The goal of this project is the development of tools and a mathematical theory to model and solve problems on vehicular traffic on road networks.
We propose an approach based on measure theory and partial differential equations to catch the multiscale nature for these phenomena.
In this setting, we want to study the mathematical aspects of our model, such as existence, uniqueness, dependence on data, qualitative behaviour for the transport equation on networks; on the other hand, we also want to use this model to study relevant applications for our society: traffic management, network design, impact of smart controls (smart traffic light and self-driving vehicles) and calibration of data.
A central part of this project is the participation to several events and conference to strengthen the transferable skills of the participant and build connections in a multidisciplinar and international network for new collaborations, researches and projects.
In the last years, there have been the emerging of new tools and technologies which provide a big amount of data and deeper insight about phenomena such as crowd motion, vehicular traffic, supply chain systems, etc.
It is a key issues to be able to use these tools to make richer prediction and solve problems for our society.
From this point of view, we think that a multiscale model is able to catch this possibility and give a deeper description of vehicular traffic on a road network, with a high number of roads, junctions and drivers.
From a mathematical point of view, this research has a big potential to provide results about theoretical and modelling issues. However, its most promising feature is its potential interdisciplinary. Indeed, there exists a large literature about vehicular and pedestrian traffic and we are confident that this research would offer fruitful collaboration with external fields from mathematics.