Modélisation du trafic autoroutier au second ordre

Lebacque, Jean-Patrick; Louis, Xavier; Mammar, Salim; Schnetzler, Bernard; Haj-Salem, Habib

doi:10.1016/j.crma.2008.09.024

Cited by 15 publications

(18 citation statements)

References 9 publications

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“…Finally, in the engineering literature, a junction model has been proposed in [16] for models extracted from the GSOM family [18,17] which encompasses a wide range of second order traffic flow models. The authors assume that all the incoming fluxes mix through a buffer at the junction before exiting on the outgoing roads.…”

Section: Review Of the Literaturementioning

confidence: 99%

Pareto-Optimal Coupling Conditions for the Aw--Rascle--Zhang Traffic Flow Model at Junctions

Kolb¹,

Costeseque²,

Goatin³

et al. 2018

SIAM J. Appl. Math.

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This article deals with macroscopic traffic flow models on a road network. More precisely, we consider coupling conditions at junctions for the Aw-Rascle-Zhang second order model consisting of a hyperbolic system of two conservation laws. These coupling conditions conserve both the number of vehicles and the mixing of Lagrangian attributes of traffic through the junction. The proposed Riemann solver is based on assignment coefficients, multi-objective optimization of fluxes and priority parameters. We prove that this Riemann solver is wellposed in the case of special junctions, including 1-to-2 diverge and 2-to-1 merge.Due to finite wave propagation speed, it is not restrictive to study a single junction. We define a junction J as the set of n incoming and m outgoing branches that meet at a single point (namely the junction point supposed to be located at x = 0) such that J = n+m i=1 J i · e i where e i ∈ R n+m are unit vectors and the branch J i for any i ∈ {1, . . . , n + m} is defined as follows:] − ∞, 0[, for any i = 1, . . . , n, ]0, +∞[, for any i = n + 1, . . . , n + m.In the remaining, we will mainly focus on the cases of a 1-to-1 junction (n = m = 1), a merge (n = 2 and m = 1) and a diverge (n = 1 and m = 2).

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Section: Review Of the Literaturementioning

confidence: 99%

Pareto-Optimal Coupling Conditions for the Aw--Rascle--Zhang Traffic Flow Model at Junctions

Kolb¹,

Costeseque²,

Goatin³

et al. 2018

SIAM J. Appl. Math.

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“…The first phase transition model for traffic has been introduced by Colombo in 2002, 5192 MAURO GARAVELLO AND FRANCESCA MARCELLINI see [4,5]. For other 2-phases and phase transition models, see [2,7,12,16,18] and the references therein.…”

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The Riemann Problem at a Junction for a Phase Transition Traffic Model

Garavello¹,

Marcellini²

2017

Discrete &Amp; Continuous Dynamical Systems - A

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We extend the Phase Transition model for traffic proposed in [8], by Colombo, Marcellini, and Rascle to the network case. More precisely, we consider the Riemann problem for such a system at a general junction with n incoming and m outgoing roads. We propose a Riemann solver at the junction which conserves both the number of cars and the maximal speed of each vehicle, which is a key feature of the Phase Transition model. For special junctions, we prove that the Riemann solver is well defined.

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“…In 2002, Colombo proposed the first second order model with two phases, see [6,7]. For other 2−phases and phase transition models see [4,8,17,19,21].…”

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confidence: 99%