LWR Traffic Flow Shockwave

Civil Engineering

How It Works

The Lighthill-Whitham-Richards (LWR) macroscopic traffic model treats vehicular movement as a continuous compressible flow field governed by conservation of vehicles. When high-speed free flow encounters a downstream speed reduction or bottleneck, traffic density increases abruptly, forming a kinematic shockwave. The discontinuity boundary propagates backward upstream at a velocity proportional to the ratio of flow rate difference to density difference.

Governing Equation
∂k/∂t + ∂q/∂x = 0  |  v_s = (q₂ - q₁) / (k₂ - k₁)