Volume 53, Number 1, January–February 2019
|Page(s)||1 - 34|
|Published online||14 March 2019|
Representation of capacity drop at a road merge via point constraints in a first order traffic model
Dipartimento di Ingegneria e Scienze de l’Informazione e Matematica, Università dell’Aquila, Via Vetoio, 67100 L’Aquila, Italy
2 Laboratoire de mathématiques, CNRS UMR 6623, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030 Besançon, France
3 Dipartimento di Matematica, Università di Bari, Via E. Orabona 4, 70126 Bari, Italy
4 Dipartimento di Matematica e Informatica, Università di Ferrara, Via Machiavelli 35, 44121 Ferrara, Italy
5 Uniwersytet Marii Curie-Skł odowskiej, Plac Marii Curie-Skł odowskiej 1, 20-031 Lublin, Poland
* Corresponding author: firstname.lastname@example.org
Accepted: 28 December 2018
We reproduce the capacity drop phenomenon at a road merge by implementing a non-local point constraint at the junction in a first order traffic model. We call capacity drop the situation in which the outflow through the junction is lower than the receiving capacity of the outgoing road, as too many vehicles trying to access the junction from the incoming roads hinder each other. In this paper, we first construct an enhanced version of the locally constrained model introduced by Haut et al. (Proceedings 16th IFAC World Congress. Prague, Czech Republic 229 (2005) TuM01TP/3), then we propose its counterpart featuring a non-local constraint and finally we compare numerically the two models by constructing an adapted finite volumes scheme.
Mathematics Subject Classification: 35L65 / 35R02 / 90B20 / 76M12
Key words: Scalar conservation law / LWR model / traffic flow on networks / point constraint on the flux / finite volumes schemes
© EDP Sciences, SMAI 2019
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