We propose to investigate traffic phenomena from the macroscopic point of view, using models derived from fluid-dynamics consisting in hyperbolic conservation laws. In fact, even if the continuum hypothesis is clearly not physically satisfied, macroscopic quantities can be regarded as measures of traffic features and allow to depict the spatio-temporal evolution of traffic waves.
Continuum models have shown to be in good agreement with empirical data. Moreover, they are suitable for analytical investigations and very efficient from the numerical point of view. Therefore, they provide the right framework to state and solve control and optimization problems, and we believe that the use of macroscopic models can open new horizons in traffic management.
The major mathematical difficulties related to this study follow from the mandatory use of weak (possibly discontinuous) solutions in distributional sense. Indeed, due to the presence of shock waves and interactions among them, standard techniques are generally useless for solving optimal control problems, and the available esults are scarce and restricted to particular and unrealistic cases. This strongly limits their applicability.
Our scope is to develop a rigorous analytical framework and fast and efficient numerical tools for solving optimization and control problems, such as queues lengths control or buildings exits design. This will allow to elaborate reliable predictions and to optimize traffic fluxes. To achieve this goal, we will move from the detailed structure of the solutions in order to construct ad hoc methods to tackle the analytical and numerical difficulties arising in this study. The foreseen applications target the sustainability and safety issues of modern society.
Call for proposal
See other projects for this call