Transport / Continuity: UE Density
Equation: ∂ρ/∂t + ∇·(ρu) = S(x,t) is the conservation law for UE density ρ(x,y,t). Total UEs are conserved modulo source/sink terms.
Velocity field u: Combines rotation ω (circular traffic flow, e.g. ring-road commute) and radial component β (β>0 outward dispersion from CBD, β<0 inward rush-hour convergence).
Source S⁺: UEs appearing (call session arrivals, entering coverage area). Placed at configurable hotspot.
Sink S⁻: UEs disappearing (session termination, leaving coverage). Distributed evenly as a density-proportional drain.
LTE relevance: eNB load balancing (MLB) algorithms compute a discretized version of this PDE to predict near-future cell loads. The divergence ∇·(ρu) at a cell boundary drives handoff preparation (HO Preparation events).
Colormap: Black → Dark green → Yellow-green → White, representing increasing UE density.
Arrows: Velocity field u(x,y) shown as arrows. Arrow length ∝ speed.
Try: Set β = -1.5 (strong inward pull = rush hour convergence) and watch density compress. Then add source to simulate call arrivals.