Lighthill-Whitham-Richards model on a ring road. Shockwaves travel backwards.
The LWR model: ∂ρ/∂t + ∂(ρv)/∂x = 0, with v(ρ) = v₀(1 − ρ/ρmax). A traffic jam (high density arc) spawns backward-propagating shockwaves — cars slow before reaching the jam. Color: green=free flow, yellow=congested, red=standstill.