A mixed system modeling two-directional pedestrian flows

Goatin, Paola; Mimault, Matthias

doi:10.3934/mbe.2015.12.375

Cited by 10 publications

(14 citation statements)

References 22 publications

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“…We believe that conservation law system (11) can produce and propagate sharp gradients in the solution, while such sharp gradients are typically 'smoothed out' rather quickly in stochastic simulations. Further, as pointed out in [15,23], conservation laws which are conditionally hyperbolic can potentially develop high-frequency, non-physical oscillations in the non-hyperbolic regime. Therefore, this set of simulations is designed to test how well the macroscopic model performs in the non-hyperbolic regime with large initial gradients.…”

Section: Simulations With Non-uniform Initial Densitymentioning

confidence: 99%

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Ott

Timofeyev

Weber

2020

Physica D: Nonlinear Phenomena

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We study the evolution of interacting groups of agents in two-dimensional geometries. We introduce a microscopic stochastic model that includes floor fields modeling the global flow of individual groups as well as local interaction rules. From this microscopic model we derive an analytically-tractable system of conservation laws that governs the evolution of the macroscopic densities. Numerical simulations show good agreement between the system of conservation laws and the microscopic model, though the latter is slightly more diffusive. We conclude by deriving second-order corrections to the system of conservation laws.

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Section: Simulations With Non-uniform Initial Densitymentioning

confidence: 99%

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Ott

Timofeyev

Weber

2020

Physica D: Nonlinear Phenomena

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“…The limit τ → 0: Let ρ k denote a sequence of solutions to (21). We define ρ τ (x, t) = ρ k (x) for x ∈ Ω and t ∈ ((k − 1)τ, kτ ] Then ρ τ solves the following problem where σ τ denotes the shift operator, that is (…”

Section: The Dissipation Inequality and The Recursion Yieldsmentioning

confidence: 99%

Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data

Gomes¹,

Stuart²,

Wolfram³

2019

SIAM J. Appl. Math.

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In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -microscopic data. We consider a unidirectional flow of pedestrians in a corridor and assume that the velocity decreases with the average density according to the fundamental diagram. Our model is formed from a coupling between a density dependent stochastic differential equation and a nonlinear partial differential equation for the density, and is hence of McKean-Vlasov type. We discuss identifiability of the parameters appearing in the fundamental diagram from trajectories of individuals, and we introduce optimization and Bayesian methods to perform the identification. We analyze the performance of the developed methodologies in various situations, such as for different in-and outflow conditions, for varying numbers of individual trajectories and for differing channel geometries.

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“…In this paper, we do another type of aggregation that aims to approximate traffic flow as fluid in the 2D plane. Mathematically, these models are identical to those of pedestrian [12] but have also some fundamental difference starting from the fact that pedestrians generally evolve in the 2D-plane, whereas the propagation of traffic depends on the underlying network. Some two-dimensional traffic flow models are inspired from pedestrian modeling [13], [14].…”

Section: Introductionmentioning

confidence: 99%

“…One way to accomodate the multiple directions of flow is to extend the existing model in [18] to a system of conservation laws. However, these systems of equations are not always hyperbolic as for the case of two populations of pedestrian evolving in opposite direction [12]. This loss of hyperbolicity can produce instability and oscillation on usual numerical methods.…”

Section: Introductionmentioning

confidence: 99%

A decision support and planning mobility method for large scale traffic networks

Mollier

Monache

Canudas‐de‐Wit

2019

2019 18th European Control Conference (ECC)

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This paper presents a new planning and decisionmaking method in large scale traffic networks for predicting how traffic evolves in special events, emergencies and changes in the city mobility demands. The proposed method is based on a 2-D aggregated traffic model for large scale traffic networks [1], [2] which describes traffic evolution as a fluid in two space dimensions. We propose an extension of the model by including additional state density variables, each one associated to a particular layer describing vehicles evolving in different directions. The model is a 2D-PDE described by a system of conservation laws. For this specific case, the resulting PDE is not anymore hyperbolic as typically the LWR model but results in a hybrid hyperbolic-elliptic PDE depending on the density level. In this case, usual numerical schemes may be not valid and often lead to oscillation in the solution. Thus, we consider a high order numerical scheme to improve the numerical solution. Finally, the model is used to predict how the typical traffic evolution will be impacted in particular scenarios like special events or changes in demands. Comparative simulations are provided.

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A mixed system modeling two-directional pedestrian flows

Cited by 10 publications

References 22 publications

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Stochastic and coarse-grained two-dimensional modeling of directional particle movement

Parameter Estimation for Macroscopic Pedestrian Dynamics Models from Microscopic Data

A decision support and planning mobility method for large scale traffic networks

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