Lighthill–Whitham–Richards Model

A macroscopic traffic-flow model that treats vehicle density ρ(x,t) as a conserved scalar satisfying a hyperbolic conservation law ρ_t + q(ρ)_x = 0, where the flux q(ρ) = ρ v(ρ) is given by a fundamental diagram relating density to mean speed; it describes kinematic waves, shocks, and rarefactions in traffic.