The aim of this project is the developing of a mathematical model to accurately reproduce the traffic evolution in order to improve the drivers' safety and to estimate vehiculars' emissions and pollution produced by traffic jams or stop and go waves.
Investigations about these phenomena suggest to mix different scales and define a new multiscale model, which couples macroscopic and microscopic approaches, combining in a unique system ODEs and PDEs.
The perspective is to study the wellposedness of the problem both from a theoretical and a numerical point of view, including the calibration and the validation of the Euler-Godunov numerical scheme associated since both Eulerian (flux-based) and Lagrangian (GPS) traffic data are available as real measurements.
The strenght of the multiscale model is the management of two different scales in a unique framework, that allows us to make use of the big amount of data and technologies which are available today, in order to improve traffic forecasts. This means accurate estimates on pollution and an improving in the drivers' safety, including also acting on the transport planning.
This research will lead to several developments both in theoretical and modelling fields, indeed the coupling between ODEs' and PDEs' systems are more and more crucial in applied mathematics.
Moreover we develop a reliable easy-to-use algorithm to predict traffic evolution that will take to enhancements in traffic management and air quality.
In addiction, the same strategy we presented could be applied in different frameworks, i. e. the study of collective behaviours, pipes or conveyor belts problems and so on.