Interacting moving bottlenecks in traffic flow

Paola Goatin; Chiara Daini; Maria Laura Delle Monache; Antonella Ferrara; Paola Goatin; Chiara Daini; Maria Laura Delle Monache; Antonella Ferrara

doi:10.3934/nhm.2023040

Networks and Heterogeneous Media

2023, Volume 18, Issue 2: 930-945. doi: 10.3934/nhm.2023040

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Interacting moving bottlenecks in traffic flow

1.
Université Côte d'Azur, Inria, CNRS, LJAD Sophia Antipolis, France
2.
Inria Paris, Kopernic Research Group Paris, France
3.
Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA
4.
Department of Electrical, Computer and Biomedical Engineering, University of Pavia, Pavia, Italy

Received: 12 November 2021 Revised: 10 May 2022 Accepted: 08 July 2022 Published: 17 March 2023

We present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow. The model consists of a scalar conservation law for the bulk traffic, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. In turn, AVs are forced to adapt their speed to the downstream traffic average velocity in congested situations. We analyze the model solutions in a Riemann-type setting, and propose an adapted finite volume scheme to compute approximate solutions for general initial data. The work paves the way to the study of general optimal control strategies for AV velocities, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities.
- Conservation laws,
- PDE-ODE systems,
- macroscopic traffic flow models,
- moving bottlenecks,
- autonomous vehicles
Citation: Paola Goatin, Chiara Daini, Maria Laura Delle Monache, Antonella Ferrara. Interacting moving bottlenecks in traffic flow[J]. Networks and Heterogeneous Media, 2023, 18(2): 930-945. doi: 10.3934/nhm.2023040

Related Papers:

Abstract

We present a general multi-scale approach for modeling the interaction of controlled autonomous vehicles (AVs) with the surrounding traffic flow. The model consists of a scalar conservation law for the bulk traffic, coupled with ordinary differential equations describing the possibly interacting AV trajectories. The coupling is realized through flux constraints at the moving bottleneck positions, inducing the formation of non-classical jump discontinuities in the traffic density. In turn, AVs are forced to adapt their speed to the downstream traffic average velocity in congested situations. We analyze the model solutions in a Riemann-type setting, and propose an adapted finite volume scheme to compute approximate solutions for general initial data. The work paves the way to the study of general optimal control strategies for AV velocities, aiming at improving the overall traffic flow by reducing congestion phenomena and the associated externalities.

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