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The modelling of human crowd behaviors offers many challenging questions to science in general. Specifically, the social human behavior consists of many physiological and psychological processes which are still largely unknown. To model reliably such human crowd systems with complex social interactions, stochastic tools play an important role for the setting of mathematical formulations of the problems. In this work, using the description based on an exclusion principle, we study a statistical-mechanics-based lattice gas model for active-passive population dynamics with an application to human crowd behaviors. We provide representative numerical examples for the evacuation dynamics of human crowds, where the main focus in our considerations is given to an interacting particle system of active and passive human groups. Furthermore, our numerical results show that the communication between active and passive humans strongly influences the evacuation time of the whole population even when a local “faster-is-slower” phenomenon is taken into account. To provide an additional inside into the problem, a stationary state of our model is analyzed via current representations and heat map techniques. Finally, future extensions of the proposed models are discussed in the context of coupled data-driven modelling of human crowds and traffic flows, vital for the design strategies in developing intelligent transportation systems. [ABSTRACT FROM AUTHOR]

This paper introduces a kinetic model of crowd evacuation from a bounded domain, integrating social behavior and contagion dynamics. The model describes the spatial movement of individuals in a crowd, taking into account interactions with other people and the geometry of the environment. Interactions between healthy and infectious individuals can lead to disease transmission and are considered. The approach is grounded in the kinetic theory of active particles, where the activity variable represents both the infectious disease status of individuals (e.g., susceptible, infected) and the psychological state of pedestrians, including contagion awareness. Varying awareness levels influence individual behavior, leading to more cautious movement patterns, potentially reducing the overall infection rate. The performance of the model is evaluated through a series of numerical simulations. Different scenarios are examined to investigate the impact of awareness levels on pedestrian behavior, infectious disease spread, and evacuation times. Additionally, the effects of population immunization and individual contagion awareness are assessed to determine the most effective strategy for reducing infections. The results provide valuable insights into targeted strategies to mitigate contagion. [ABSTRACT FROM AUTHOR]

This article presents a kinetic model based on the BGK equation to simulate pedestrian dynamics, with a specific focus on anxiety conditions. The proposed model is based on the idea that for pedestrians in equilibrium, where this term is used to indicate that the system is characterized by a symmetric equilibrium velocity distribution with a relaxation term, the anxiety factor is incorporated into the equilibrium distribution through the preferred velocity, leading to potential symmetry-breaking effects in pedestrian dynamics. In addition, this paper introduces a numerical resolution scheme using the Monte Carlo particle method that effectively captures both symmetric and asymmetric behaviors of pedestrians. This method is applied to simulate crowd evacuation during stressful situations and pedestrian bidirectional flow in a straight corridor. [ABSTRACT FROM AUTHOR]

Abstract Due to simultaneous horizontal and vertical displacement during vertical evacuation, the consequences of stampede congestion accidents can be more severe. Generally, pedestrians trigger a synchronization mechanism at some point during the vertical evacuation process. This synchronization behavior helps prevent stampede congestion and improves evacuation efficiency. This paper designs a well-controlled single-file vertical evacuation experiment. After the experiment, the video footage is imported into the TRACKER system to extract the coordinates of pedestrian step movements, after which the experimental data undergo calculations and visual analysis. The research findings indicate the following: Firstly, when the crowd coordinates trigger the synchronization mechanism, this behavior remains stable as long as pedestrian speed and direction are unchanged; Secondly, the variation in footstep speed over time is not directly related to the footstep synchronization rate of the crowd; Lastly, this study calculated the characteristic density value most likely to trigger the synchronization mechanism during vertical evacuation. This research deepens our understanding of crowd dynamics, reveals the characteristics of pedestrian movement during vertical evacuation, and proposes evacuation guidance strategies based on these features.

Empirical studies of large gatherings and natural disasters have revealed two important features of dense crowds: extremely high crowd pressure and crowd turbulence. In this study, a mixed-type continuum model for multidirectional pedestrian flow was developed that explicitly considered the phase transition of different anticipation characteristics under different densities. Non-hyperbolicity was used to model the strong instabilities during crowd turbulence. In addition, by estimating the aggregated crowd pressure, the proposed model could clarify the effects of both force chains and panic sentiment, phenomena commonly observed during crowd disasters. The non-hyperbolic partial differential equations were solved using the mixed-type finite difference method, and Eikonal equations were solved using the fast sweeping method. Subsequently, the continuum model was applied to simulations of two real-world scenarios – the 2015 Hajj crowd disaster and the 2010 Love Parade crowd disaster – and validated through comparison with empirical observations. Overall, the proposed model is an efficient tool for evaluating crowd management strategies to predict and assess the crowd state. [ABSTRACT FROM AUTHOR]

Due to simultaneous horizontal and vertical displacement during vertical evacuation, the consequences of stampede congestion accidents can be more severe. Generally, pedestrians trigger a synchronization mechanism at some point during the vertical evacuation process. This synchronization behavior helps prevent stampede congestion and improves evacuation efficiency. This paper designs a well-controlled single-file vertical evacuation experiment. After the experiment, the video footage is imported into the TRACKER system to extract the coordinates of pedestrian step movements, after which the experimental data undergo calculations and visual analysis. The research findings indicate the following: Firstly, when the crowd coordinates trigger the synchronization mechanism, this behavior remains stable as long as pedestrian speed and direction are unchanged; Secondly, the variation in footstep speed over time is not directly related to the footstep synchronization rate of the crowd; Lastly, this study calculated the characteristic density value most likely to trigger the synchronization mechanism during vertical evacuation. This research deepens our understanding of crowd dynamics, reveals the characteristics of pedestrian movement during vertical evacuation, and proposes evacuation guidance strategies based on these features. [ABSTRACT FROM AUTHOR]

Analyzing the microscopic dynamics of pushing behavior within crowds can offer valuable insights into crowd patterns and interactions. By identifying instances of pushing in crowd videos, a deeper understanding of when, where, and why such behavior occurs can be achieved. This knowledge is crucial to creating more effective crowd management strategies, optimizing crowd flow, and enhancing overall crowd experiences. However, manually identifying pushing behavior at the microscopic level is challenging, and the existing automatic approaches cannot detect such microscopic behavior. Thus, this article introduces a novel automatic framework for identifying pushing in videos of crowds on a microscopic level. The framework comprises two main components: (i) feature extraction and (ii) video detection. In the feature extraction component, a new Voronoi-based method is developed for determining the local regions associated with each person in the input video. Subsequently, these regions are fed into EfficientNetV1B0 Convolutional Neural Network to extract the deep features of each person over time. In the second component, a combination of a fully connected layer with a Sigmoid activation function is employed to analyze these deep features and annotate the individuals involved in pushing within the video. The framework is trained and evaluated on a new dataset created using six real-world experiments, including their corresponding ground truths. The experimental findings demonstrate that the proposed framework outperforms state-of-the-art approaches, as well as seven baseline methods used for comparative analysis. [ABSTRACT FROM AUTHOR]

Social behavior in crowds, such as herding or increased interpersonal spacing, is driven by the psychological states of pedestrians. Current macroscopic crowd models assume that these are static, limiting the ability of models to capture the complex interplay between evolving psychology and collective crowd dynamics that defines a "social crowd". This paper introduces a novel approach by explicitly incorporating an "activity" variable into the modeling framework, which represents the evolving psychological states of pedestrians and is linked to crowd dynamics. To demonstrate the role of activity, we model pedestrian egress when this variable captures stress and awareness of contagion. In addition, to highlight the importance of dynamic changes in activity, we examine a scenario in which an unexpected incident necessitates alternative exits. These case studies demonstrate that activity plays a pivotal role in shaping crowd behavior. The proposed modeling approach thus opens avenues for more realistic macroscopic crowd descriptions with practical implications for crowd management. [ABSTRACT FROM AUTHOR]

Pedestrian evacuation in a corridor can de described mathematically by different variants of the model introduced by R. L. Hughes [Transp. Res. Part B Methodol., 36 (2002), pp. 507--535]. We identify a class of such models for which existence of a solution is obtained via a topological fixed point argument. In these models, the dynamics of the pedestrian density ρ (governed by a discontinuous-flux Lighthill, Whitham, and Richards model ρt + (sign(x - ξ (t))ρ ν (ρ))x = 0) is coupled to the computation of a Lipschitz continuous "turning curve" ξ. We illustrate this construction by several examples, including the Hughes model with affine cost (a variant of the original problem that is encompassed in the framework of El-Khatib, Goatin, and Rosini [Z. Angew. Math. Phys., 64 (2013), pp. 223--251]. Existence holds either with open-end boundary conditions or with boundary conditions corresponding to panic behavior with capacity drop at exits. Other examples put forward versions of the Hughes model with inertial dynamics of the turning curve and with general costs. [ABSTRACT FROM AUTHOR]

Crowd motion simulation requires specification of a range of parameters, each reflecting certain aspects of agent behavior. But what parameters matter the most? Are they all equally important? The question is important given that available data and resources for parameter calibration are limited, and priorities often need to be made. Here, for the first time, a full-spectrum sensitivity analysis of crowd model parameters is reported. It is shown that estimates of simulated evacuation time are, by far, most dependent on the value of locomotion/operational parameters, especially those that determine discharge rate at bottlenecks. The next most critical set of parameters are those that influence change of direction choices. If a crowd simulation model fails to reproduce bottleneck flows accurately, efforts to refine other modeling layers will be in vain. Similarly, if the model fails to represent exit choice adaptation/changing accurately, efforts to refine the exit choice model will be fruitless. [ABSTRACT FROM AUTHOR]

Panic evacuation, also known as mass panic or stampede, refers to a situation in which a large group of people react with fear and rush to escape a perceived threat, often resulting in chaos, injuries and sometimes death. The "faster is slower" effect is a phenomenon related to the fact that acting quickly in a panic will have slower consequences. It is used to explain the negative consequences of uncoordinated action by a panicking crowd. This makes crowd evacuation inefficient. Calm and controlled movements can ensure a safe exit. Anthropometry is the science that deals with the measurement and dimensions of the human body, and this information can provide insight into people's mobility and behavior in crowded places or emergency situations. The force generated by each individual in these situations is different. Therefore, it can be studied separately. In this study, the relationship between anthropometric characteristics of humans and the "fast is slower" effect was investigated. 19% difference in evacuation time was found between simulation experiments with and without anthropometric characteristics. These results are important for understanding human behavior in emergency situations and developing effective response strategies in these situations. In addition, these findings can contribute to practical applications to understand how anthropometric factors affect certain skills and to create more effective building evacuation plans considering individual differences.

A ubiquitous type of collective behavior and decision-making is the coordinated motion of bird flocks, fish schools, and human crowds. Collective decisions to move in the same direction, turn right or left, or split into subgroups arise in a self-organized fashion from local interactions between individuals without central plans or designated leaders. Strikingly similar phenomena of consensus (collective motion), clustering (subgroup formation), and bipolarization (splitting into extreme groups) are also observed in opinion formation. As we developed models of crowd dynamics and analyzed crowd networks, we found ourselves going down the same path as models of opinion dynamics in social networks. In this article, we draw out the parallels between human crowds and social networks. We show that models of crowd dynamics and opinion dynamics have a similar mathematical form and generate analogous phenomena in multiagent simulations. We suggest that they can be unified by a common collective dynamics, which may be extended to other psychological collectives. Models of collective dynamics thus offer a means to account for collective behavior and collective decisions without appealing to a priori mental structures. [ABSTRACT FROM AUTHOR]

We study crowd dynamics by means of both non-atomic and atomic differential games, which are also known as macroscopic and microscopic models, respectively; and we consider few crowd-related applications and experiments. Mainly, we study the modeling for Hajj motion (Tawaf), the most important event for Muslim pilgrims taking place in Mecca. We formally show that the proposed game-theoretical model is a potential-cost-dependent version of the well-known Hughes model, and the existing connection with the Lighthill–Whitham–Richards traffic model. We show that for a particular value in the potential cost, one obtains the same Hughes crowd model. Hence, we introduce a mild approximation that allows the computation of semi-explicit/explicit solutions for the proposed game problems. We study four main components that may be used by a central planner: (i) the effect of the clusters (delegations) over the motion, (ii) the inflow control to optimize the flux, (iii) how organized crowds evolve in comparison to disorganized ones, and (iv) how the creation of corrals with time-delays over their motion can be beneficial for the crowd evolution efficiency. We show that a faster performance is exhibited when pilgrims do Tawaf individually than when clustered groups are made, suggesting a possible direction for the policies design. Hence, we also present a simple ON/OFF control over the inflow that can be implemented by a central planner such that the flux is maximized. Related to this last mentioned policy, we have shown that delaying a group to integrate into the crowd can be beneficial for their efficient and faster motion. Also, we show that organized crowds evolve faster than disorganized ones, suggesting that education programs to perform Tawaf may potentially improve the flow. Finally, we show that other type of behaviors could be captured by means of the appropriate design of the cost functional. For example, the consideration of stress during an evacuation can be captured by means of the suitable modification of the cost functional, and as another example, we model the drafting tactics in bicycling where small densities can be beneficial for the performance. We present numerical and simulation results for all the applications using both the macroscopic and microscopic models, which certify the suitability of these models to capture the main features of the real behavior. [ABSTRACT FROM AUTHOR]

The terrorist attack has been widely modeled, in terms of crowd behavior, complex environments, attack patterns, and evacuation systems. However, most models are two-dimensional, which is unreal. The 3D factors, especially individual heights, will significantly shape both the process and outcome of terrorist attacks. Hence, the 3D model is more realistic. Taking the example of the Peshawar shooting in 2014, we apply 3D agents to reveal real-world behaviors of individuals, such as hiding, fighting, and escaping during the whole process. Based on the optimal solution out of simulations, the validity and robustness of our model can be well supported. To reveal the exact effects of key factors or mechanisms, we use counterfactual experiments and have some findings. For the fighting, more fighting of heroes can save more civilians. The hiding action of civilians can reduce the death probability. When the fighting rate in the crowd is higher, choosing to hide may be advisable for civilians. Meanwhile, hiding also has more benefits from increasing the hiding rate. A huge crowd hiding may reduce the fighting rate and then cause more deaths. Based on situations, the hiding should be chosen to maximize the gains. Our 3D model has made theoretical contributions to the field of public health and human behavior. It implies that civilians should hide properly, and be self-encouraged to be heroes, which should be advocated by the public. [ABSTRACT FROM AUTHOR]

Visual motion segmentation (VMS) is an important and key part of many intelligent crowd systems. It can be used to figure out the flow behavior through a crowd and to spot unusual life-threatening incidents like crowd stampedes and crashes, which pose a serious risk to public safety and have resulted in numerous fatalities over the past few decades. Trajectory clustering has become one of the most popular methods in VMS. However, complex data, such as a large number of samples and parameters, makes it difficult for trajectory clustering to work well with accurate motion segmentation results. This study introduces a spatial-angular stacked sparse autoencoder model (SA-SSAE) with l2-regularization and softmax, a powerful deep learning method for visual motion segmentation to cluster similar motion patterns that belong to the same cluster. The proposed model can extract meaningful high-level features using only spatial-angular features obtained from refined tracklets (a.k.a 'trajectories'). We adopt l2-regularization and sparsity regularization, which can learn sparse representations of features, to guarantee the sparsity of the autoencoders. We employ the softmax layer to map the data points into accurate cluster representations. One of the best advantages of the SA-SSAE framework is it can manage VMS even when individuals move around randomly. This framework helps cluster the motion patterns effectively with higher accuracy. We put forward a new dataset with itsmanual ground truth, including 21 crowd videos. Experiments conducted on two crowd benchmarks demonstrate that the proposed model can more accurately group trajectories than the traditional clustering approaches used in previous studies. The proposed SA-SSAE framework achieved a 0.11 improvement in accuracy and a 0.13 improvement in the F-measure compared with the best current method using the CUHK dataset. [ABSTRACT FROM AUTHOR]

The purpose of this review article is to present some recent results on the modeling and control of large systems of agents. We focus on particular applications where the agents are capable of independent actions instead of simply reacting to external forces. In the literature, such agents were referred to as autonomous, intelligent, self-propelled, greedy, and others. The main applications we have in mind are social systems (as opinion dynamics), pedestrians’ movements (also called crowd dynamics), animal groups, and vehicular traffic. We note that the last three examples include physical constraints; however, the agents are able to inject energy into the system, thus preventing the typical conservation of momentum and energy. In addition, the control problems posed by such systems are new and require innovative methods. We illustrate some ideas developed recently, including the use of sparse controls, limiting the total variation of controls, and defining new control problems for measures. After reviewing various approaches, we discuss some future research directions of potential interest. The latter encompasses both new types of equations and new types of limiting procedures to connect several scales at which a system can be represented. We conclude by illustrating a recent real-life experiment using autonomous vehicles on an open highway to smooth traffic waves. This opens the door to a new era of interventions to control real-time multi-agent systems and to increase the societal impact of such interventions guided by control research.

Short‐range exposure to airborne virus‐laden respiratory droplets is an effective transmission route of respiratory diseases, as exemplified by Coronavirus Disease 2019 (COVID‐19). In order to assess the risks associated with this pathway in daily‐life settings involving tens to hundreds of individuals, the chasm needs to be bridged between fluid dynamical simulations and population‐scale epidemiological models. This is achieved by simulating droplet trajectories at the microscale in numerous ambient flows, coarse‐graining their results into spatio‐temporal maps of viral concentration around the emitter, and coupling these maps to field‐data about pedestrian crowds in different scenarios (streets, train stations, markets, queues, and street cafés). At the individual scale, the results highlight the paramount importance of the velocity of the ambient air flow relative to the emitter's motion. This aerodynamic effect, which disperses infectious aerosols, prevails over all other environmental variables. At the crowd's scale, the method yields a ranking of the scenarios by the risks of new infections, dominated by the street cafés and then the outdoor market. While the effect of light winds on the qualitative ranking is fairly marginal, even the most modest air flows dramatically lower the quantitative rates of new infections. [ABSTRACT FROM AUTHOR]

This paper presents a survey and critical analysis of the mathematical literature on modeling and simulation of human crowds taking into account behavioral dynamics. The main focus is on research papers published after the review [N. Bellomo and C. Dogbè, On the modeling of traffic and crowds: A survey of models, speculations, and perspectives, SIAM Rev. 53 (2011) 409–463], thus providing important research perspectives related to new, emerging trends. The presentation addresses the scaling problem corresponding to microscopic (individual-based), mesoscopic (kinetic), and macroscopic (hydrodynamic) modeling and analysis. A multiscale vision guides the overall content of the paper. The critical analysis of the overall content naturally leads to research perspectives. A selection of them is brought to the attention of the interested reader together with hints on how to deal with them. [ABSTRACT FROM AUTHOR]

The dynamics of pedestrian crowds during exceptional tragic events are very complex depending on a series of human behaviors resulting from combinations of basic interaction principles and self-organization. The Alert–Panic–Control (APC) model is one of the mathematical models in the literature for representing such complicated processes, mainly focusing on psychologists' points of view (i.e., emotion contagion). This work proposes a Hybrid APC (HAPC) model including new processes, such as the effect of resonance, the victims caused by people in state of panic, new interactions between populations based on imitation and emotional contagion phenomena and the ability to simulate multiple disaster situations. Results from simulated scenarios showed that in the first 5 min 54.45% of population move towards a state of alert, 13.82% enter the control state and 31.73% pass to the state of panic, highlighting that individuals respond to a terrible incident very quickly, right away after it occurs. [ABSTRACT FROM AUTHOR]

This paper proposes a kinetic theory approach coupling together the modeling of crowd evacuation from a bounded domain with exit doors and infectious disease contagion. The spatial movement of individuals in the crowd is modeled by a proper description of the interactions with people in the crowd and the environment, including walls and exits. At the same time, interactions among healthy and infectious individuals may generate disease spreading if exposure time is long enough. Immunization of the population and individual awareness to contagion is considered as well. Interactions are modeled by tools of game theory, that let us propose the so-called tables of games that are introduced in the general kinetic equations. The proposed model is qualitatively studied and, through a series of case studies, we explore different scenarios related to crowding and gathering formation within indoor venues under the spread of a respiratory infectious disease, obtaining insights on specific policies to reduce contagion that may be implemented. [ABSTRACT FROM AUTHOR]

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A cognitive-based routing algorithm is proposed. Concepts like local form and path algorithms are developed. Unlike current mainstream routing algorithms assume that all people know everything about the environment, the proposed algorithm allows people to have a complete or incomplete map knowledge and built up their own map knowledge in a piecemeal fashion. Using a hospital floor plan as the scenario, numerical experiments are conducted by assuming pedestrians to have different levels of map knowledge. Results show that reasonable routes could be frequently found even if pedestrians only have an incomplete knowledge of the network. Also pedestrians generally need to traverse more rooms if having zero or less map knowledge. Hence the proposed algorithm's effectiveness is validated to some extent. [ABSTRACT FROM AUTHOR]

The design of safe and efficient pedestrian facilities necessitates the knowledge of complex human movements, such as intersecting pedestrian streams, under different conditions. This study aims to experimentally investigate the impact of intersecting angles on collective crowd dynamics under two different urgency levels. Data were collected from a controlled laboratory experiment with scenarios consisting of three intersection angles (30°, 90°, and 150°) and two desired speed levels (normal walking and slow running). Trajectory data of individual experiment participants were extracted from the recorded video footage. The results indicate that the 30° intersection has the lowest bottleneck effect compared to the other angles. Moreover, the time-to-target analysis shows that the 150° intersection has a higher waiting time at the intersection compared to the other angles for the jogging scenarios. The speed distribution and space utilization maps implied an asymmetrical reduction in speed in the two corridors of the intersection, even though the physical and geometrical configurations are symmetric. The lane-based analysis of collective speeds revealed that the inner lane (the lane that initially encounters the intersecting flow) has the maximum reduction in speed. The outcomes of this study may be useful to evaluate the congestion effects associated with crossing configurations and in calibrating and validating simulation tools to reproduce such effects accurately. [ABSTRACT FROM AUTHOR]

This paper investigates a new method to simulate pedestrian crowd movement in a large and complex virtual environment, representing a public space such as a shopping mall. To demonstrate pedestrian dynamics, we consider groups of pedestrians of different size, sharing a crowded environment. A pedestrian has its own characteristics, such as gender, age, position, velocity, and energy. The proposed method uses a multi-group microscopic model to generate real-time trajectories for all people moving in the defined virtual environment. Additionally, a dynamic model is introduced for modelling group behaviour. Based on the proposed method, all pedestrians in each group can continuously adjust their attributes and optimize their path towards the desired visiting targets, while avoiding obstacles and other pedestrians. Simulation results show that the proposed method can describe a realistic simulation of dynamic behaviour. [ABSTRACT FROM AUTHOR]

A parallel algorithm is proposed for modeling of crowd multi-cell occupancy and velocity variety. Methods are devised to solve issues such as space competitions so that each pedestrian can autonomously determines his or her own movement. As pedestrians are modeled independently and simultaneously, the proposed algorithm can be easily implemented into heterogeneous computing frameworks such as OpenCL, CUDA etc, which support large scale parallel computation, and preserve these frameworks’ high performance while the issues are efficiently solved. In the section of numerical experiments, the proposed algorithm is firstly validated through two different experiments. Then a quite thorough investigation of impacts of multi-cell occupancy and velocity variety upon crowd macroscopic dynamics is applied. [ABSTRACT FROM AUTHOR]

With the development of urbanization and the growth of population, there is a growing demand for safety in public building facilities. As one of the essential building components of urban architecture, bottlenecks have a significant impact on the evacuation efficiency of crowds. Furthermore, the heterogeneity of crowds also contributes to the complexity of crowd movement through bottlenecks, while aggravating the magnitude of congestion induced by bottlenecks. The objective of this paper is to explore the movement characteristics of heterogeneous crowds passing through a corridor with a bottleneck by conducting a controlled experiment. There were three variables in this experiment, namely the individual categories (i.e., able-bodied individuals, simulated individuals on crutches and simulated wheelchair users), bottleneck width (i.e., 1.2, 1.6 and 2.0 m) and proportion of simulated disabilities in crowds (i.e., 0 %, 5 % and 10 %). Then offset angle, passing efficiency, fundamental diagram, etc., were analyzed. In trials involving simulated individuals on crutches, a higher detouring degree is observed compared to trials involving simulated wheelchair users or mixed groups of two types of simulated disabilities. There is an increase in flow rate induced by increasing the bottleneck width and decreasing the proportion of simulated disabilities. The passing efficiency at the upstream of the bottleneck in all tests is primarily influenced by the bottleneck width, while by the type and proportion of simulated disabilities at the downstream or inside the bottleneck. The findings are intended to complement the dynamic theory of heterogeneous crowds at building bottlenecks, while providing a reference for congestion control of crowds at bottlenecks. [ABSTRACT FROM AUTHOR]

With the increasing scale of crowds in public places, the study of modeling crowd evacuation has become a significant research field. However, most previous research ignores to incorporate behavioral heterogeneity of individuals into the modeling framework, making it hard to replicate more realistic evacuation processes. Therefore, a behavioral heterogeneity-based social force model (BHSFM) is proposed to reveal the heterogeneity characteristics from the aspect of individual behavior. Numerical experiments show that the BHSFM provides a general mathematical framework for describing behavioral heterogeneity and forms a more reasonable and elaborate evacuation process. Notably, some interesting evacuation phenomena can emerge by integrating the behavioral heterogeneity coefficient with temporal-spatial dynamic risk indexes. Compared with the social force model (SFM), higher frequencies of small-scale displacements are performed by BHSFM due to more pushing behaviors. Furthermore, the periods and areas of a potential crowd disaster are revealed by our model under different numbers of pedestrians, which has important guiding significance for formulating reasonable evacuation schemes in specific scenarios. [ABSTRACT FROM AUTHOR]

This study examined the impact of congestion-related controls on runner density, flow rate, perceived safety, and satisfaction during an Australian running event. Runner congestion was compared between races organized at the Sunshine Coast Marathon and Running Festival in 2019 without controls and in 2021 with added controls, including modifications to the start corral design and use of wave starts. Following a mixed-method design, runner congestion was quantitatively measured via determining runner density and flow rate in the start corrals with video analyses, while post-event surveys were used to gather qualitative evidence regarding the prevalence of congestion and its impact on runner safety and satisfaction. Descriptive analyses for quantitative data showed runner density (1.48–3.01 vs. 0.52–1.20 runners per m2) and flow rate (102–152 vs. 36–59 runners per min per m) were reduced across races with controls. Regarding qualitative data, Wilcoxon–Mann–Whitney rank-sum tests demonstrated a significantly (p < 0.01) lower prevalence of congestion was perceived on course while running, alongside a reduced (p = 0.08) perceived impact of congestion on event satisfaction across races with controls. Furthermore, descriptive analyses for qualitative data showed a reduced proportion of runners indicated the start corrals were "somewhat" to "extremely" (rating of at least 3 on a 5-point scale) congested upon race commencement with controls (64% vs. 75%), and perceived safety (10% vs. 17%) and satisfaction (17% vs. 30%) were "somewhat" to "extremely" impacted by congestion across races with controls. Adopting suitable start corral designs with wave starts may enable race directors to reduce runner congestion to enhance continued participation among the public and viability of their running events. [ABSTRACT FROM AUTHOR]

We study the collective motion of autonomous mobile agents in a ringlike environment. The agents' dynamics are inspired by known laboratory experiments on the dynamics of locust swarms. In these experiments, locusts placed at arbitrary locations and initial orientations on a ring-shaped arena are observed to eventually all march in the same direction. In this work we ask whether, and how fast, a similar phenomenon occurs in a stochastic swarm of simple locust-inspired agents. The agents are randomly initiated as marching either clockwise or counterclockwise on a discretized, wide ring-shaped region, which we subdivide into k concentric tracks of length n. Collisions cause agents to change their direction of motion. To avoid this, agents may decide to switch tracks to merge with platoons of agents marching in their direction. We prove that such agents must eventually converge to a local consensus about their direction of motion, meaning that all agents on each narrow track must eventually march in the same direction. We give asymptotic bounds for the expected time it takes for such convergence or "stabilization" to occur, which depends on the number of agents, the length of the tracks, and the number of tracks. We show that when agents also have a small probability of "erratic", random track-jumping behavior, a global consensus on the direction of motion across all tracks will eventually be reached. Finally, we verify our theoretical findings in numerical simulations. [ABSTRACT FROM AUTHOR]

As one of the most effective models for human collective motion, the social force model (SFM) simulates the dynamics of crowd evacuation from a microscopic perspective. However, it treats pedestrians as the homogeneous rigid particles, whereas pedestrians are diverse and heterogeneous in real life. Therefore, this paper develops a pedestrian heterogeneity-based social force model (PHSFM) by introducing physique and mentality coefficients into the SFM to quantify physiology and psychology attributes of pedestrians, respectively. These two coefficients can affect the self-driven force by changing the desired speed, thus characterizing the pedestrian heterogeneity more realistically. Simulation experiments demonstrate that the PHSFM designs a more general and accurate theoretical framework for the expression of pedestrian heterogeneity, which realizes special behavior patterns caused by individual diversity. Furthermore, our model provides effective guidelines for the management of crowds in potential research fields such as transportation, architectural science and safety science. [ABSTRACT FROM AUTHOR]

In this paper, we develop two efficient numerical methods for a multiscale kinetic equation in the context of crowd dynamics with emotional contagion [A. Bertozzi, J. Rosado, M. Short and L. Wang, Contagion shocks in one dimension, J. Stat. Phys. 158 (2014) 647–664]. In the continuum limit, the mesoscopic kinetic equation produces a natural Eulerian limit with nonlocal interactions. However, such limit ceases to be valid when the underlying microscopic particle characteristics cross, corresponding to the blow up of the solution in the Eulerian system. One method is to couple these two situations — using Eulerian dynamics for regions without characteristic crossing and kinetic evolution for regions with characteristic crossing. For such a hybrid setting, we provide a regime indicator based on the macroscopic density and fear level, and propose an interface condition via continuity to connect these two regimes. The other method is based on a level set formulation for the continuum system. The level set equation shares similar forms as the kinetic equation, and it successfully captures the multi-valued solution in velocity, which implies that the multi-valued solution other than the viscosity solution should be the physically relevant ones for the continuum system. Numerical examples are presented to show the efficiency of these new methods.

How does the presence of a robot affect pedestrians and crowd dynamics, and does this influence vary across robot type? In this paper, we took the first step towards answering this question by performing a crowd-robot gate-crossing experiment. The study involved 28 participants and two distinct robot representatives: A smart wheelchair and a Pepper humanoid robot. Collected data includes: video recordings; robot and participant trajectories; and participants' responses to post-interaction questionnaires. Quantitative analysis on the trajectories suggests the robot affects crowd dynamics in terms of trajectory regularity and interaction complexity. Qualitative results indicate that pedestrians tend to be more conservative and follow "social rules" while passing a wheelchair compared to a humanoid robot. These insights can be used to design a social navigation strategy that allows more natural interaction by considering the robot effect on the crowd dynamics. [ABSTRACT FROM AUTHOR]

Patterns of collective motion in bird flocks, fish schools and human crowds are believed to emerge from local interactions between individuals. Most 'flocking' models attribute these local interactions to hypothetical rules or metaphorical forces and assume an omniscient third-person view of the positions and velocities of all individuals in space. We develop a visual model of collective motion in human crowds based on the visual coupling that governs pedestrian interactions from a first-person embedded viewpoint. Specifically, humans control their walking speed and direction by cancelling the average angular velocity and optical expansion/contraction of their neighbours, weighted by visibility (1 − occlusion). We test the model by simulating data from experiments with virtual crowds and real human 'swarms'. The visual model outperforms our previous omniscient model and explains basic properties of interaction: 'repulsion' forces reduce to cancelling optical expansion, 'attraction' forces to cancelling optical contraction and 'alignment' to cancelling the combination of expansion/contraction and angular velocity. Moreover, the neighbourhood of interaction follows from Euclid's Law of perspective and the geometry of occlusion. We conclude that the local interactions underlying human flocking are a natural consequence of the laws of optics. Similar perceptual principles may apply to collective motion in other species. [ABSTRACT FROM AUTHOR]

The first part of our paper presents a general survey on the modeling, analytic problems, and applications of the dynamics of human crowds, where the specific features of living systems are taken into account in the modeling approach. This critical analysis leads to the second part which is devoted to research perspectives on modeling, analytic problems, multiscale topics which are followed by hints towards possible achievements. Perspectives include the modeling of social dynamics, multiscale problems and a detailed study of the link between crowds and swarms modeling. [ABSTRACT FROM AUTHOR]

How do people behave in the seconds after they become aware they have been caught up in a real-life transport emergency? This paper presents the first micro-behavioral, video-based analysis of the behavior of passengers during a small explosion and subsequent fire on a subway train. We analyzed the behavior of 40 passengers present in the same carriage as the explosion. We documented the first action of the passengers following the onset of the emergency and described evidence of pro- and anti-social behavior. Passengers' first actions varied widely. Moreover, anti-social behavior was rare and displays of pro-sociality were more common. In a quantitative analysis, we examined spatial clustering of running behavior and patterns in passenger exit choices. We found both homogeneity and heterogeneity in the running behavior and exiting choices of passengers. We discuss the implications of these findings for the mass emergency literature and for evacuation modeling. [ABSTRACT FROM AUTHOR]

Tourism activities essentially represent the interaction between crowds and attractions. Thus, crowd dynamics are critical to the quality of the tourism experience in personalized tour recommendations. In order to generate dynamic, personalized tour routes, this paper develops a tourist trip design problem with crowd dynamics (TTDP-CD), which is quantified with the crowd dynamics indicators derived from mobile tracking data in terms of crowd flow, crowd interaction, and crowd structure. TTDP-CD attempts to minimize the perceived crowding and maximize the assessed value of destinations while minimizing the total distance and proposes a two-stage route strategy of “global optimization first, local update later” to deal with the sudden increase in crowding in realistic scenarios. An evolutionary algorithm is extended with container-index coding, mixed mutation operators, and a global archive to create a personalized day tour route at the urban scale. To corroborate the performance of this approach, a case study was carried out in Dalian, China. The results demonstrate that the suggested method outperforms previous approaches, such as NSGA-II, MOPSO, MOACO, and WSM, in terms of performance and solution quality and decreases real-time crowding by an average of 7%.

Agent-based models of “flocking” and “schooling” have shown that a weighted average of neighbor velocities, with weights that decay gradually with distance, yields emergent collective motion. Weighted averaging thus offers a potential mechanism of self-organization that recruits an increasing, but self-limiting, number of individuals into collective motion. Previously, we identified and modeled such a ‘soft metric’ neighborhood of interaction in human crowds that decays exponentially to zero at a distance of 4–5 m. Here we investigate the limits of weighted averaging in humans and find that it is surprisingly robust: pedestrians align with the mean heading direction in their neighborhood, despite high levels of noise and diverging motions in the crowd, as predicted by the model. In three Virtual Reality experiments, participants were immersed in a crowd of virtual humans in a mobile head-mounted display and were instructed to walk with the crowd. By perturbing the heading (walking direction) of virtual neighbors and measuring the participant’s trajectory, we probed the limits of weighted averaging. 1) In the “Noisy Neighbors” experiment, the neighbor headings were randomized (range 0–90°) about the crowd’s mean direction (±10° or ±20°, left or right); 2) in the “Splitting Crowd” experiment, the crowd split into two groups (heading difference = 10–40°) and the proportion of the crowd in one group was varied (50–84%); 3) in the “Coherent Subgroup” experiment, a perturbed subgroup varied in its coherence (heading SD = 0–20°) about a mean direction (±10° or ±20°) within a noisy crowd (heading range = 180°), and the proportion of the crowd in the subgroup was varied. In each scenario, the results were predicted by the weighted averaging model, and attraction strength (turning rate) increased with the participant’s deviation from the mean heading direction, not with group coherence. However, the results indicate that humans ignore highly discrepant headings (45–90°). These findings reveal that weighted averaging in humans is highly robust and generates a common heading direction that acts as a positive feedback to recruit more individuals into collective motion, in a self-reinforcing cascade. Therefore, this “soft” metric neighborhood serves as a mechanism of self-organization in human crowds.

We present a model of crowd motion in regions with moving obstacles, which is based on the notion of measure sweeping process. The obstacle is modeled by a set-valued map, whose values are complements to r-prox-regular sets. The crowd motion obeys a nonlinear transport equation outside the obstacle and a normal cone condition (similar to that of the classical sweeping processes theory) on the boundary. We prove the well-posedness of the model, give an application to environment optimization problems, and provide some results of numerical computations. [ABSTRACT FROM AUTHOR]

• Explores enhancing evacuation efficiency through behavioural modifications. • Focusing on behaviour at bottlenecks, reaction time, and movement speed (pace). • Incremental behavioural adjustments significantly improve evacuation efficiency. • Observing a nearly linear relationship between behaviour adoption rate and efficiency gains. • Interventions targeting physical movement are more straightforward to implement and yield higher efficiency returns than decision-making interventions. In the context of evacuating crowded spaces during acute crises, every second is pivotal and can be the determinant in life-or-death situations. It is, therefore, important to explore and implement any measures or interventions that could streamline and expedite the evacuation process in such scenarios. This study aims to explore how the modification of individual behaviours can be leveraged to improve the efficiency of crowd evacuations, with a specific focus on the physical aspects of movement. We examine three crucial elements of physical movement: behaviours at bottlenecks, the initiation time of individual movement, and the pace of movement. A series of dedicated experiments, each tailored to one of these behavioural aspects, has been conducted. In these experiments, the behaviour of interest is modified incrementally within the crowd, with increases of 20% at each stage. This methodology allows for a detailed assessment of system efficiency at varying levels of instructed behaviour adoption/injection. The findings reveal that changes in each aspect of physical movement significantly influence overall efficiency. Most notably, the relationship between the uptake and increase in efficiency is nearly linear, and the rate of efficiency increase does not notably diminish with uptake, unlike interventions pertaining decision-making aspects of behaviour. This suggests that behavioural interventions targeting physical aspects of movement will likely yield higher efficiency returns. Moreover, in comparison with a related study focusing on decision-making aspects of evacuation behaviour, this research observes that modifying physical aspects of behaviour is generally more straightforward. The success rates of individuals in implementing physical movement instructions are higher, and the impact on the system is more pronounced than that observed in decision-making modifications. These results provide insights for developing simple, actionable instructions that can be effectively communicated to the public. These instructions can be disseminated as part of training and education programs or even provided on the spot during an evacuation. [ABSTRACT FROM AUTHOR]

• Investigates the impact of simple behavioural modifications on crowd evacuation efficiency. • Significant improvements in evacuation efficiency through behavioural interventions. • Influencing exit choice adaptation resulted in higher efficiency gains compared to exit choice. • Partial adoption of beneficial strategies can still enhance evacuation outcomes. • Poor strategies can have more detrimental effects than the benefits of good strategies. Crowded environments are inherently vulnerable to a range of risks, including earthquakes, fires, violent attacks, and terrorism. In such scenarios, every second counts in an evacuation, as it can significantly impact the number of lives saved. This paper introduces a novel approach to optimising crowd evacuation processes, focusing on behavioural modification rather than traditional methods such as mathematical optimisation models or architectural adjustments. We propose that by altering the behaviours of individuals within a crowd, overall system efficiency can be enhanced from within. We explore the effects of imparting simple, easily understandable strategies or instructions to individuals that can improve evacuation efficiency. The current work concentrates on how modifications in individual decision-making— namely, exit-choice and exit-choice-changing behaviour — can influence evacuation dynamics. We present the results of six major evacuation experiments, encompassing nearly 100 experimental scenarios and repetitions, which specifically investigate the effect of influencing exit choice and adaptation in exit-choice behaviour. The investigation revolves around three core questions: (a) the impact of effective strategies (b) the potential consequences of detrimental strategies, indicative of common misconceptions or poor advice, and (c) the influence of varying levels of strategy adoption, examining how system efficiency changes as more individuals embrace either beneficial or harmful strategies. The findings indicate that behavioural modification can substantially influence evacuation efficiency. Interestingly, the negative impact of poor strategies outweighs the benefits of effective ones. With respect to beneficial strategies, a significant increase in efficiency is observed at initial and intermediate levels of strategy adoption/uptake, suggesting that complete compliance is not necessary to enhance overall system performance. The benefit of influencing decision adaptation behaviour is considerably more tangible than influencing exit choice behaviour. These insights establish a novel perspective in evacuation safety. They lay a foundational framework for developing targeted public education and training programs based on empirical evidence. They highlight the importance of awareness and self-regulation among crowds, showcasing their potential to significantly increase both efficiency and safety in evacuation scenarios, potentially saving lives. [ABSTRACT FROM AUTHOR]

Previous studies indicate that the movement of pedestrians under poor visibility conditions is significantly different from that under good visibility conditions. To investigate the influence of visibility factor on the longitudinal movement of pedestrian, series of single-file experiments were performed under the quantitative control of visibility level. Based on the extracted trajectories, typical evacuation behavior and movement characteristics of pedestrians under different visibility conditions are explored. It is found that the lateral swing amplitude of pedestrians during movement is within 20 cm under low densities while it is close to 30 cm at high densities. The free velocity under the light transmission of 100 %, 2.2 %, 0.5 % and 0.1 % is 0.856 m/s, 0.823 m/s, 0.741 m/s and 0.712 m/s respectively. Individuals cannot accurately perceive the surrounding situations with the worsening of visual condition, therefore the movement speed decreases under the poor visibilities. Besides, two regimes including the constrained regime and free regime are identified in the headway-velocity relation at different visibility levels. The maximum specific flow under the light transmission of 100 %, 2.2 %, 0.5 % and 0.1 % is 0.70 s−1, 0.67 s−1, 0.62 s−1 and 0.55 s−1 respectively. The study is helpful to reveal the pedestrian dynamics of single-file movement under the limited visibility conditions. • Single-file experiments were performed under the quantitative control of visibility. • Typical behavior and movement properties at different visibilities are explored. • Two regimes are identified in the headway-velocity relation at different visibilities. • Fundamental diagrams are obtained under different visibility levels. [ABSTRACT FROM AUTHOR]

• Behavioural study investigated transmission risks and mitigations for UK mass events in 2021. • Explored non-pharmaceutical interventions (NPIs); e.g. social distancing and face coverings. • 21 events observed. Data collection method presented with overview of data. The Events Research Programme (ERP) was a multi-disciplinary study undertaken during the COVID-19 pandemic to investigate SARS-CoV-2 transmission risks and mitigations around the reopening of mass events in the UK in 2021 – including a behavioural study, exploring how non-pharmaceutical interventions (NPIs), such as social distancing, pre-event virus testing, and the use of face coverings might enable people to attend events safely. This behavioural study is discussed here. A total of 21 pilot events were involved in the study between April and July 2021. The venues used for the pilots varied in size, layout, occupancy level, and crowd management approaches. Data was extracted from manual qualitative observations and venue CCTV cameras which recorded routinely at venues. In addition, 890 cameras were installed during the events to capture attendee movement outside the venues, during arrival, in event areas, circulation spaces, bars and restaurants, and on exiting. A mixed method approach was adopted to ensure locations and activities of interest were captured, quantitative data gathered, and that this data could be placed in context. This enabled a behavioural study, quantifying crowd performance behaviours for comparison between and within events. This paper describes the background to this work, the method adopted and provides a brief overview of the data collected, relating primarily to (i) crowd densities, (ii) social distancing (captured here as contact distancing), and (iii) the use of face coverings. [ABSTRACT FROM AUTHOR]

Well-structured pedestrian experiments in a long corridor have been carried out to explore the influence of obstacle shape and size on individual and crowd level pedestrian movement characteristics. Results indicate that for individual pedestrians, the number of right-turning pedestrians and the target drift angle show clear changes with the increase of the obstacle size, while the speed only changes significantly when the obstacle size is greater than 1.5 m. For the crowd movement scenarios, a small obstacle can speed up the pedestrian flow, then, with the increase of the obstacle size, the movement time increases. The increase rate has a relation with the obstacle shape. The obstacle shape influence becomes more obvious when the individual and crowd movement scenarios are compared. The results of this paper are expected to provide practical basis for modeling pedestrian under the influence of obstacle. [ABSTRACT FROM AUTHOR]

The modeling of living systems composed of many interacting entities is treated in this paper with the aim of describing their collective behaviors. The mathematical approach is developed within the general framework of the kinetic theory of active particles. The presentation is in three parts. First, we derive the mathematical tools, subsequently, we show how the method can be applied to a number of case studies related to well defined living systems, and finally, we look ahead to research perspectives. [ABSTRACT FROM AUTHOR]