A two-dimensional multi-class traffic flow model

Caterina Balzotti; Simone Göttlich; Caterina Balzotti; Simone Göttlich

doi:10.3934/nhm.2020034

Networks and Heterogeneous Media

2021, Volume 16, Issue 1: 69-90. doi: 10.3934/nhm.2020034

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A two-dimensional multi-class traffic flow model

Caterina Balzotti ^{1
,
,},
Simone Göttlich ^{2
,}

1.
Dipartimento di Scienze di Base e Applicate per l'Ingegneria, Sapienza Università di Roma, Via Antonio Scarpa 16, 00161 Rome, Italy
2.
Department of Mathematics, University of Mannheim, B6 28-29, 68159 Mannheim, Germany

Received: 01 June 2020 Revised: 01 October 2020 Published: 08 December 2020
Primary: 90B20, 35L65; Secondary: 35Q91

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [21], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles.
- Macroscopic traffic flow,
- two-dimensional model,
- multi-class model,
- Riemann problems,
- data-fitting
Citation: Caterina Balzotti, Simone Göttlich. A two-dimensional multi-class traffic flow model[J]. Networks and Heterogeneous Media, 2021, 16(1): 69-90. doi: 10.3934/nhm.2020034

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Abstract

The aim of this work is to introduce a two-dimensional macroscopic traffic model for multiple populations of vehicles. Starting from the paper [21], where a two-dimensional model for a single class of vehicles is proposed, we extend the dynamics to a multi-class model leading to a coupled system of conservation laws in two space dimensions. Besides the study of the Riemann problems we also present a Lax-Friedrichs type discretization scheme recovering the theoretical results by means of numerical tests. We calibrate the multi-class model with real data and compare the fitted model to the real trajectories. Finally, we test the ability of the model to simulate the overtaking of vehicles.

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