Thesis title: Multi-lane models for vehicular traffic flow
This dissertation focuses on the mathematical modeling of traffic flow, with special emphasis on multi-lane models in the microscopic and macroscopic scales. First, an overview on the modelling of micro and macro single-lane and multi-lane models is provided, also discussing the connection between the two scales of representation in the micro-to-macro limit. Furthermore, a second order multi-lane microscopic hybrid model is proposed, providing simple lane changing conditions and investigating the stability of the equilibria with the careful design of the lane changing rules. Finally, a novel first order multi-lane macroscopic model is introduced, derived from microscopic dynamics with lane changing, leading to a coupled system of hyperbolic balance laws. The macroscopic limit is derived without assuming ad hoc space and time scalings. The analysis of the stability of the equilibria of the macroscopic model is discussed. Several numerical tests are presented, which confirm the theoretical results and include an application in simulations of a realistic traffic scenario. A numerical comparison with other existing traffic models is also reported.