This course aims to teach learners how to mathematically model traffic, specifically focusing on the phenomenon of stop-and-go behavior in a single lane of cars. The course covers the process of defining a problem, choosing variables, making assumptions, building microscopic models for each car, and assessing the model. Learners will also be introduced to differential-delay equations and how to solve them. The course is designed for individuals interested in mathematical modeling of real-world problems and those looking to understand traffic behavior through a mathematical lens.
The Problem of Traffic: A Mathematical Modeling Journey
Overview
Syllabus
The Challenge of Traffic.
#SoME2 .
The Modelling Process.
Defining the Problem.
Choosing Which Variables to Consider.
Making Assumptions.
Building the Microscopic Model for Each Car.
Macroscopic Equilibrium .
The Relationship between Density and Velocity.
Maximizing Flux and the Optimal Oensity.
Modelling a Sequence of Cars.
Modelling the First Car.
Full Model: A Differential Delay System.
Assessing the Model Graphically.
Assessing the Model Qualitatively.
Solving Differential Delay Systems.
Taught by
Dr. Trefor Bazett
