A Microscopic-To-Macroscopic Crowd Dynamic Model

Al-nasur, Sadeq J.; Kachroo, Pushkin

doi:10.1109/itsc.2006.1706808

Cited by 22 publications

(16 citation statements)

References 9 publications

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“…Other IBM's are based on traffic models [37]. CM have been pioneered by [29] and the link to the underlying IBM, explored in [1,9,10,13,26,52]. Direct derivation of CM from optimization rules can be developed [31,32,33,35].…”

mentioning

confidence: 99%

Vision-based macroscopic pedestrian models

Degond¹,

Appert-Rolland²,

Pettré³

et al. 2013

Kinetic &Amp; Related Models

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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 earlier work 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 time-to-interaction (time before reaching the closest distance between the two subjects). A mean-field 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 Mises-Fisher 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

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mentioning

confidence: 99%

Vision-based macroscopic pedestrian models

Degond¹,

Appert-Rolland²,

Pettré³

et al. 2013

Kinetic &Amp; Related Models

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show abstract

“…Note that in [1,2], a derivation of a two-dimensional macroscopic crowd model from a microscopic model was proposed. In contrast to these studies, here we provide a detailed analysis of the approximation of the solution to the associated Riemann problem.…”

Section: Multi-lane Models Based On the Coupling Of One-dimensional mentioning

confidence: 99%

“…i be the local density in the one-dimensional (see (2)) and in the two-dimensional case (see (8)), respectively. Observe that…”

Section: Derivation Of a Two-dimension Spatial Extension Of The Arz Mmentioning

confidence: 99%

Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow

Herty¹,

Moutari²,

Visconti³

2018

SIAM J. Appl. Math.

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Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in a one dimensional framework, henceforth lane changing behavior is either not explicitly modeled or explicitly forbidden. In this paper, we propose a macroscopic model, which accounts for lane-changing behavior on motorway, based on a two-dimensional extension of the Aw and Rascle [4] and Zhang [39] macroscopic model for traffic flow. Under conditions, when lane changing maneuvers are no longer possible, the model "relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same approach as in [3], we derive the two-dimensional macroscopic model through scaling of time discretization of a microscopic follow-the-leader model with driving direction. We provide a detailed analysis of the space-time discretization of the proposed macroscopic model as well as an approximation of the solution to the associated Riemann problem. Furthermore, we illustrate some promising features of the proposed model through some numerical experiments.

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“…As the escalation of theoretical and experimental studies, some researchers [10][11][12] discovered that first-order partial differential equations are always in an equilibrium state. In addition, the function of density and velocity cannot reflect the instantaneous changes in a crowd, which means that the first-order model is not capable of explaining some complex phenomena, such as stop-and-go waves and bottleneck clogging [13].…”

Section: Introductionmentioning

confidence: 99%

Cluster Risk of Walking Scenarios Based on Macroscopic Flow Model and Crowding Force Analysis

Zhou

Feng

et al. 2018

Sustainability

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Abstract:In recent years, accidents always happen in confined space such as metro stations because of congestion. Various researchers investigated the patterns of dense crowd behaviors in different scenarios via simulations or experiments and proposed methods for avoiding accidents. In this study, a classic continuum macroscopic model was applied to simulate the crowded pedestrian flow in typical scenarios such as at bottlenecks or with an obstacle. The Lax-Wendroff finite difference scheme and artificial viscosity filtering method were used to discretize the model to identify high-density risk areas. Furthermore, we introduced a contact crowding force test of the interactions among pedestrians at bottlenecks. Results revealed that in the most dangerous area, the individual on the corner position bears the maximum pressure in such scenarios is 90.2 N, and there is an approximate exponential relationship between crowding force and density indicated by our data. The results and findings presented in this paper can facilitate more reasonable and precise simulation models by utilizing crowding force and crowd density and ensure the safety of pedestrians in high-density scenarios.

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A Microscopic-To-Macroscopic Crowd Dynamic Model

Cited by 22 publications

References 9 publications

Vision-based macroscopic pedestrian models

Vision-based macroscopic pedestrian models

Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow

Cluster Risk of Walking Scenarios Based on Macroscopic Flow Model and Crowding Force Analysis

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