From experiments to hydrodynamic traffic flow models: I—modelling and parameter identification

Bonzani, Ida; Mussone, Lorenzo

doi:10.1016/s0895-7177(03)90051-3

Cited by 31 publications

(29 citation statements)

References 19 publications

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“…Fundamental relationships are either measured experimentally, cf. e.g., [4,13], or expressed analytically, cf. e.g., [11,16].…”

Section: Quick Overview Of Discrete Kinetic Modelsmentioning

confidence: 99%

Fundamental diagrams for kinetic equations of traffic flow

Fermo¹,

Tosin²

2014

Discrete &Amp; Continuous Dynamical Systems - S

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In this paper we investigate the ability of some recently introduced discrete kinetic models of vehicular traffic to catch, in their large time behavior, typical features of theoretical fundamental diagrams. Specifically, we address the so-called "spatially homogeneous problem" and, in the representative case of an exploratory model, we study the qualitative properties of its solutions for a generic number of discrete microstates. This includes, in particular, asymptotic trends and equilibria, whence fundamental diagrams originate.Comment: 14 page

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“…Fundamental relationships are either measured experimentally, cf. e.g., [4,13], or expressed analytically, cf. e.g., [11,16].…”

Section: Quick Overview Of Discrete Kinetic Modelsmentioning

confidence: 99%

Fundamental diagrams for kinetic equations of traffic flow

Fermo¹,

Tosin²

2014

Discrete &Amp; Continuous Dynamical Systems - S

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“…6(a), observa-se que quando a densidade atinge valores superiores a ρ crit ocorre uma descontinuidade no gráfico. Quando faz-se ajustes em gráficos experimentais [29], como pode-se observar na Fig. 7, após um certo valor para a densidade, a função de ajuste não se adéqua perfeitamente aos dados devido a uma alta dispersão destes naquela região.…”

Section: Resultsunclassified

Modelagem do fluxo de pedestres pela teoria macroscópica

Vargas

Gramani

Kaviski

et al. 2012

Rev. Bras. Ensino Fís.

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A necessidade de modelar o tráfego de pedestres tem se tornado uma prioridade em ambientes por onde os pedestres possam circular. As pesquisas avançam na tentativa de solucionar acidentes relacionados a multidões. Além disso, analisar estruturas para pedestres antes que elas tenham sido construídas tem se tornado uma exigência das autoridades, assim como poder gerenciar o fluxo de pedestres nessas instalações. Para caracterizar este comportamento, surgiram estudos abrangendo teorias da física e da matemática, que analisam o tráfego de pedestres através de modelos descritos por equações diferenciais eíntegro-diferenciais. Neste trabalho apresenta-se um exemplo de modelo para o tráfego, abordando-o sob a escala macroscópica de modelagem do tráfego e sua ligação direta com a física e os modelos hidrodinâmicos. Aplica-se o modelo criado a uma situação de caminhada, onde os resultados foram comparados a outros trabalhos referentes a simulações e observações experimentais sobre o tráfego de pedestres, encontrados na bibliografia. Palavras-chave: teoria macroscópica, fluxo de pedestres. The need to model the traffic of pedestrians has become a priority in environments where pedestrians can circulate. The research has advanced in an attempt to solve accidents related to large crowds. Furthermore, analyzing structures for pedestrians before they have been built has become a requirement of the authorities, as well as being able to manage the flow of pedestrians in those facilities. To characterize this behavior, studies have emerged including theories of physics and mathematics, which analyze pedestrian traffic through models described by differential and integral-differential equations. This work presents the macroscopic scale modeling of traffic and its direct connection with physics and hydrodynamic models. The model was applied to a walk situation where the results were compared with other work on the simulations and experimental observations on the pedestrian traffic, found in the bibliography. Keywords: macroscopic theory, flow of pedestrians. IntroduçãoCada vez mais a necessidade de modelar o fluxo de pedestres tem se tornado uma prioridade nas grandes cidades e vias urbanas em geral. Com esse objetivo, surgem pesquisas no campo da matemática, física e engenharia, analisando o pedestre individualmente ou considerando o fluxo de multidões.O fluxo de pedestres pode ser representado por três diferentes escalas. Especificamente tem-se:

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“…therefore integrating (7) with respect to w gives that such a density is actually constant in time (conservation of mass). For the study of basic qualitative properties of (7) the reader may refer to Appendix A, where we tackle the well-posedness of the Cauchy problem associated with (7) in the frame of measure-valued differential equations in Wasserstein spaces. Such a theoretical setting, which is more abstract than the one usually considered in the literature for similar equations, see e.g., [6, Appendix A] and [26], is here motivated by the specialisation of the model that we are going to discuss in the next section.…”

Section: Evolution Equation For the Distribution Functionmentioning

confidence: 99%

“…Then the corresponding unique solution to (7) is (8) with coefficients f ij (t) given by (9) along with the initial conditions f ij (0) = f 0 ij . In addition, it depends continuously on the initial datum as stated by Theorem A.5.…”

Section: Discrete Microscopic Statesmentioning

confidence: 99%

Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

Freguglia

Tosin

2017

Communications in Mathematical Sciences

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Abstract. This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.

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From experiments to hydrodynamic traffic flow models: I—modelling and parameter identification

Cited by 31 publications

References 19 publications

Fundamental diagrams for kinetic equations of traffic flow

Fundamental diagrams for kinetic equations of traffic flow

Modelagem do fluxo de pedestres pela teoria macroscópica

Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

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