Paola Goatin - Inria Sophia Antipolis - Mediterranee, EPI Acumes - Keywords: traffic flow, macroscopic models, PDEs, optimization

Paola Goatin - Inria Sophia Antipolis - Mediterranee, EPI Acumes - Keywords: traffic flow, macroscopic models, PDEs, optimization

Contribution title: Macroscopic models for traffic management

Macroscopic models of vehicular traffic have been used by engineers since the mid ‘50ies to simulate and optimize traffic flows. Indeed, traffic states can be described by averaged quantities such as density and mean velocity, whose spatio-temporal evolution can be described by (systems of) partial differential equations derived from fluid dynamics. Compared to more intuitive microscopic models, in which each vehicle’s trajectory is taken into account, they are suitable to analytical investigations and very efficient from the numerical point of view. Moreover, they contain only few variables and parameters and they can be very versatile, allowing to describe different situations encountered in practice.
In the last two decades, traffic flow modeling has driven an increasing interest in the mathematical community, which has contributed to the development of richer models able to take into account different features of traffic flows. In particular, the Inria project-team ACUMES has contributed to the study of dynamics at road intersections, phase transitions, non-local interaction phenomena, moving bottlenecks and finite acceleration of vehicles. This leads respectively to the definition of proper coupling conditions at network nodes, coupling of different models describing different phases, non-local equations involving integral (convolution) terms and PDE-ODE coupling accounting for multi-scale dynamics.
Besides, we have been involved in the development of innovative traffic management approaches relying on the above macroscopic descriptions. The techniques include coordinated variable speed limits and ramp metering, optimal rerouting and controlled autonomous vehicles. The proposed algorithms are efficient and allow for real-time implementations.