Advances in PDE Modeling of Vehicular Traffic and Its Societal Impact

Description

From a large-scale network modeling perspective, traffic flow can be represented as a fluid flowing on the road network. In order to characterize the evolution of the system, one considers aggregated quantities such as the flow and the density of vehicles, whose spatio-temporal dynamics can be described by Partial Differential Equations. This macroscopic approach has been developed for several decades by transportation engineers and applied mathematicians, and it is nowadays a well-deployed tool for traffic management. Indeed, the available analytical and numerical tools allow recast the problem of (optimally) control traffic flow as PDE-constrained control and optimization problems, aiming at reducing congestion impact in terms of time consumptions, pollutant emissions and other negative effects. While classical regulation actions, such as ramp-metering, variable speed limit signals and traffic light control, have already been largely studied and deployed, the new technological advances open the way to new approaches in traffic management, such as partial user dynamic rerouting and variable speed limits induced by controlled automated vehicles. The aim of the workshop is to dig in the latest advances and perspectives on the mathematical models needed in this perspective.