LWR TRAFFIC FLOW MODEL
Lighthill-Whitham-Richards PDE: ∂ρ/∂t + ∂(ρV(ρ))/∂x = 0 — shock waves and rarefaction fans in traffic
Scenario:
Traffic Jam (shock)
Green Light (rarefaction)
Riemann Problem
Density Wave
Bottleneck
Model:
Greenshields
Triangular FD
Drake
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Step
Density ρ(x,t) — red = congested, green = free flow. Click/drag to add cars.
Fundamental Diagram: Flow q = ρ·V(ρ). Working point shown in yellow.
Space-time diagram — darker = higher density. Shock waves appear as diagonal discontinuities.