Both the bridge and the pedestrians walking on the bridge are affected by the movement of each other. The crowd acts according to local behavioral rules. Each pedestrian is provided with a kinematic walking system. We extend a current mathematical model of crowd synchronization on footbridges to include human walking model and crowd simulation techniques. We run experiments to evaluate the influence of these extensions on synchronization.     

Entropy of jammed matter

We investigate the nature of randomness in disordered packings of frictional spheres. We calculate the entropy of 3D packings through the force and volume ensemble of jammed matter, a mesoscopic ensemble and numerical simulations using volume fluctuation analysis and graph theoretical methods. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter. At the mesoscopic level the entropy vanishes at random close packing, while the microscopic states contribute to a finite entropy. The entropy of the jammed system reveals that the random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits.     

Jamming III: Characterizing randomness via the entropy of jammed matter

The nature of randomness in disordered packings of frictional and frictionless spheres is investigated using theory and simulations of identical spherical grains. The entropy of the packings is defined through the force and volume ensemble of jammed matter and this is shown to be difficult to calculate analytically. A mesoscopic ensemble of isostatic states is then utilized in an effort to predict the entropy through the definition of a volume function that is dependent on the coordination number. Equations of state are obtained relating entropy, volume fraction and compactivity characterizing the different states of jammed matter, and elucidating the phase diagram for jammed granular matter. Analytical calculations are compared to numerical simulations using volume fluctuation analysis and graph theoretical methods, with reasonable agreement. The entropy of the jammed system reveals that random loose packings are more disordered than random close packings, allowing for an unambiguous interpretation of both limits. Ensemble calculations show that the entropy vanishes at random close packing (RCP), while numerical simulations show that a finite entropy remains in the microscopic states at RCP. The notion of a negative compactivity, which explores states with volume fractions below those achievable by existing simulation protocols, is also explored, expanding the equations of state. The mesoscopic theory reproduces the simulations results in shape well, though a difference in magnitude implies that the entire entropy of the packing may not be captured by the methods presented herein. We discuss possible extensions to the present mesoscopic approach describing packings from random loose packing (RLP) to RCP to the ordered branch of the equation of state in an effort to understand the entropy of jammed matter in the full range of densities from RLP to face-centered cubic (FCC) packing.     

Quantitative comparison between crowd models for evacuation planning and evaluation

Crowd simulation is rapidly becoming a standard tool for evacuation planning and evaluation. However, the many crowd models in the literature are structurally different, and few have been rigorously calibrated against real-world egress data, especially in emergency situations. In this paper we describe a procedure to quantitatively compare different crowd models or between models and real-world data. We simulated three models: (1) the lattice gas model, (2) the social force model, and (3) the RVO2 model, and obtained the distributions of six observables: (1) evacuation time, (2) zoned evacuation time, (3) passage density, (4) total distance traveled, (5) inconvenience, and (6) flow rate. We then used the DISTATIS procedure to compute the compromise matrix of statistical distances between the three models. Projecting the three models onto the first two principal components of the compromise matrix, we find the lattice gas and RVO2 models are similar in terms of the evacuation time, passage density, and flow rates, whereas the social force and RVO2 models are similar in terms of the total distance traveled. Most importantly, we find that the zoned evacuation times of the three models to be very different from each other. Thus we propose to use this variable, if it can be measured, as the key test between different models, and also between models and the real world. Finally, we compared the model flow rates against the flow rate of an emergency evacuation during the May 2008 Sichuan earthquake, and found the social force model agrees best with this real data.     

Simulation of evacuation processes using a multi-grid model for pedestrian dynamics

Introducing the force concept of a social force model into the lattice gas (LG) model, a new LG-based discrete model entitled “multi-grid model” is composed. In the new model, finer lattice is used; thus each pedestrian occupies multiple grids instead of one, and the rules of interactions among pedestrians or pedestrians and constructions are built. The interaction forces including extrusion, repulsion and friction are considered as passive factors for evacuation. The strength of the drift, or the intensity of the pedestrians to move toward the exit rapidly, is considered an active factor. A simple situation is studied in which pedestrians try to evacuate from a large room with only one door. The influences of interaction forces and drift on evacuation time are analyzed. The mutual restriction relation of the two factors in the course of evacuating is found.     

Simulation of crowd dynamics in pedestrian evacuation concerning panic contagion: A cellular automaton approach

The study of the panic evacuation process is of great significance to emergency management. Panic not only causes negative emotions such as irritability and anxiety, but also affects the pedestrians decision-making process, thereby inducing the abnormal crowd behavior. Prompted by the epidemiological SIR model, an extended floor field cellular automaton model was proposed to investigate the pedestrian dynamics under the threat of hazard resulting from the panic contagion. In the model, the conception of panic transmission status (PTS) was put forward to describe pedestrians' behavior who could transmit panic emotions to others. The model also indicated the pedestrian movement was governed by the static and hazard threat floor field. Then rules that panic could influence decision-making process were set up based on the floor field theory. The simulation results show that the stronger the pedestrian panic, the more sensitive pedestrians are to hazards, and the less able to rationally find safe exits. However, when the crowd density is high, the panic contagion has a less impact on the evacuation process of pedestrians. It is also found that when the hazard position is closer to the exit, the panic will propagate for a longer time and have a greater impact on the evacuation. The results also suggest that as the extent of pedestrian's familiarity with the environment increases, pedestrians spend less time to escape from the room and are less sensitive to the hazard. In addition, it is essential to point out that, compared with the impact of panic contagion, the pedestrian's familiarity with environment has a more significant influence on the evacuation.     

A least-effort principle based model for heterogeneous pedestrian flow considering overtaking behavior

In the context of global aging, how to design traffic facilities for a population with a different age composition is of high importance. For this purpose, we propose a model based on the least effort principle to simulate heterogeneous pedestrian flow. In the model, the pedestrian is represented by a three-disc shaped agent. We add a new parameter to realize pedestrians' preference to avoid changing their direction of movement too quickly. The model is validated with numerous experimental data on unidirectional pedestrian flow. In addition, we investigate the influence of corridor width and velocity distribution of crowds on unidirectional heterogeneous pedestrian flow. The simulation results reflect that widening corridors could increase the specific flow for the crowd composed of two kinds of pedestrians with significantly different free velocities. Moreover, compared with a unified crowd, the crowd composed of pedestrians with great mobility differences requires a wider corridor to attain the same traffic efficiency. This study could be beneficial in providing a better understanding of heterogeneous pedestrian flow, and quantified outcomes could be applied in traffic facility design.     

Extraction and quantitative analysis of microscopic evacuation characteristics based on digital image processing

In this study, experiments of single-file pedestrian movement were conducted and the movement parameters of pedestrians were extracted with a digital image processing method based on a mean-shift algorithm. The microscopic characteristics of pedestrian dynamics, including velocity, density, and lateral oscillation, as well as their interrelations, were obtained and analyzed. Firstly, we studied the lateral oscillation phenomena of pedestrian movement. The result indicates that the trajectory of pedestrians presents a wavy form and the amplitude of the oscillation remains about 5.5 cm when the pedestrians move with free walking velocity, which is the velocity when there is no obvious interaction between sequential pedestrians; but when the movement velocity decreases to 0.27 m/s, the amplitude of oscillation increases to 13 cm. With increasing density, the velocity decreases and the amplitude of oscillation presents a linear increase trend. The increasing oscillation amplitude widens the occupation area of a pedestrian with low velocity, so as to make the moving efficiency even worse. Secondly, we studied the frequency of the oscillation; the result indicates that the frequency remains at 2 Hz when pedestrians move with a free walking velocity, but it presents a similar linear decrease trend when the velocity changes to a lower value. The decrease of oscillation frequency is also a negative feedback to the moving efficiency. Thirdly, it is found that with the increase of crowd density, the time interval between two sequential pedestrians increases, though the space gap between them decreases. The quantitative relation between time interval and crowd density is obtained. The study in this paper provides fundamental data and a basic method for understanding pedestrian dynamics, developing and validating evacuation models. The results are also expected to be useful for evacuation design.     

Kinetic theory of situated agents applied to pedestrian flow in a corridor

A situated agent-based model for simulation of pedestrian flow in a corridor is presented. In this model, pedestrians choose their paths freely and make decisions based on local criteria for solving collision conflicts. The crowd consists of multiple walking agents equipped with a function of perception as well as a competitive rule-based strategy that enables pedestrians to reach free access areas. Pedestrians in our model are autonomous entities capable of perceiving and making decisions. They apply socially accepted conventions, such as avoidance rules, as well as individual preferences such as the use of specific exit points, or the execution of eventual comfort turns resulting in spontaneous changes of walking speed. Periodic boundary conditions were considered in order to determine the density-average walking speed, and the density-average activity with respect to specific parameters: comfort angle turn and frequency of angle turn of walking agents. The main contribution of this work is an agent-based model where each pedestrian is represented as an autonomous agent. At the same time the pedestrian crowd dynamics is framed by the kinetic theory of biological systems.     

Complex force network in marginally and deeply jammed solids

This paper studies the force network properties of marginally and deeply jammed packings of frictionless soft particlesfrom the perspective of complex network theory. We generate zero-temperature granular packings at different pressures by minimizing the inter-particle potential energy. The force networks are constructed as nodes representing particles and links representing normal forces between the particles. Deeply jammed solids show remarkably different behavior from marginally jammed solids in their degree distribution, strength distribution, degree correlation, and clustering coefficient. Bimodal and multi-modal distributions emerge when the system enters the deep jamming region. The results also show that small and large particles can show different correlation behavior in this simple system.     

Simulating pedestrian flow through narrow exits

Introduction: The flow of pedestrians through narrow doorways is one of the most common features of crowd motions and evacuations. It is particularly an important aspect of pedestrian simulations models since their accuracy depends highly on their ability to produce realistic exit flow rates. The problem has been extensively studied in the literature, but many aspects of it have remained controversial with mixed (and often contradictory) evidence emerging from different studies and different methods. Methods: We discuss the significance of parameter calibration for accurate simulation of pedestrian flow through narrow exits using social force model. Based on sensitivity analyses, we show how simulated exit throughput rate can vastly differ by changing the value of certain parameters. We identify the two parameters that are most critical, and then calibrate them based on a set of experimental observations (at macro level). Using these calibrated parameters, we then re-examine three fundamental questions related to pedestrian flow at bottlenecks, (1) the relation between desired velocity and simulated egress time; (2) the effect of barricade at exits; and (3) the effect of exit in the corner versus the middle. Results: Our numerical analyses showed that, with the calibrated parameters, increasing the desired velocity in the social-force model results in monotonically shorter egress times (at a marginal rate that rapidly diminishes as the desired velocity increases). We showed that placing a panel-like barricade at exit can facilitate the outflow and reduces the egress time, but its effect depends on the widths of exit, as well as the size of the barricade and its distance to exit. We show that the positioning the exit in the corner is also effective in terms of reducing egress time, but only for very narrow exits. The benefit diminishes quickly as the exit becomes wider. Applications: These outcomes demonstrated the significance of parameter calibration for accurate simulation of crowd flows. The findings may also help to identify simple modifications that can facilitate crowd flows at narrow bottlenecks.