The LWR model (Lighthill-Whitham-Richards model) is a first-order macroscopic traffic flow model that describes the evolution of pedestrian or vehicular density over space and time using a scalar hyperbolic conservation law, relating density to flux through a fundamental diagram. It matters for crowd and pedestrian flow research because it provides a mathematically tractable continuum framework for analyzing propagation of density waves, shock formation, and congestion phenomena without tracking individual agents. Key variants include extensions to two-dimensional walking facilities, such as Hughes' dynamic continuum model, which couples the LWR conservation equation with an Eikonal equation to capture directional route choice, as well as multi-class and network-level adaptations that accommodate heterogeneous pedestrian populations or complex spatial geometries.
Source Papers
- Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications ↗ — Continuum theory for pedestrian traffic flow: Local route ch
- Crowds in Equations ↗ — Crowds in Equations
- Physics of Human Crowds ↗ — Physics of Human Crowds
- Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm ↗ — Revisiting Hughes’ dynamic continuum model for pedestrian fl