The Problem of Traffic: A Mathematical Modeling Journey

This course introduces mathematical modeling through the emergence of stop-and-go traffic in a single lane. It develops a car-following model using density, velocity, following distance, and reaction delay, then analyzes the resulting differential-delay system graphically and qualitatively.

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.