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

1. Front Matter

   Pages i-xii

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2. Reconstruction of Traffic Speed Distributions from Kinetic Models with Uncertainties

   • Michael Herty, Andrea Tosin, Giuseppe Visconti, Mattia Zanella

   Pages 1-16

3. From Kinetic to Macroscopic Models and Back

   • Michael Herty, Gabriella Puppo, Giuseppe Visconti

   Pages 17-34

4. Structural Properties of the Stability of Jamitons

   • Rabie Ramadan, Rodolfo Ruben Rosales, Benjamin Seibold

   Pages 35-62

5. Stop-and-Go Waves: A Microscopic and a Macroscopic Description

   • Caterina Balzotti, Elisa Iacomini

   Pages 63-78

6. An Overview of Non-local Traffic Flow Models

   • Felisia Angela Chiarello

   Pages 79-91

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.

• Multiscale models
• Follow-the-leader models
• Boltzmann-type and BGK kinetic models
• Local and non-local conservation laws
• Partial Differential Equations

• Department of Mathematics, Sapienza University of Rome, Roma, Italy

  Gabriella Puppo

• Department of Mathematical Sciences “G. L. Lagrange”, Politecnico di Torino, Torino, Italy

  Andrea Tosin

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.

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