Fokker-Planck: UE Mobility Model
Equation: ∂p/∂t = −∇·(F·p) + D·∇²p tracks the probability density p(x,y,t) of a UE being at location (x,y) at time t.
Drift term −∇·(F·p): UEs are attracted toward hotspot locations (eNBs / POIs). The force F(x) pulls density toward the nearest attractor, modeling commute patterns and coverage-seeking behaviour.
Diffusion term D·∇²p: Random walk component representing pedestrian wandering or vehicle detours. Higher D → faster spreading, broader steady-state distribution.
Hotspots: Orange rings mark eNB / attractor positions. Density concentrates around them at steady-state — mapping directly to long-term cell load.
LTE relevance: The steady-state p(x,y) determines long-term user distribution per cell sector. This directly drives Mobility Load Balancing (MLB) and antenna tilt optimization decisions.
Colormap: Blue = low UE probability, White = medium, Red = high concentration.
Controls: Adjust D and α and watch the competition between spreading and focusing. Try α=0 for pure diffusion (heat equation). Try D=0.1 and α=5 for sharp hotspot focusing.