A macroscopic model for platooning in highway traffic

Giulia Piacentini (1) , Paola Goatin (2, 3, 4) , Antonella Ferrara (1)

1 DIII UNIPV - Dipartimento di Ingegneria Industriale e dell'Informazione = Department of Electrical, Computer and Biomedical Engineering [Univ Pavia]
2 ACUMES - Analysis and Control of Unsteady Models for Engineering Sciences
3 JAD - Laboratoire Jean Alexandre Dieudonné
4 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)

We consider a model describing the presence of a platoon of vehicles moving in the traffic flow. The model consists of a coupled PDE-ODE system describing the interaction between the platoon and the surrounding traffic flow. The scalar conservation law takes into account the main traffic evolution, while the ODEs describe the trajectories of the initial and final points of the platoon, whose length can vary in time. The presence of the platoon acts as a road capacity reduction, resulting in a space-time discontinuous flux function. We describe the solutions of Riemann problems and design a finite volume numerical scheme sharply capturing non-classical discontinuities. Some numerical tests are presented to show the effectiveness of the method.

Mots clés: Scalar conservation laws with space-time discontinuous flux; Traffic flow mod- eling; PDE-ODE systems; conservative finite volume schemes

Domaines: Equations aux dérivées partielles [math.AP]

Giulia Piacentini, Paola Goatin, Antonella Ferrara. A macroscopic model for platooning in highway traffic. SIAM Journal on Applied Mathematics, 2020, 80 (1), pp.639-656. ⟨hal-02309950⟩