From the Microscale to Collective Crowd Dynamics
24 Sep 2013-Multiscale Modeling & Simulation (Society for Industrial and Applied Mathematics)-Vol. 11, Iss: 3, pp 943-963
TL;DR: This paper deals with the kinetic theory modeling crowd dynamics with the aim of showing how the dynamics at the microscale is transferred to the dynamics of collective behaviors.
Abstract: This paper deals with the kinetic theory modeling crowd dynamics with the aim of showing how the dynamics at the microscale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations are treated by finite difference methods for hyperbolic equations. Some preliminary reasoning toward the modeling of panic conditions is proposed.
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TL;DR: This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems.
Abstract: This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of ...
203 citations
TL;DR: A revisiting of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions, based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games.
Abstract: This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for a general mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.
149 citations
TL;DR: This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS--CoV--2 Severe Acute Respiratory Syndrome, corona virus n.2.
Abstract: This paper is devoted to the multidisciplinary modelling of a pandemic initiated by an aggressive virus, specifically the so-called SARS–CoV–2 Severe Acute Respiratory Syndrome, corona virus n.2. T...
110 citations
Cites background or methods from "From the Microscale to Collective C..."
...Applications of kinetic theory methods to crowd dynamics indicates that a key modelling approach has been introduced in [17] for a crowd supposed to move along a finite number of discrete velocity directions....
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...Different examples can be found in the pertinent literature, for instance, finite differences have been used in [17], while Monte Carlo particle methods [110] and splitting methods have been developed, respectively, in [19] and in [86]....
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TL;DR: This paper proposes an essay concerning the understanding of human behaviours and crisis management of crowds in extreme situations, such as evacuation through complex venues, using a model derived by the methods of the mathematical kinetic theory and theoretical tools of evolutionary game theory.
109 citations
TL;DR: This paper presents a kinetic equation incorporating the Cucker–Smale flocking force and stochastic game theoretic interactions in collision operators, and presents a sufficient framework leading to the asymptotic velocity alignment and global existence of smooth solutions for the proposed kinetic model with a special kernel.
Abstract: This paper addresses some preliminary steps toward the modeling and qualitative analysis of swarms viewed as living complex systems. The approach is based on the methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlocal, nonlinearly additive and modeled by theoretical tools of stochastic game theory. Collective learning theory can play an important role in the modeling approach. We present a kinetic equation incorporating the Cucker–Smale flocking force and stochastic game theoretic interactions in collision operators. We also present a sufficient framework leading to the asymptotic velocity alignment and global existence of smooth solutions for the proposed kinetic model with a special kernel. Analytic results on the global existence and flocking dynamics are presented, while the last part of the paper looks ahead to research perspectives.
101 citations
References
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TL;DR: A model of pedestrian behaviour is used to investigate the mechanisms of panic and jamming by uncoordinated motion in crowds, and an optimal strategy for escape from a smoke-filled room is found, involving a mixture of individualistic behaviour and collective ‘herding’ instinct.
Abstract: One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings; at other times, stampedes can arise during the rush for seats or seemingly without cause. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events. But systematic studies of panic behaviour and quantitative theories capable of predicting such crowd dynamics are rare. Here we use a model of pedestrian behaviour to investigate the mechanisms of (and preconditions for) panic and jamming by uncoordinated motion in crowds. Our simulations suggest practical ways to prevent dangerous crowd pressures. Moreover, we find an optimal strategy for escape from a smoke-filled room, involving a mixture of individualistic behaviour and collective 'herding' instinct.
4,334 citations
"From the Microscale to Collective C..." refers background in this paper
...On the other hand, the behavioral influence of panic conditions can play an important role in the modification of the usual dynamics [19, 20]....
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TL;DR: Video recordings of the crowd disaster in Mina/Makkah during the Hajj in 1426H on 12 January 2006 are analyzed and reveal two subsequent, sudden transitions from laminar to stop-and-go and "turbulent" flows, which question many previous simulation models.
Abstract: 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 et al., 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.
1,013 citations
"From the Microscale to Collective C..." refers background in this paper
...micro-scale by ordinary differential equations, see among others [18, 20, 21]; at the macro-scale obtained by the classical approach by conservation equations, among others [10, 24]; or by stochastic models related to evolving probability measure [26]....
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...On the other hand, the behavioral influence of panic conditions can play an important role in the modification of the usual dynamics [19, 20]....
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TL;DR: It is shown that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior.
Abstract: Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.
955 citations
"From the Microscale to Collective C..." refers methods in this paper
...iii) The output of interactions is modeled, by using tools of the game theory [28, 29], by the discrete probability density function Ahk,pq(ij), which...
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TL;DR: The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions.
Abstract: In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic individual-level experimental verification, and the local mechanisms underlying the formation of collective patterns are not yet known in detail. We have conducted a set of well-controlled experiments with pedestrians performing simple avoidance tasks in order to determine the laws ruling their behaviour during interactions. The analysis of the large trajectory dataset was used to compute a behavioural map that describes the average change of the direction and speed of a pedestrian for various interaction distances and angles. The experimental results reveal features of the decision process when pedestrians choose the side on which they evade, and show a side preference that is amplified by mutual interactions. The predictions of a binary interaction model based on the above findings were then compared with bidirectional flows of people recorded in a crowded street. Simulations generate two asymmetric lanes with opposite directions of motion, in quantitative agreement with our empirical observations. The knowledge of pedestrian behavioural laws is an important step ahead in the understanding of the underlying dynamics of crowd behaviour and allows for reliable predictions of collective pedestrian movements under natural conditions.
473 citations
TL;DR: A review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena and a critical analysis focused on research perspectives that consider the development of a unified modeling strategy are presented.
Abstract: This paper presents a review and critical analysis of the mathematical literature concerning the modeling of vehicular traffic and crowd phenomena. The survey of models deals with the representation scales and the mathematical frameworks that are used for the modeling approach. The paper also considers the challenging objective of modeling complex systems consisting of large systems of individuals interacting in a nonlinear manner, where one of the modeling difficulties is the fact that these systems are difficult to model at a global level when based only on the description of the dynamics of individual elements. The review is concluded with a critical analysis focused on research perspectives that consider the development of a unified modeling strategy.
434 citations