Advection-Diffusion: Mixed UE Mobility
Equation: ∂ρ/∂t + u·∇ρ = D·∇²ρ combines directed transport (advection) with random spreading (diffusion).
Péclet Number Pe = |u|·L/D: The dimensionless ratio governing regime:
• Pe ≪ 1 → Diffusion dominated: smooth Gaussian spreading (pedestrian zones)
• Pe ≈ 1 → Mixed regime: asymmetric plume (suburban mixed traffic)
• Pe ≫ 1 → Advection dominated: sharp front propagation (highway corridor)
LTE relevance: At high Pe (highway scenario), UE density creates a sharp wavefront approaching a cell boundary — the cell experiences a sudden load spike (shock-like, analogous to Burgers equation). Standard MLB needs predictive look-ahead here. At low Pe (dense urban), the diffuse distribution allows reactive MLB to suffice.
Sources: Represent UE arrival hotspots (e.g., train station exits). Multiple sources create interfering plumes.
Colormap: Purple (low) → Orange → Yellow → White (high density).
Try: D=0.05, |u|=1.5 → Pe≫1, watch the sharp propagating front. Then D=1.5, |u|=0.2 → Pe≪1, Gaussian spreading in all directions.