Macroscopic traffic flow models allow describing the spatio-temporal evolution of traffic density. Their sound mathematical structure consisting of partial differential equations of hyperbolic type and the related efficient numerical schemes enable fast computations to monitor traffic evolution. The aim of the internship was to validate these models against processed data provided by the industrial partners Autoroutes Trafic and VINCI Autoroutes. Targeted applications included congestion detection, congestion starting and ending points location, congestion evolution in time and traveling time estimation. To this end, we used the first-order Lighthill-Whitham-Richards model with a parabolic-linear flux function. The first part of the internship has been devoted to parameters identification, performing different calibration methods and finally choosing a hybrid compromise in order to exploit to the best the available data. Afterwards, numerical simulations have been performed on a selected case study, and results have been compared to real data to assess the validity and relevancy of the model. Numerical simulations consisted in established finite volume discretization of the hyperbolic partial differential equation. Numerical results show that, while reproducing traffic evolution during all the morning is really challenging, short term predictions are reliable.
Validation of traffic flow models on processed GPS data