Comparative study of macroscopic traffic flow models at road junctions

Goatin, Paola; Rossi, Elena

doi:10.3934/nhm.2020012

Cited by 3 publications

(3 citation statements)

References 20 publications

(49 reference statements)

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“…The situation is completely different for junctions involving at least 3 branches. Indeed, although many works have been devoted to such junctions (see for instance [5,21,26,28,30,37,43]), the problem is still poorly understood and the general picture is far from clear. For instance, if the germ approach of [6] has been recently extended to general junctions in [21,37] (and we strongly use this extension in the paper), there are still few examples of germs which are maximal and complete; one of the outcome of our paper is to describe a new class of such germs (note however that a particular case was previously discussed in [43]).…”

Section: Review Of the Literaturementioning

confidence: 99%

“…It is interesting to compare our class of germs (that we call here the class of traffic light germs, TLgerms in brief) with some of the known germs in the literature on junctions (see in particular [28]). We only consider 1:2 junctions because a reversed germ is automatically constructed for 2:1 junctions, by reversion transform.…”

Section: Review Of the Literaturementioning

confidence: 99%

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From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

Cardaliaguet¹,

Forcadel²

2021

SIAM J. Math. Anal.

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We consider traffic flows described by conservation laws. We study a 2:1 junction (with two incoming roads and one outgoing road) or a 1:2 junction (with one incoming road and two outgoing roads). At the mesoscopic level, the priority law at the junction is given by traffic lights, which are periodic in time and the traffic can also be slowed down by periodic in time flux-limiters.After a long time, and at large scale in space, we intuitively expect an effective junction condition to emerge. Precisely, we perform a rescaling in space and time, to pass from the mesoscopic scale to the macroscopic one. At the limit of the rescaling, we show rigorous homogenization of the problem and identify the effective junction condition, which belongs to a general class of germs (in the terminology of [6,21,37]). The identification of this germ and of a characteristic subgerm which determines the whole germ, is the first key result of the paper.The second key result of the paper is the construction of a family of correctors whose values at infinity are related to each element of the characteristic subgerm. This construction is indeed explicit at the level of some mixed Hamilton-Jacobi equations for concave Hamiltonians (i.e. fluxes). The explicit solutions are found in the spirit of representation formulas for optimal control problems.

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Section: Review Of the Literaturementioning

confidence: 99%

Section: Review Of the Literaturementioning

confidence: 99%

From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

Cardaliaguet¹,

Forcadel²

2021

SIAM J. Math. Anal.

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“…A number of such scalar models have been proposed, mostly differing in how the junction is modeled. An incomplete list of such models can be found in [4,5,6,8,7,12,11,13,14,15,16,18,19]. In this paper we focus on the so-called vanishing viscosity solution proposed and analyzed in [7] and [2].…”

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confidence: 99%

An explicit finite volume algorithm for vanishing viscosity solutions on a network

Towers¹

2022

NHM

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<p style='text-indent:20px;'>In [Andreianov, Coclite, Donadello, Discrete Contin. Dyn. Syst. A, 2017], a finite volume scheme was introduced for computing vanishing viscosity solutions on a single-junction network, and convergence to the vanishing viscosity solution was proven. This problem models <inline-formula><tex-math id="M1">\begin{document}$ m $\end{document}</tex-math></inline-formula> incoming and <inline-formula><tex-math id="M2">\begin{document}$ n $\end{document}</tex-math></inline-formula> outgoing roads that meet at a single junction. On each road the vehicle density evolves according to a scalar conservation law, and the requirements for joining the solutions at the junction are defined via the so-called vanishing viscosity germ. The algorithm mentioned above processes the junction in an implicit manner. We propose an explicit version of the algorithm. It differs only in the way that the junction is processed. We prove that the approximations converge to the unique entropy solution of the associated Cauchy problem.</p>

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Traffic flow density study at traffic light junction

Saliev,

Damyanov

2024

12th International Scientific Conference “Techsys 2023” – Engineering, Technologies and Systems

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Comparative study of macroscopic traffic flow models at road junctions

Cited by 3 publications

References 20 publications

From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

From Heterogeneous Microscopic Traffic Flow Models to Macroscopic Models

An explicit finite volume algorithm for vanishing viscosity solutions on a network

Traffic flow density study at traffic light junction

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