Lattice gas simulation of experimentally studied evacuation 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.

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.

Ordering leads to multiple fast tracks in simulated collective escape of human crowds

Elucidating emergent regularities in intriguing crowd dynamics is a fundamental scientific problem arising in multiple fields. In this work, based on the social force model, we simulate the typical scenario of collective escape towards a single exit and reveal the striking analogy of crowd dynamics and crystallisation. With the outflow of the pedestrians, crystalline order emerges in the compact crowd. In this process, the local misalignment and global rearrangement of pedestrians are well rationalized in terms of the characteristic motions of topological defects in the crystal. Exploiting the notions from the physics of crystallisation further reveals the emergence of multiple fast tracks in the collective escape.

An Efficient Staged Evacuation Planning Algorithm Applied to Multi-Exit Buildings

When the occupant density of buildings is large enough, evacuees are prone to congestion during emergency evacuation, which leads to the extension of the overall escape time. Especially for multi-exit buildings, it’s a challenging problem to afford an effective evacuation plan. In this paper, a novel evacuation planning algorithm applied to multi-exit buildings is proposed, which is based on an indoor route network model. Firstly, evacuees are grouped by their location proximity, then all groups are approximately equally classified into several evacuation zones, each of which has only one safe exit. After that, all evacuation groups in the same zone are sorted by their shortest path length, then the time window of each evacuation group occupying the safe exit is calculated in turn. In the case of congestion at the safe exit, the departure time of each evacuation group is delayed in its arrival order. The objectives of the proposed algorithm include minimizing the total evacuation time of all evacuees, the travel time of each evacuee, avoiding traffic congestion, balancing traffic loads among different exits, and achieving high computational efficiency. Case studies are conducted to examine the performance of our algorithm. The influences of group number, group size, evacuation speed on the total evacuation time are discussed on a single-exit network, and that of partitioning methods and evacuation density on the performance and applicability in different congestion levels are also discussed on a multi-exit network. Results demonstrate that our algorithm has a higher efficiency and performs better for evacuations with a large occupant density.

Robot-assisted pedestrian flow control of a controlled pedestrian corridor

Pedestrian evacuation and modification of traffic facilities were previously studied to increase the traffic efficiency and the safety of pedestrians. In this article, we first design a new robot-assisted pedestrian control scheme. We consider a different scenario that the inflow of all the entrances to the corridor can be controlled by mobile robots. Based on the collected image data of the experimental corridor, we obtain the regulated pedestrian velocity and build the relationship function between the adjustable motion frequency of the robot and the regulated pedestrian velocity. To achieve the optimal traffic flow in the designed scenario, we set up the macroscopic pedestrian model for the modified unidirectional pedestrian corridor with several controlled entrances. The pedestrian inflow of each entrance is controlled by adjusting the motion frequency of the robot moving in a transverse direction. Then the state feedback controller is designed and the stability of the controller is analyzed based on the Lyapunov stability theory. The theoretical analysis guides the movement of robots. Finally, the simulation results demonstrate the efficiency of the controlled pedestrian system. Our study can flexibly manage the pedestrian flow by applying advanced robotics technology on macro level, which can provide ideal global control effect.

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.

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.

Game theory in models of pedestrian room evacuation

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

Evacuation of pedestrians from a single room by using snowdrift game theories

Game theory is introduced to simulate the complicated interaction relations among the conflicting pedestrians in a pedestrian flow system, which is defined on a square lattice with the parallel update rule. Modified on the traditional lattice gas model, each pedestrian can move to not only an empty site, but also an occupied site. It is found that each individual chooses its neighbor randomly and occupies the site with the probability W(x→y)=1/1+exp[-(P(x)-U(x))/κ], where P(x) is the x's payoff representing his personal energy, and U(x) is the average payoff of its neighborhood indicating the potential well energy if he stays. Two types of pedestrians are considered, and they interact with their neighbors following the payoff matrix of snowdrift game theory. The cost-to-benefit ratio r=c/(2b-c) (where b is the perfect payoff and c is the labor cost) represents the fear index of the pedestrians in this model. It is found that there exists a moderate value of r leading to the shortest escape time, and the situation for large values of r is better than that for small ones in general. In addition, the pedestrian flow system always arrives at a consistent state in which the two types of walkers have the same number and evolve by the same law irrespectively of the parameters, which can be interpreted as the self-organization effect of pedestrian flow. It is also proven that the time point of the onset of the steady state is unrelated to the scale of the pedestrians and the square lattice. Meanwhile, the system exhibits different dynamics before reaching the consistent state: the number of the two types of walkers oscillates when P(C)>0.5 (i.e., probability to change the present strategy), while no oscillation happens for P(C)≤0.5. Finally, it is shown that a smaller density of pedestrians ρ induces a shorter average escape time.

Pedestrian flow dynamics in a lattice gas model coupled with an evolutionary game

This paper studies unidirectional pedestrian flow by using a lattice gas model with parallel update rules. Game theory is introduced to deal with conflicts that two or three pedestrians want to move into the same site. Pedestrians are either cooperators or defectors. The cooperators are gentle and the defectors are aggressive. Moreover, pedestrians could change their strategy. The fundamental diagram and the cooperator fraction at different system width W have been investigated in detail. It is found that a two-lane system exhibits a first-order phase transition while a multilane system does not. A microscopic mechanism behind the transition has been provided. Mean-field analysis is carried out to calculate the critical density of the transition as well as the probability of games at large value of W. The spatial distribution of pedestrians is investigated, which is found to be dependent (independent) on the initial cooperator fraction when W is small (large). Finally, the influence of the evolutionary game rule has been discussed.

Pedestrian flow in a lattice gas model with parallel update

This paper studies unidirectional pedestrian flow in a channel using the lattice gas model with parallel update rule. The conflict (i.e., several pedestrians intend to move to the same site) is solved by introducing probabilities as in floor field models. The fundamental diagram (FD) is investigated and it is found that when the drift strength D≲0.5, the FD is a concave curve. With the further increase in drift strength, a turning point appears on FD. The empirical findings show that both concave FD and FD with a turning point exist. Thus, the model might be able to reproduce both by tuning drift strength. It is also shown that in the special case D=1, two congested branches exist in the FD. We have carried out mean-field analysis of the FD and the mean-field results are in approximate agreement with simulations when the drift strength D is small. A comparison with random sequential update rule model is also made.

Dynamic continuum pedestrian flow model with memory effect

In this paper, we develop a macroscopic model for pedestrian flow using the dynamic continuum modeling approach. We consider a two-dimensional walking facility that is represented as a continuum within which pedestrians can move freely in any direction. A pedestrian chooses a route based on his or her memory of the shortest path to the desired destination when the facility is empty and, at the same time, tries to avoid high densities. In this model, pedestrian flow is governed by a two-dimensional conservation law, and a general speed-flow-density relationship is considered. The model equation is solved numerically using the discontinuous Galerkin method, and a numerical example is employed to demonstrate both the model and the effectiveness of the numerical method.

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.

Static floor field and exit choice for pedestrian evacuation in rooms with internal obstacles and multiple exits

A modified floor field model is proposed to simulate pedestrian evacuation in rooms with internal obstacles and multiple exits. The modifications lie in developing a method to calculate the static floor field for every lattice site, which is determined by the most feasible distance to an exit, and employing a logit-based discrete choice principle to govern the exit selection. Simulation results show that the evacuation time is sensitive to the exit position and some model parameters. For pedestrians unfamiliar with the exit location, additional doors may not be necessary and can cause a negative effect on evacuation time. It is also found that unfamiliarity with the room's inner configuration and blindly following others will lead to an increase of the evacuation time.

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.

Experiment, theory, and simulation of the evacuation of a room without visibility

We study the evacuation process from a smoky room by means of experiments and simulations. People in a dark or smoky room are mimicked by "blind" students wearing eye masks. The evacuation of the disoriented students from the room is observed by video cameras, and the escape time of each student is measured. We find that the disoriented students exhibit a distinctly different behavior compared to a situation in which people can see their environment. Our experimental results are related to a theoretical approach and reproduced by an extended lattice gas model taking into account the empirically observed behavior. Our particular focus is on the mean value and distribution of escape times. For a large number of people in the room, the escape time distribution is wide because of jamming. Surprisingly, adding more exits does not improve the situation in the expected way, since most people use the exit that is discovered first, which may be viewed as a kind of herding effect based on nonlocal, but direct acoustic interactions. Moreover, the average escape time becomes minimal for a certain finite number of people in the dark or smoky room. These nonlinear effects have practical implications for emergency evacuation and the planning of safer buildings.