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

Freguglia, Paolo; Tosin, Andrea

doi:10.4310/cms.2017.v15.n1.a10

Cited by 12 publications

(17 citation statements)

References 27 publications

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“…In particular, such conditions are met iff * (τ, v) = ∂ vf * (τ, v) = 0 for v = 0, 1 and all τ > 0. Using the expression (3) of I and taking (27) into account we have that the asymptotic speed distributionf * ∞ (v) that the system approaches for τ → +∞ solves…”

Section: Asymptotic Speed Variance and Risk Mitigationmentioning

confidence: 99%

Kinetic-Controlled Hydrodynamics for Traffic Models with Driver-Assist Vehicles

Tosin¹,

Zanella²

2019

Multiscale Model. Simul.

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We develop a hierarchical description of traffic flow control by means of driver-assist vehicles aimed at the mitigation of speed-dependent road risk factors. Microscopic feedback control strategies are designed at the level of vehicle-to-vehicle interactions and then upscaled to the global flow via a kinetic approach based on a Boltzmann-type equation. Then first and second order hydrodynamic traffic models, which naturally embed the microscopic control strategies, are consistently derived from the kinetic-controlled framework via suitable closure methods. Several numerical examples illustrate the effectiveness of such a hierarchical approach at the various scales.

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Section: Asymptotic Speed Variance and Risk Mitigationmentioning

confidence: 99%

Kinetic-Controlled Hydrodynamics for Traffic Models with Driver-Assist Vehicles

Tosin¹,

Zanella²

2019

Multiscale Model. Simul.

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“…It can be proven [9] that the Cauchy problem associated to (2) is well posed provided the probability density A is Lipschitz continuous with respect to v * and v * in a suitable Wasserstein metric. This is indeed the case of the A defined in (3), with P 1 = P 2 .…”

Section: Choice Of the Probability Density Amentioning

confidence: 99%

“…In order to compute the A j χ matrices, we observe that the gain operator of the δ model given in (9) differs from the gain operator of the χ model only in the terms proportional to P appearing in the equation (16). Therefore, we just show the terms resulting from…”

Section: A Matrix Elements For the Discretization Of The χ Modelmentioning

confidence: 99%

Kinetic models for traffic flow resulting in a reduced space of microscopic velocities

Puppo¹,

Semplice²,

Tosin³

et al. 2017

Kinetic &Amp; Related Models

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The purpose of this paper is to study the properties of kinetic models for traffic flow described by a Boltzmann-type approach and based on a continuous space of microscopic velocities. In our models, the particular structure of the collision kernel allows one to find the analytical expression of a class of steady-state distributions, which are characterized by being supported on a quantized space of microscopic speeds. The number of these velocities is determined by a physical parameter describing the typical acceleration of a vehicle and the uniqueness of this class of solutions is supported by numerical investigations. This shows that it is possible to have the full richness of a kinetic approach with the simplicity of a space of microscopic velocities characterized by a small number of modes. Moreover, the explicit expression of the asymptotic distribution paves the way to deriving new macroscopic equations using the closure provided by the kinetic model

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“…[13,14] where both the acceleration and the slowing down interactions are modeled with a Vlasov-type relaxation towards a desired speed. Kinetic theory is also used to model multilane traffic flow [12,19,20,25,3], flows on networks [8], inhomogeneous space problems with non local interactions [18], control problems [15] and safety aspects in vehicular traffic [9]. For a review on kinetic traffic models, see [21].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a multi-population kinetic model for traffic flow

Puppo

Semplice

Tosin

et al. 2017

Communications in Mathematical Sciences

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In this work we extend a recent kinetic traffic model [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Kinet. Relat. Models, in press, 2016] to the case of more than one class of vehicles, each of which is characterized by few different microscopic features. We consider a Boltzmann-like framework with only binary interactions, which take place among vehicles belonging to the various classes. Our approach differs from the multi-population kinetic model proposed in [G. Puppo, M. Semplice, A. Tosin, G. Visconti, Commun. Math. Sci., 14:643-669, 2016] because here we assume continuous velocity spaces and we introduce a parameter describing the physical velocity jump performed by a vehicle that increases its speed after an interaction. The model is discretized in order to investigate numerically the structure of the resulting fundamental diagrams and the system of equations is analyzed by studying well posedness. Moreover, we compute the equilibria of the discretized model and we show that the exact asymptotic kinetic distributions can be obtained with a small number of velocities in the grid. Finally, we introduce a new probability law in order to attenuate the sharp capacity drop occurring in the diagrams of traffic

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

Cited by 12 publications

References 27 publications

Kinetic-Controlled Hydrodynamics for Traffic Models with Driver-Assist Vehicles

Kinetic-Controlled Hydrodynamics for Traffic Models with Driver-Assist Vehicles

Kinetic models for traffic flow resulting in a reduced space of microscopic velocities

Analysis of a multi-population kinetic model for traffic flow

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