2. LWR traffic model

In this article, we have chosen to focus on a single traffic flow model and to detail its use for specific applications. The traffic model chosen is the LWR model (Lighthill and Whitham, 1955; Richard, 1956). Inspired by fluid mechanics, this model represents traffic as a continuous flow. Based on few parameters, this model is renowned for its robustness and ease of calibration. It was initially introduced in an Eulerian frame of reference, where vehicles are not represented individually but as a continuous flow (by analogy with a fluid). The scale of representation is then called macroscopic. As this term can lead to confusion, we prefer to speak of Eulerian representation. This is a good example of a continuous Eulerian model, which is easy to solve analytically for simple but realistic cases.

The aggregated, Eulerian scale of representation has long been a weakness,...