Abstract
Vehicular traffic is one of most serious problems facing modern urban life. We will describe some classical mathematical models for traffic flow. There are two rather distinct ways to model traffic. On the one hand one can track individual vehicles, often called Follow-the-Leader models (FtL). This leads to systems of ordinary differential equations. However, if traffic is dense, a classical model is the so-called Lighthill–Whitham–Richards model (LWR), which is a nonlinear partial differential equation, more specifically, a hyperbolic conservation law. We study these models, and, in particular, the connection between the discrete (FtL) and the continuous (LWR) when traffic becomes dense. We will also briefly discuss traffic on a network or roads, and traffic on multilane roads.