The Traffic Reaction Model: A kinetic compartmental approach to road traffic modeling
Journal article, 2024

In this work, a family of finite volume discretization schemes for LWR-type first order traffic flow models (with possible on- and off-ramps) is proposed: the Traffic Reaction Model (TRM). These schemes yield systems of ODEs that are formally equivalent to the kinetic systems used to model chemical reaction networks. An in-depth numerical analysis of the TRM is performed. On the one hand, the analytical properties of the scheme (nonnegative, conservative, capacitypreserving, monotone) and its relation to more traditional schemes for traffic flow models (Godunov, CTM) are presented. Finally, the link between the TRM and kinetic systems is exploited to offer a novel compartmental interpretation of traffic models. In particular, kinetic theory is used to derive dynamical properties (namely persistence and Lyapunov stability) of the TRM for a specific road configuration. Two extensions of the proposed model, to networks and changing driving conditions, are also described.

traffic flow

chemical reaction network

stability

FVT

transformation

traffic network

numerical scheme

PDE

flow model

Author

Mike Pereira

Université Paris PSL

Chalmers, Electrical Engineering, Systems and control

Balázs Adam Kulcsár

Chalmers, Electrical Engineering, Systems and control

Gyorgy Liptak

Pázmány Péter Catholic University

Institute for Computer Science and Control

Mihaly Kovacs

Institute for Computer Science and Control

Pázmány Péter Catholic University

Transportation Research, Part C: Emerging Technologies

0968-090X (ISSN)

Vol. 158 104435

E-Laas: Energy optimal urban Logistics As A Service

European Commission (EC) (F-ENUAC-2022-0003), 2023-05-01 -- 2025-04-30.

Swedish Energy Agency (2023-00021), 2023-05-02 -- 2025-04-30.

STOchastic Traffic NEtworks (STONE)

Chalmers AI Research Centre (CHAIR), -- .

Chalmers, 2020-02-01 -- 2022-01-31.

Areas of Advance

Transport

Subject Categories

Computational Mathematics

Transport Systems and Logistics

Control Engineering

DOI

10.1016/j.trc.2023.104435

More information

Latest update

1/10/2024