Discrete element crowd model for pedestrian evacuation through an exit

A series of accidents caused by crowds within the last decades evoked a lot of scientific interest in modeling the movement of pedestrian crowds. Based on the discrete element method, a granular dynamic model, in which the human body is simplified as a self-driven sphere, is proposed to simulate the characteristics of crowd flow through an exit. In this model, the repulsive force among people is considered to have an anisotropic feature, and the physical contact force due to body deformation is quantified by the Hertz contact model. The movement of the human body is simulated by applying the second Newton's law. The crowd flow through an exit at different desired velocities is studied and simulation results indicated that crowd flow exhibits three distinct states, i.e., smooth state, transition state and phase separation state. In the simulation, the clogging phenomenon occurs more easily when the desired velocity is high and the exit may as a result be totally blocked at a desired velocity of 1.6 m/s or above, leading to faster-to-frozen effect.     

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.     

Simulation of pedestrian evacuation with asymmetrical exits layout

A simulation of pedestrian evacuation from a room with asymmetrical exit layout is presented based on the improved Dynamic Parameter Model in this paper. A special technique is introduced to compute two basic dynamic parameters: Direction-parameter and Empty-parameter considering the effects of pedestrian jam around exits and the width of exits on evacuation path selection in order to reduce evacuation imbalance caused by the asymmetry of exits layout. Two new coefficients: cognition coefficient and imbalance coefficient are introduced to respectively describe pedestrian cognitive ability and the layout imbalance of exits. The simulation results of the improved and original models are compared and analyzed. Simulation results show that evacuation time depends on the cognition coefficient and imbalance coefficient under normal evacuation condition with reasonable pedestrian. It is also found that there are phase transitions and critical points in the simulation curves of evacuation time against cognition coefficient and that the pedestrian flow shows distinctive characteristics at different phases. The values of critical cognition coefficient points depend on the initial pedestrian density and imbalance coefficient.     

Effect of exit location on flow of mice under emergency condition

The evacuation of crowds in a building has always emerged as a vital issue in many accidents. The geometrical structure of a room, especially the exit design has a great influence on crowd evacuation under emergency conditions. In this paper, the effect of exit location of a room on crowd evacuation in an emergency is investigated with mice. Two different exits are set in a rectangular chamber. One is located in the middle of a wall(middle-exit) and the other is at the corner of the chamber(corner-exit). Arching and clogging are observed in the flow of mice. The result based on the escape trajectories of mice shows a dynamic balance in the arch near the exit wherever the exit is located. We demonstrate that the occupant position in the arch has an effect on the escape sequence of mice. At a low stimulation level, the narrow middle-exit is more effective in increasing the flow rate of mice than the narrow corner-exit. However, the opposite result appears when the exit becomes wider. At a high stimulation level, the effect of exit location on flow of mice tends to be weakened. The results suggest that the specific level of stimulation needs to be taken into account when optimizing the evacuation efficiency of a crowd through the geometrical structure of a room.     

基于元胞自动机的行人疏散流仿真研究

基于元胞自动机对行人疏散流进行仿真研究.模型利用两个动态参数反映行人移动区域内的疏散情况,从而决定行人的行为选择.模型中行人可以根据自身周围的情况选择移动、等待行为.本文仿真研究了行人在正常疏散环境下,系统规模、疏散人数、安全出口宽度、多个安全出口布局对行人疏散时间的影响.研究结果表明,行人疏散时间随行人数量呈线性增加;随安全出口宽度呈负指数性减少;同时,多个安全出口布局的不平衡也会对行人的疏散过程和疏散时间产生一定的影响. 关键词： 元胞自动机 行人疏散流 动态参数 疏散时间     

A numerical study of contact force in competitive evacuation

Crowd force by the pushing or crushing of people has resulted in a number of accidents in recent decades. The aftermath investigations have shown that the physical interaction of a highly competitive crowd could produce dangerous pressure up to 4500 N/m, which leads to compressive asphyxia or even death. In this paper, a numerical model based on discrete element method(DEM) as referenced from granular flow was proposed to model the evacuation process of a group of highly competitive people, in which the movement of people follows Newton's second law and the body deformation due to compression follows Hertz contact model. The study shows that the clogs occur periodically and flow rate fluctuates greatly if all people strive to pass through a narrow exit at high enough desired velocity. Two types of contact forces acting on people are studied. The first one, i.e., vector contact force, accounts for the movement of the people following Newton's second law. The second one, i.e., scale contact force, accounts for the physical deformation of the human body following the contact law. Simulation shows that the forces chain in crowd flow is turbulent and fragile. A few narrow zones with intense forces are observed in the force field, which is similar to the strain localization observed in granular flow. The force acting on a person could be as high as 4500 N due to force localization, which may be the root cause of compressive asphyxia of people in many crowd incidents.     

Effect of a static pedestrian as an exit obstacle on evacuation

Building exit as a bottleneck structure is the last and the most congested stage in building evacuation. It is well known that obstacles at the exit affect the evacuation process, but few researchers pay attention to the effect of stationary pedestrians (the elderly with slow speed, the injured, and the static evacuation guide) as obstacles at the exit on the evacuation process. This paper explores the influence of the presence of a stationary pedestrian as an obstacle at the exit on the evacuation from experiments and simulations. We use a software, Pathfinder, based on the agent-based model to study the effect of ratios of exit width ($D$) to distance ($d$) between the static pedestrian and the exit, the asymmetric structure by shifting the static pedestrian upward, and types of obstacles on evacuation. Results show that the evacuation time of scenes with a static pedestrian is longer than that of scenes with an obstacle due to the unexpected hindering effect of the static pedestrian. Different ratios of $D/d$ have different effects on evacuation efficiency. Among the five $D/d$ ratios in this paper, the evacuation efficiency is the largest when $d$ is equal to $0.75D$, and the existence of the static pedestrian has a positive impact on evacuation in this condition. The influence of the asymmetric structure of the static pedestrian on evacuation efficiency is affected by $D/d$. This study can provide a theoretical basis for crowd management and evacuation plan near the exit of complex buildings and facilities.     

Microscopic information processing and communication in crowd dynamics

Due, perhaps, to the historical division of crowd dynamics research into psychological and engineering approaches, microscopic crowd models have tended toward modelling simple interchangeable particles with an emphasis on the simulation of physical factors. Despite the fact that people have complex (non-panic) behaviours in crowd disasters, important human factors in crowd dynamics such as information discovery and processing, changing goals and communication have not yet been well integrated at the microscopic level. We use our Microscopic Human Factors methodology to fuse a microscopic simulation of these human factors with a popular microscopic crowd model. By tightly integrating human factors with the existing model we can study the effects on the physical domain (movement, force and crowd safety) when human behaviour (information processing and communication) is introduced.In a large-room egress scenario with ample exits, information discovery and processing yields a crowd of non-interchangeable individuals who, despite close proximity, have different goals due to their different beliefs. This crowd heterogeneity leads to complex inter-particle interactions such as jamming transitions in open space; at high crowd energies, we found a freezing by heating effect (reminiscent of the disaster at Central Lenin Stadium in 1982) in which a barrier formation of naïve individuals trying to reach blocked exits prevented knowledgeable ones from exiting. Communication, when introduced, reduced this barrier formation, increasing both exit rates and crowd safety.     

Exit selection strategy in pedestrian evacuation simulation with multi-exits

A mixed strategy of the exit selection in a pedestrian evacuation simulation with multi-exits is constructed by fusing the distance-based and time-based strategies through a cognitive coefficient, in order to reduce the evacuation imbalance caused by the asymmetry of exits or pedestrian layout, to find a critical density to distinguish whether the strategy of exit selection takes effect or not, and to analyze the exit selection results with different cognitive coefficients. The strategy of exit selection is embedded in the computation of the shortest estimated distance in a dynamic parameter model, in which the concept of a jam area layer and the procedure of step-by-step expending are introduced. Simulation results indicate the characteristics of evacuation time gradually varying against cognitive coefficient and the effectiveness of reducing evacuation imbalance caused by the asymmetry of pedestrian or exit layout. It is found that there is a critical density to distinguish whether a pedestrian jam occurs in the evacuation and whether an exit selection strategy is in effect. It is also shown that the strategy of exit selection has no effect on the evacuation process in the no-effect phase with a low density, and that evacuation time and exit selection are dependent on the cognitive coefficient and pedestrian initial density in the in-effect phase with a high density.     

A higher-order macroscopic model for pedestrian flows

This paper develops a higher-order macroscopic model of pedestrian crowd dynamics derived from fluid dynamics that consists of two-dimensional Euler equations with relaxation. The desired directional motion of pedestrians is determined by an Eikonal-type equation, which describes a problem that minimizes the instantaneous total walking cost from origin to destination. A linear stability analysis of the model demonstrates its ability to describe traffic instability in crowd flows. The algorithm to solve the macroscopic model is composed of a splitting technique introduced to treat the relaxation terms, a second-order positivity-preserving central-upwind scheme for hyperbolic conservation laws, and a fast-sweeping method for the Eikonal-type equation on unstructured meshes. To test the applicability of the model, we study a challenging pedestrian crowd flow problem of the presence of an obstruction in a two-dimensional continuous walking facility. The numerical results indicate the rationality of the model and the effectiveness of the computational algorithm in predicting the flux or density distribution and the macroscopic behavior of the pedestrian crowd flow. The simulation results are compared with those obtained by the two-dimensional Lighthill-Whitham-Richards pedestrian flow model with various model parameters, which further shows that the macroscopic model is able to correctly describe complex phenomena such as “stop-and-go waves” observed in empirical pedestrian flows.     

Lattice gas simulation and experiment study of evacuation dynamics

In this paper, evacuation dynamics in an office building is studied by experiment and simulation. A lattice gas (LG) model is developed. A parameter called ‘exit bias’ is introduced into the model to describe the occupants’ familiarity with different exits in a building. The evacuation experiment, which consists of seven scenarios under various conditions, is conducted to verify the model and calibrate the model’s input parameters such as pedestrian speed and exit bias. The effect of exit width on flow rate, and the effect of occupants’ familiarity with the building on their route selections, are studied. It is found that the accuracy of simulation depends a lot on the model’s pedestrian speed. The optimal pedestrian speed is decided by not only occupant characteristics, but also flow features determined by people distribution, building structure, environment pressure, etc. LG models with proper pedestrian speed are capable of simulating the dynamic process of orderly emergency evacuations.     

Discretization effect in a multi-grid egress model

In the traditional egress model based on cellular automata, building spaces are divided into discrete grids, the size of which is usually as large as that of a pedestrian. In order to explore the influences of the grid size on the evacuation results, we studied the evacuation process using a multi-grid egress model. In the multi-grid model, a finer grid is used and each pedestrian occupies n×n basic grids. It is found that if the pedestrian always moves one grid at each time step, the evacuation time increases with the decrease of the grid size, and reaches a stable, grid-independent value when the grid size is small enough. Another factor which influences the evacuation results is the length of the time step. It is found that with the increasing length of the time step, the evacuation time has a tendency to increase but endures complex changes. The differences between the single-grid model and multi-grid model may be due to two main reasons. First, in the multi-grid model, the pedestrians are out of alignment so that there are patches of unusable empty spaces as they are smaller in size than a pedestrian. Second, in the multi-grid model, pedestrians tend to reach the exit at the same time, leading to more serious conflicts among pedestrians.     

Required width of exit to avoid the faster-is-slower effect in highly competitive evacuation

A group of competitive people escaping through an exit could lead to the formation of a deadlock, which significantly increases the evacuation time. Such a phenomenon is called the faster-is-slower effect(FIS) and it has been experimentally verified in different systems of particles flowing through an opening. In this paper, the numerical simulation based on discrete element method(DEM) is adopted to study a group of highly competitive people through an exit of varying widths. The FIS effect is observed for a narrow exit whilst it is not observed for the exit wide enough to accommodate two people through it side-by-side. Experimental validation of such a phenomenon with humans is difficult due to ethical issues. The mouse is a kind of self-driven and soft-body creature and it exhibits selfish behaviour under stressed conditions.Particles flowing through an opening in different systems, such as pedestrian flow, animal flow, silo flow, etc. have similar characteristics. Therefore, experimental study is conducted by driving mice to escape through an exit of different widths at varying levels of stimulus. The escape time through a narrow exit(i.e., 2 cm) increases obviously with the increase of stimulus level but it is quite opposite to a wider exit(i.e., 4 cm). The FIS effect is avoided for an exit wide enough to accommodate two mice passing through it side-by-side. The study illustrates that FIF effect could be effectively prevented for an exit when its width is twice the size of particles.     

An extended model for describing pedestrian evacuation under the threat of artificial attack

An extended floor field model was proposed to investigate evacuation behaviors of pedestrians under the threat of artificial attack. In this model, pedestrian movement governed by the static and dynamic floor field, and the motion and assault of artificial attacker were involved simultaneously. Further, injuries with lower velocity and deaths of pedestrians caused by the attacker during evacuation were considered. And a new parameter $k_t$ was introduced. It is the sensitivity coefficient of attack threat floor field and could reflect quantitatively the extent of effect of attack threat on the decision-making of the individual. Moreover, effects of several key parameters such as the sensitivity coefficient, assault intensity and pedestrian density on evacuation dynamics were studied. Results show that pedestrian evacuation would display interesting phenomena transiting from rolling behavior to along-the-wall motion with aggravating extent of the impact of attackers on pedestrians, which refers $k_t$ in the model varying from 0.5 to 0.8. As assault intensity increases, more casualties would be caused and the available evacuation time would decrease, which means people have to flee the room in a shorter time period for survival. When the pedestrian density increases, more clogging at the exit would be generated and pedestrians would be more difficult to evacuate due to the limited capacity of egress and the reduction in the average speed of pedestrian flow caused by the injured. And the injured with limited motion capacity could hardly complete the evacuation owing to that they need more evacuation time and would retard the speed of the pedestrian flow.     

Experimental study and numerical simulation of evacuation from a dormitory

The evacuation process of students from a dormitory is investigated by both experiment and modeling. We investigate the video record of pedestrian movement in a dormitory, and find some typical characteristics of evacuation, including continuous pedestrian flow, mass behavior and so on. Based on the experimental observation, we found that simulation results considering pre-movement time are closer to the experimental results. With the model considering pre-movement time, we simulate the evacuation process and compare the simulation results with the experimental results, and find that they agree with each other closely. The crowd massing phenomenon is conducted in this paper. It is found that different crowd massing phenomena will emerge due to different desired velocities. The crowd massing phenomenon could be more serious with the increase of the desired velocity. In this study, we also found the faster-is-slower effect. When the positive effect produced by increasing the desired velocity is not sufficient for making up for its negative effect, the phenomenon of the greater the desired velocity the longer the time required for evacuation will emerge. From the video record, it can be observed that the mass behavior is obvious during the evacuation process. And the mass phenomenon could also be found in simulation. The results obtained from our study are also suitable to all these buildings in which both living and resting areas occupy the majority space, such as dormitories, residential buildings, hotels (restaurants) and so on.     

Simulation of pedestrian evacuation based on an improved dynamic parameter model

An improved dynamic parameter model is presented based on cellular automata. The dynamic parameters, including direction parameter, empty parameter, and cognition parameter, are formulated to simplify tactically the process of making decisions for pedestrians. The improved model reflects the judgement of pedestrians on surrounding conditions and the action of choosing or decision. According to the two-dimensional cellular automaton Moore neighborhood we establish the pedestrian moving rule, and carry out corresponding simulations of pedestrian evacuation. The improved model considers the impact of pedestrian density near exits on the evacuation process. Simulated and experimental results demonstrate that the improvement makes sense due to the fact that except for the spatial distance to exits, people also choose an exit according to the pedestrian density around exits. The impact factors α, β, and γ are introduced to describe transition payoff, and their optimal values are determined through simulation. Moreover, the effects of pedestrian distribution, pedestrian density, and the width of exits on the evacuation time are discussed. The optimal exit layout, i.e., the optimal position and width, is offered. The comparison between the simulated results obtained with the improved model and that from a previous model and experiments indicates that the improved model can reproduce experimental results well. Thus, it has great significance for further study, and important instructional meaning for pedestrian evacuation so as to reduce the number of casualties.     

Agitated behavior and elastic characteristics of pedestrians in an alternative floor field model for pedestrian dynamics

An alternative floor field (FF) model is proposed by incorporating the agitated behavior and elastic characteristics of pedestrians. The agitated behavior which is regarded as an important factor to pedestrian dynamics is depicted by introducing a parameter to revise the transition probability of pedestrians to move to the neighboring cells. To characterize elasticity of pedestrians, it is assumed that a cell can hold more than one pedestrians in crowd condition, while it can hold only one pedestrian in normal condition. In addition, a method to deal with conflicts is employed by considering the effects of agitated behavior and desired velocity. Numerical simulations are carried out to investigate pedestrian evacuation from a room. The results show, that as the value of agitated parameter increases, the evacuation time decreases to the minimum value and then increases gradually. Also, the faster-is-slower effect which is obtained by some other simulation models can be reproduced by the proposed model. Finally, the influence of exit width and the corresponding mechanism on evacuation process is investigated which is expected to be helpful to the exit design of public rooms.     

Logit-based exit choice model of evacuation in rooms with internal obstacles and multiple exits

A logit-based discrete choice model is proposed to study the exit choice behaviour of evacuees in rooms with internal obstacles and multiple exits. Several factors influencing the exit choice behaviour, including the information obtained by evacuees, the tendency of following others, the visibility and familiarity of exits and the physical conditions of nearby exits, are considered. Evacuees are allowed to re-select their target exits for minimizing the perceived disutility during evacuation process. Numerical results from applying the model to cellular automata simulation of evacuation are presented and the effects of some model parameters on evacuation time are investigated.     

Allelomimesis as escape strategy of pedestrians in two-exit confinements

We study the efficacy of allelomimesis as an escape strategy of mobile agents (pedestrians) that aim to leave a two-exit room within the shortest possible time. Allelomimesis is the act of copying one’s kindred neighbors. To escape, an agent employs one of the following strategies: (1) It chooses its own route independently (non-copying, α=0), (2) It imitates the actions of its neighbors at all times (blind copying, α=1), or (3) It either copies or acts independently according to a certain probability that is set by the copying parameter . Not more than one agent could occupy a given room location. An agent’s knowledge of the two exit locations is set by its information content . When left alone, an agent with complete knowledge of the exit whereabouts (β=1) always takes the shortest possible path to an exit. We obtain plots of the (group) evacuation time T and exit throughput Q as functions of α and β for cases where the two exits are near (on same room side) and far (on opposite sides of room) from each other. For an isolated agent, T is inversely proportional to β. The chances of escape for an isolated agent with β≤0.2 are higher with adjacent exits. However, for an agent with β>0.4 the chance is better with opposite exits. In a highly occupied room (occupancy rate R=80%) with adjacent exits, agents with β>0.8 escape more quickly if they employ a mixed strategy of copying and non-copying (0.4<α<0.6). On the other hand, blind copying (α≈1) gives agents with β<0.1 a better chance of escaping from the same room. For the same α and R values, opposite exits allow faster evacuation for agents with β<0.1 due to the likelihood of streaming and the lower probability of exit clogging. Streaming indicates an efficient utilization of an exit and it happens when the arcs that are formed are smaller and arch interference is less likely. Allelomimesis provides a simple yet versatile mechanism for studying the egress behavior of confined crowds in a multi-exit room.