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Timeevolving measures and macroscopic modeling of pedestrian flow
, 2008
"... This paper deals with the early results of a new model of pedestrian flow, conceived within a measuretheoretical framework. The modeling approach consists in a discretetime Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, pr ..."
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Cited by 49 (11 self)
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This paper deals with the early results of a new model of pedestrian flow, conceived within a measuretheoretical framework. The modeling approach consists in a discretetime Eulerian macroscopic representation of the system via a family of measures which, pushed forward by some motion mappings, provide an estimate of the space occupancy by pedestrians at successive time steps. From the modeling point of view, this setting is particularly suitable to treat nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, analysis and numerical approximation of the resulting mathematical structures, which is the main target of this work, follow more easily and straightforwardly than in case of standard hyperbolic conservation laws, also used in the specialized literature by some Authors to address analogous problems.
Pedestrian flows in bounded domains with obstacles
 Contin. Mech. Thermodyn
"... Abstract. In this paper we systematically apply the mathematical structures by timeevolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discretetime Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Ra ..."
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Cited by 28 (9 self)
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Abstract. In this paper we systematically apply the mathematical structures by timeevolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discretetime Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon positive measures generated by a pushforward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: On the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address twodimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles. 1.
Modeling MicroMacro Pedestrian Counterflow
 in Heterogeneous Domains, Nonlinear Phenomena in Complex Systems, Volume 14, Number 1
, 2011
"... Abstract We present a micromacro strategy able to describe the dynamics of crowds in heterogeneous media. Herein we focus on the example of pedestrian counterflow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of ..."
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Cited by 15 (8 self)
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Abstract We present a micromacro strategy able to describe the dynamics of crowds in heterogeneous media. Herein we focus on the example of pedestrian counterflow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of a version of RadonNikodym Theorem formulated for finite measures. Finally, we illustrate numerically our microscopic model and emphasize the effects produced by an implicitly defined social velocity.
Modeling selforganization in pedestrians and animal groups from macroscopic and microscopic viewpoints
 Mathematical Modeling of Collective Behavior in SocioEconomic and Life Sciences, Modeling and Simulation in Science, Engineering and Technology. Birkhäuser
, 2010
"... Abstract. This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different selforganized patterns from nonlocality and anisotropy of the interactions among individuals. A mathematical techni ..."
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Cited by 12 (6 self)
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Abstract. This paper is concerned with mathematical modeling of intelligent systems, such as human crowds and animal groups. In particular, the focus is on the emergence of different selforganized patterns from nonlocality and anisotropy of the interactions among individuals. A mathematical technique by timeevolving measures is introduced to deal with both macroscopic and microscopic scales within a unified modeling framework. Then selforganization issues are investigated and numerically reproduced at the proper scale, according to the kind of agents under consideration. 1. Selforganization in manyparticle systems One of the most outstanding expressions of intelligence in nonclassical physical systems, such as human crowds or animal groups, is their selforganization ability. Selforganization means that the individuals composing the system can give rise to complex patterns without using intercommunication as an essential mechanism. For instance, in normal conditions pedestrians are known to arrange in specific patterns, chiefly lanes (cf. Fig. 1ab), as demonstrated by many experimental investigations [19, 20, 23, 28, 29]. Lane formation may be fostered by a suitable setup of the space, as reported in [19, 23]: a test performed in a tunnel connecting two subway stations in Budapest showed that a series of columns, placed in the middle of the walkway, induce pedestrians to organize in two oppositely walking lanes, preventing each of them to expand up to the full width of the corridor. More in general, lanes form also spontaneously, i.e., without the need for being triggered by environmental factors, provided the density of pedestrians is sufficiently large [20]. This is particularly evident if one considers the case of two groups of people, walking in opposite directions, which meet and cross (see also [28]). Grouping and selforganization are well known and largely observed also in animals, see for example [34]. These phenomena are in fact ubiquitous, ranging from bird flocks in the sky to migrating lobsters on the sea floor. Many papers on this
Congestion in a macroscopic model of selfdriven particles . . .
, 2009
"... We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finitesize particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reac ..."
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Cited by 12 (5 self)
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We analyze a macroscopic model with a maximal density constraint which describes short range repulsion in biological systems. This system aims at modeling finitesize particles which cannot overlap and repel each other when they are too close. The parts of the fluid where the maximal density is reached behave like incompressible fluids while lower density regions are compressible. This paper investigates the transition between the compressible and incompressible regions. To capture this transition, we study a onedimensional Riemann problem and introduce a perturbation problem which regularizes the compressibleincompressible transition. Specific difficulties related to the nonconservativity of the problem are discussed.
Recognition of crowd behavior from mobile sensors with pattern analysis and graph clustering methods. Networks and Heterogeneous
, 2011
"... Abstract. Mobile onbody sensing has distinct advantages for the analysis and understanding of crowd dynamics: sensing is not geographically restricted to a specific instrumented area, mobile phones offer onbody sensing and they are already deployed on a large scale, and the rich sets of sensors th ..."
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Cited by 11 (1 self)
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Abstract. Mobile onbody sensing has distinct advantages for the analysis and understanding of crowd dynamics: sensing is not geographically restricted to a specific instrumented area, mobile phones offer onbody sensing and they are already deployed on a large scale, and the rich sets of sensors they contain allows one to characterize the behavior of users through pattern recognition techniques. In this paper we present a methodological framework for the machine recognition of crowd behavior from onbody sensors, such as those in mobile phones. The recognition of crowd behaviors opens the way to the acquisition of largescale datasets for the analysis and understanding of crowd dynamics. It has also practical safety applications by providing improved crowd situational awareness in cases of emergency. The framework comprises: behavioral recognition with the user’s mobile device, pairwise analyses of the activity relatedness of two users, and graph clustering in order to uncover globally, which users participate in a given crowd behavior. We illustrate this framework for the identification of groups of persons walking, using empirically collected data. We discuss the challenges and research avenues for theoretical and applied mathematics arising from the mobile sensing of crowd behaviors. 1. Introduction. Nowadays
A hierarchy of heuristicbased models of crowd dynamics,”
 Journal of Statistical Physics,
, 2013
"... Abstract We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral IndividualBased Model of Acknowledgments: This work has been supported by the French 'Agence Nationale pour la Recherche (ANR)' in the frame of the contracts 'Pedigree& ..."
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Cited by 6 (1 self)
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Abstract We derive a hierarchy of kinetic and macroscopic models from a noisy variant of the heuristic behavioral IndividualBased Model of Acknowledgments: This work has been supported by the French 'Agence Nationale pour la Recherche (ANR)' in the frame of the contracts 'Pedigree' (ANR08SYSC01501) and 'CBDifFr' (ANR08BLAN033301)
Visionbased macroscopic pedestrian models
, 2013
"... We propose a hierarchy of kinetic and macroscopic models for a system consisting of a large number of interacting pedestrians. The basic interaction rules are derived from [44] where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the beari ..."
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Cited by 3 (0 self)
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We propose a hierarchy of kinetic and macroscopic models for a system consisting of a large number of interacting pedestrians. The basic interaction rules are derived from [44] where the dangerousness level of an interaction with another pedestrian is measured in terms of the derivative of the bearing angle (angle between the walking direction and the line connecting the two subjects) and of the timetointeraction (time before reaching the closest distance between the two subjects). A meanfield kinetic model is derived. Then, three different macroscopic continuum models are proposed. The first two ones rely on two different closure assumptions of the kinetic model, respectively based on a monokinetic and a von MisesFisher distribution. The third one is derived through a hydrodynamic limit. In each case, we discuss the relevance of the model for practical simulations of pedestrian crowds.