On the modelling and management of traffic

Colombo, Rinaldo M.; Goatin, Paola; Rosini, Massimiliano D.

doi:10.1051/m2an/2010105

Cited by 49 publications

(50 citation statements)

References 47 publications

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“…Another extension of this work is to consider the ADR model with constraints that are non-local in time. Such constraints allow to tackle optimal management problems in the spirit of [27,28].…”

Section: Discussionmentioning

confidence: 99%

Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

et al. 2016

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In this paper we investigate numerically the model for pedestrian traffic proposed in [B. Andreianov, C. Donadello, M.D. Rosini, Crowd dynamics and conservation laws with nonlocal constraints and capacity drop, Mathematical Models and Methods in Applied Sciences 24 (13) (2014) 2685-2722] . We prove the convergence of a scheme based on a constraint finite volume method and validate it with an explicit solution obtained in the above reference. We then perform ad hoc simulations to qualitatively validate the model under consideration by proving its ability to reproduce typical phenomena at the bottlenecks, such as Faster Is Slower effect and the Braess' paradox.

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Section: Discussionmentioning

confidence: 99%

Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

et al. 2016

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“…It is obtained by coupling the Aw-Rascle-Zhang (ARZ) model, see [4,21], with a fixed local point constraint on the (density) flux. Conservation laws with unilateral constraints on the flux were first introduced in [11] and then studied in [1,3,8,9] in the case of first order traffic flow models (consisting in scalar conservation laws) to describe the situations in which "obstacles" like toll gates, traffic lights or construction sites are present, see [10,19]. We recall that in this case the presence of the constraint may enforce the appearance of undercompressive stationary jump discontinuities, which do not satisfy the Kruzhkov entropy condition [16] even though the first Rankine-Hugoniot condition remains valid, ensuring mass conservation.…”

Section: Introductionmentioning

confidence: 99%

Existence of BV solutions for a non-conservative constrained Aw–Rascle–Zhang model for vehicular traffic

Dymski

Goatin

Rosini

2018

Journal of Mathematical Analysis and Applications

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In this paper we study the Aw-Rascle-Zhang (ARZ) model with non-conservative local point constraint on the density flux introduce in [Garavello, M., and Goatin, P. The Aw-Rascle traffic model with locally constrained flow. Journal of Mathematical Analysis and Applications 378, 2 (2011), 634-648], its motivation being, for instance, the modeling of traffic across a toll gate. We prove the existence of weak solutions under assumptions that result to be more general than those required in [Garavello, M., and Villa, S. The Cauchy problem for the Aw-Rascle-Zhang traffic model with locally constrained flow. Journal of Hyperbolic Differential Equations 14, 03 (2017), 393-414]. More precisely, we do not require that the waves of the first characteristic family have strictly negative speeds of propagation. The result is achieved by showing the convergence of a sequence of approximate solutions constructed via the wave-front tracking algorithm. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.

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“…We recall that the concept of point constraints was introduced in the framework of vehicular traffic in [19] and in the framework of crowd dynamics in [26]. We defer to [1,2,3,4,5,6,16,17,21,22,23,28,29,40,50] for further developments and applications also to crowd dynamics.…”

Section: Introductionmentioning

confidence: 99%

Entropy solutions for a traffic model with phase transitions

Benyahia

Rosini

2016

Nonlinear Analysis: Theory, Methods & Applications

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In this paper, we consider the two phases macroscopic traffic model introduced in [P. Goatin, The Aw-Rascle vehicular traffic flow with phase transitions, Mathematical and Computer Modeling 44 (2006) 287-303]. We first apply the wave-front tracking method to prove existence and a priori bounds for weak solutions. Then, in the case the characteristic field corresponding to the free phase is linearly degenerate, we prove that the obtained weak solutions are in fact entropy solutionsà la Kruzhkov. The case of solutions attaining values at the vacuum is considered. We also present an explicit numerical example to describe some qualitative features of the solutions.

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On the modelling and management of traffic

Cited by 49 publications

References 47 publications

Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

Qualitative behaviour and numerical approximation of solutions to conservation laws with non-local point constraints on the flux and modeling of crowd dynamics at the bottlenecks

Existence of BV solutions for a non-conservative constrained Aw–Rascle–Zhang model for vehicular traffic

Entropy solutions for a traffic model with phase transitions

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