Parameter and density estimation from real-world traffic data: A kinetic compartmental approach
Preprint, 2021

The main motivation of this work is to assess the validity of a LWR traffic flow model to model measurements obtained from trajectory data, and propose extensions of this model to improve it. A formulation for a discrete dynamical system is proposed aiming at reproducing the evolution in time of the density of vehicles along a road, as observed in the measurements. This system is formulated as a chemical reaction network where road cells are interpreted as compartments, the transfer of vehicles from one cell to the other is seen as a chemical reaction between adjacent compartment and the density of vehicles is seen as a concentration of reactant. Several degrees of flexibility on the parameters of this system, which basically consist of the reaction rates between the compartments, can be considered: a constant value or a function depending on time and/or space. Density measurements coming from trajectory data are then interpreted as observations of the states of this system at consecutive times. Optimal reaction rates for the system are then obtained by minimizing the discrepancy between the output of the system and the state measurements. This approach was tested both on simulated and real data, proved successful in recreating the complexity of traffic flows despite the assumptions on the flux-density relation.

Traffic reaction model

parameter estimation


viscosity solutions

Lax–Friedrichs scheme

macroscopic model

CFL condition

hyperbolic PDE

real traffic data

finite volume scheme

gradient descent


Mike Pereira

Chalmers, Electrical Engineering, Systems and control, Automatic Control

Pinar Boyraz Baykas

Chalmers, Mechanics and Maritime Sciences, Vehicle Safety, Crash Analysis and Prevention

Balázs Adam Kulcsár

Chalmers, Electrical Engineering, Systems and control, Automatic Control

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

OPerational Network Energy managemenT for electrified buses (OPNET)

Swedish Energy Agency, 2018-10-01 -- 2021-12-31.

Efficient approximation methods for random fields on manifolds

Swedish Research Council (VR), 2021-01-01 -- 2024-12-31.

Stochastic Continuous-Depth Neural Networks

Chalmers AI Research Centre (CHAIR), 2020-08-15 -- .

Real-Time Robust and AdaptIve Learning in ElecTric VEhicles (RITE)

Chalmers AI Research Centre (CHAIR), 2020-01-01 -- 2021-12-31.

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

STOchastic Traffic NEtworks (STONE)

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

Chalmers AI Research Centre (CHAIR), -- .

Areas of Advance


Subject Categories

Computational Mathematics

Probability Theory and Statistics

Control Engineering


Basic sciences

Related datasets

arXiv:2101.11485 [dataset]


More information


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