A non-local traffic flow model for 1-to-1 junctions

Felisia Angela A Chiarello (1, 2) , Jan Friedrich (3) , Paola Goatin (1, 2) , Simone Göttlich (3) , Oliver Kolb (3)

1 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
2 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
3 Universität Mannheim

We present a model for a class of non-local conservation laws arising in traffic flow modeling at road junctions. Instead of a single velocity function for the whole road, we consider two different road segments, which may differ for their speed law and number of lanes (hence their maximal vehicle density). We use an upwind type numerical scheme to construct a sequence of approximate solutions and we provide uniform L∞ and total variation estimates. In particular, the solutions of the proposed model stay positive and below the maximum density of each road segment. Using a Lax-Wendroff type argument and the doubling of variables technique, we prove the well-posedness of the proposed model. Finally, some numerical simulations are provided and compared with the corresponding (discontinuous) local model.

Mots clés: Macroscopic traffic flow models on networks.; Non-local scalar conservation laws; Upwind scheme; Macroscopic traffic flow models on networks AMS subject classifications: 35L65

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Physique mathématique [math-ph]

Felisia Angela A Chiarello, Jan Friedrich, Paola Goatin, Simone Göttlich, Oliver Kolb. A non-local traffic flow model for 1-to-1 junctions. European Journal of Applied Mathematics, 2020, 31 (6), pp.1029-1049. ⟨hal-02142345v2⟩