Mathematical modeling | Traffic flow

Macroscopic traffic flow model

A Macroscopic traffic flow model is a mathematical traffic model that formulates the relationships among traffic flow characteristics like density, flow, mean speed of a traffic stream, etc.. Such models are conventionally arrived at by integrating microscopic traffic flow models and converting the single-entity level characteristics to comparable system level characteristics. An example is the Two-fluid model. The method of modeling traffic flow at macroscopic level originated under an assumption that traffic streams as a whole are comparable to fluid streams. The first major step in macroscopic modeling of traffic was taken by Lighthill and Whitham in 1955, when they indexed the comparability of ‘traffic flow on long crowded roads’ with ‘flood movements in long rivers’. A year later, Richards (1956) complemented the idea with the introduction of ‘shock-waves on the highway’, completing the so-called LWR model. Macroscopic modeling may be primarily classified according to the type of traffic as homogeneous and heterogeneous, and further with respect to the order of the mathematical model. (Wikipedia).

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Simona Sacone: "Hybrid micro-macro modelling for platoon control in freeway traffic networks"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop III: Large Scale Autonomy: Connectivity and Mobility Networks "Hybrid micro-macro modelling for platoon control in freeway traffic networks" Simona Sacone - Università di Genova Abstract: The definition of a

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Simone Göttlich: Traffic flow models with non-local flux and extensions to networks

We present a Godunov type numerical scheme for a class of scalar conservation laws with nonlocal flux arising for example in traffic flow modeling. The scheme delivers more accurate solutions than the widely used Lax-Friedrichs type scheme and also allows to show well-posedness of the mode

From playlist Numerical Analysis and Scientific Computing

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Benjamin Seibold: "Basic Traffic Models and Traffic Waves" (Part 2/2)

Watch part 1/2 here: https://youtu.be/9_1cEtimRNE Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials 2020 "Basic Traffic Models and Traffic Waves" (Part 2/2) Benjamin Seibold - Temple University Institute for Pure and Applied Mathematics, UCLA September 17, 2020

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Talk Andrea Tosin: Kinetic modelling of traffic flow control

The lecture was held within the of the Hausdorff Trimester Program: Kinetic Theory Abstract: In this talk, we present a hierarchical description of control problems for vehicular traffic, which aim to mitigate speed-dependent risk factors and to dampen structural uncertainties responsible

From playlist Summer School: Trails in kinetic theory: foundational aspects and numerical methods

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Paola Goatin: "Macroscopic models for Autonomous Vehicles"

Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials 2020 "Macroscopic models for Autonomous Vehicles" Paola Goatin - Inria Sophia Antipolis-Méditerranée Abstract: My lecture will give an introduction to macroscopic traffic flow models (first and second order), the

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Sequential Model - TensorFlow Essentials #1

Learn how to use the sequential model building approach in TensorFlow 2. 🤖 70% Discount on the NLP With Transformers in Python course: https://bit.ly/3DFvvY5 Background thumbnail by Aryan Dhiman on Unsplash https://unsplash.com/@mylifeasaryan_?utm_source=unsplash&utm_medium=referral&

From playlist TensorFlow Essentials

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Concept of a vector

This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com

From playlist Chapter 2 - Vectors

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Benjamin Seibold: "Basic Traffic Models and Traffic Waves" (Part 1/2)

Watch part 2/2 here: https://youtu.be/tDzbGUBWtcI Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials 2020 "Basic Traffic Models and Traffic Waves" (Part 1/2) Benjamin Seibold - Temple University Institute for Pure and Applied Mathematics, UCLA September 16, 2020

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Antonella Ferrara: "From connected & autonomous vehicles control to vehicular traffic control"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop II: Safe Operation of Connected and Autonomous Vehicle Fleets "From connected and autonomous vehicles control to vehicular traffic control, a multi-scale perspective" Antonella Ferrara - Università di Pavia A

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Benjamin Seibold: "Energy Impact of Automated Vehicles used as Sparse Traffic Controllers"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop II: Safe Operation of Connected and Autonomous Vehicle Fleets "Energy Impact of Automated Vehicles used as Sparse Traffic Controllers" Benjamin Seibold - Temple University, Mathematics Abstract: It is a popul

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Rinaldo Colombo: "On the Interplay between Mathematical Analysis and Traffic Modeling"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop IV: Social Dynamics beyond Vehicle Autonomy "On the Interplay between Mathematical Analysis and Traffic Modeling" Rinaldo Colombo - Università di Brescia Abstract: Mathematical Analysis offers a variety of to

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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A 2D shear flow rendered in 3D

This is a 3D rendering of the shear flow shown in the video https://youtu.be/xYboEUdzui0 In a shear flow, several layers of fluid move at different speeds, causing vortices to form where the layers touch each other. This simulation starts with horizontal layers, whose velocity has a small

From playlist Fluid dynamics (Euler and similar equations)

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Simone Göttlich: "On the influence of time delays in vehicular traffic"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop III: Large Scale Autonomy: Connectivity and Mobility Networks "On the influence of time delays in vehicular traffic" Simone Göttlich - Universität Mannheim Abstract: Starting from microscopic follow-the-leade

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Paola Goatin: "A multi-population traffic flow model on networks accounting for vehicle automation"

Mathematical Challenges and Opportunities for Autonomous Vehicles 2020 Workshop III: Large Scale Autonomy: Connectivity and Mobility Networks "A multi-population traffic flow model on networks accounting for vehicle automation" Paola Goatin - INRIA Sophia Antipolis-Méditerranée Abstract:

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Dan Work: "Transportation Engineering for Connected and Automated Vehicles" (Part 2/2)

Watch part 1/2 here: https://youtu.be/nQBTMTZoBhU Mathematical Challenges and Opportunities for Autonomous Vehicles Tutorials 2020 "Transportation Engineering for Connected and Automated Vehicles" (Part 2/2) Dan Work - Vanderbilt University Institute for Pure and Applied Mathematics, UC

From playlist Mathematical Challenges and Opportunities for Autonomous Vehicles 2020

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Martin Burger: Propagation of gradient flow structures from microscopic to macroscopic models

The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory Abstract: In this talk we will discuss the propagation of gradient flow structures from microscopic models in statistical mechanics such as overdamped particle dynamics or interacting particle syst

From playlist Workshop: Probabilistic and variational methods in kinetic theory

Related pages

Traffic model | Two-fluid model | Density | Mathematical model | Traffic flow