Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models

The book originates from the mini-symposium "Mathematical descriptions of traffic flow: micro, macro and kinetic models" organised by the editors within the ICIAM 2019 Congress held in Valencia, Spain, in July 2019. The book is composed of five chapters, which address new research lines in the mathematical modelling of vehicular traffic, at the cutting edge of contemporary research, including traffic automation by means of autonomous vehicles. The contributions span the three most representative scales of mathematical modelling: the microscopic scale of particles, the mesoscopic scale of statistical kinetic description and the macroscopic scale of partial differential equations.The work is addressed to researchers in the field.

Mathematical methods and models of vehicular traffic at the three representative scales in a unique book Frontier research topics in the mathematical modelling of vehicular traffic, including vehicle automation and data integration, addressed in various chapters under different points of view Up-to-date representation of the most advanced research topics in the mathematical modelling of vehicular traffic

Autorentext

Gabriella Puppo is professor of numerical analysis at Sapienza, Università di Roma. Previously, she has had positions at Università dell'Insubria and Politecnico di Torino. She obtained a PhD in Applied Mathematics at the Courant Institute of NYU. Her research interests range from scientific computing for hyperbolic and kinetic equations, to modelling of physical and social phenomena using kinetic theory and hyperbolic PDE's.

Andrea Tosin is full professor of Mathematical Physics at Politecnico di Torino, Italy. His main research interests consist in revisiting the classical methods and concepts of kinetic theory, such as Boltzmann-type collisional equations and Fokker-Planck asymptotics, to investigate emerging problems in the realm of interacting multi-agent systems. Applications include vehicular traffic, crowd dynamics and social systems.

Inhalt
M. Herty et al., Reconstruction of traffic speed distributions from kinetic models with uncertainties.- M. Herty et al., From kinetic to macroscopic models and back.- R. Ramadan et al., Structural Properties of the Stability of Jamitons.- C. Balzotti and E. Iacomini, Stop-and-go waves: A Microscopic and a Macroscopic Description.- F. A. Chiarello, An overview of non-local traffic flow models.