Traffic Reaction Model
Preprint, 2021

In this paper a novel non-negative finite volume discretization scheme is proposed for certain first order nonlinear partial differential equations describing conservation laws arising in traffic flow modelling. The spatially discretized model is shown to preserve several fundamentally important analytical properties of the conservation law (e.g., conservativeness, capacity) giving rise to a set of (second order) polynomial ODEs. Furthermore, it is shown that the discretized traffic flow model is formally kinetic and that it can be interpreted in a compartmental context. As a consequence, traffic networks can be represented as reaction graphs. It is shown that the model can be equipped with on- and off- ramps in a physically meaningful way, still preserving the advantageous properties of the discretization. Numerical case studies include empirical convergence tests, and the stability analysis presented in the paper paves the way to scalable observer and controller design.

numerical scheme


traffic flow theory

hyperbolic PDE

chemical reation network

nonlinear ODE

traffic modeling LWR


Gyorgy Liptak

Mike Pereira

Chalmers, Electrical Engineering, Systems and control

Balázs Adam Kulcsár

Chalmers, Electrical Engineering, Systems and control

Mihaly Kovacs

Chalmers, Mathematical Sciences

Gabor Szederkenyi

IRIS: Inverse Reinforcement-Learning and Intelligent Swarm Algorithms for Resilient Transportation Networks

Chalmers, 2020-01-01 -- 2021-12-31.

STOchastic Traffic NEtworks (STONE)

Chalmers AI Research Centre (CHAIR), -- .

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

OPerational Network Energy managemenT for electrified buses (OPNET)

Swedish Energy Agency (46365-1), 2018-10-01 -- 2021-12-31.

Areas of Advance


Subject Categories

Applied Mechanics

Computational Mathematics

Control Engineering

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4/8/2021 1