The Problem of Traffic: A Mathematical Modeling Journey

Embark on a mathematical modeling journey to understand and predict traffic behavior in this 34-minute video lecture. Explore the complexities of single-lane traffic flow, focusing on the ripple effect caused by one car braking and how it amplifies down the line due to drivers' reaction times. Delve into the process of building a mathematical model, from defining the problem and selecting relevant variables to making assumptions and constructing both microscopic and macroscopic models. Investigate the relationship between traffic density and velocity, learn how to maximize flux, and discover the concept of optimal density. Examine the challenges of modeling a sequence of cars and develop a full differential delay system. Assess the model's effectiveness through graphical and qualitative analysis, and gain insights into solving differential delay equations. This comprehensive exploration serves as an introduction to mathematical modeling of real-world problems and is part of the Summer of Math Exposition (#SoME2).

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.