Mathematical Descriptions of Traffic Flow: Micro, Macro and Kinetic Models (SEMA SIMAI Springer Series, 12)

✍ Scribed by Gabriella Puppo (editor), Andrea Tosin (editor)

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 102
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Preface
Contents
Editors and Contributors
About the Editors
Contributors
Reconstruction of Traffic Speed Distributions from Kinetic Models with Uncertainties
1 Introduction
2 Kinetic Modelling with Uncertain Interactions
2.1 The Interaction Function
2.2 Kinetic Description and Equilibria
2.3 Quantities of Interest
3 Description of Traffic Data
4 Calibration and Results
5 Conclusions
References
From Kinetic to Macroscopic Models and Back
1 Introduction
2 Backward Propagation of Waves in a Kinetic Traffic Model
2.1 A Boltzmann-Type Kinetic Model for Traffic Flow
2.2 Propagation of Waves
3 Analysis of Instabilities via Chapman-Enskog Expansion
3.1 BGK Approximations with and Without Non-local Terms
3.2 The Aw-Rascle and Zhang Model
4 The Modified Formulation of the BGK Approximation in Traffic Flow
4.1 BGK-Type Model Derived from the FTL-Bando Model
4.2 Chapman-Enskog Expansion of the Modified BGK Model
5 Conclusions and Future Perspectives
References
Structural Properties of the Stability of Jamitons
1 Introduction
2 Macroscopic Traffic Models with Instabilities and Traveling Waves
2.1 Specific Model Functions
2.2 Linear Stability of Uniform Flow
2.3 Traveling Wave Analysis and Jamitons
3 Computational Study of Jamiton Stability
3.1 Numerical Scheme for the ARZ Model with Relaxation Term
3.2 Results on the Stability of Jamitons
4 Stability Analysis of Jamiton Solutions
4.1 Perturbation System for Single-Jamiton Waves
4.2 Qualitative Characterization of the Jamiton Perturbation System
4.3 Fundamental Challenges Caused by the Sonic Point
4.4 Quantitative Results: Asymptotic Stability
4.5 Quantitative Results: Transient Growth
5 Discussion and Outlook
References
Stop-and-Go Waves: A Microscopic and a Macroscopic Description
1 Introduction
1.1 Paper Organization
1.2 Goal
2 Microscopic Model
2.1 Real Data Validation
3 Macroscopic Model
3.1 CGARZ Model
3.2 Generating Stop-and-go Waves
3.3 Numerical Implementation
4 Conclusions
References
An Overview of Non-local Traffic Flow Models
1 Introduction
2 A Class of Scalar Non-local Traffic Flow Models
2.1 Analytical Results for a Class of Scalar Non-local Traffic Flow Models
3 Non-Local Multi-Class Traffic Flow Models
4 An Upwind Numerical Scheme
5 Numerical Tests
5.1 Test 1: Impact of Connected Autonomous Trucks on a Circular Road
5.2 Test 2: Stretch of Straight Road with Autonomous Trucks
References