Parameter and density estimation from real-world traffic data: A kinetic compartmental approach
Journal article, 2022

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.

CFL condition

gradient descent

macroscopic model

real traffic data

Traffic reaction model


Lax–Friedrichs scheme

hyperbolic PDE

finite volume scheme

viscosity solutions

parameter estimation


Mike Pereira

University of Gothenburg

Chalmers, Electrical Engineering, Systems and control

Chalmers, Mathematical Sciences

Pinar Boyraz Baykas

Chalmers, Mechanics and Maritime Sciences (M2), Vehicle Safety

Balázs Adam Kulcsár

Chalmers, Electrical Engineering, Systems and control

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Transportation Research Part B: Methodological

0191-2615 (ISSN)

Vol. 155 210-239

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

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

Efficient approximation methods for random fields on manifolds

Swedish Research Council (VR) (2020-04170), 2021-01-01 -- 2024-12-31.

OPerational Network Energy managemenT for electrified buses (OPNET)

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

Stochastic Continuous-Depth Neural Networks

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

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

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

Chalmers AI Research Centre (CHAIR), 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

Computer and Information Science

Transport Systems and Logistics

Other Mathematics

Control Engineering



More information

Latest update