HJB Optimal Handoff: Value Function
Model: The Hamilton-Jacobi-Bellman equation governs the optimal handoff policy. The value function V(x) = max_k RSRP_k(x) represents the best achievable signal quality at any position.
RSRP model: RSRP_k(x) = P_tx − 10γ·log₁₀(d(x, x_k)) where γ is the path loss exponent (2 = free space, 3–4 = urban macro).
A3 Event (3GPP TS 36.331): Handoff is triggered when the target cell's RSRP exceeds the serving cell's RSRP by A3 offset (dB) for a duration of TTT (Time-To-Trigger). Higher A3 → fewer but more reliable handoffs. Lower A3 → more frequent handoffs (ping-pong risk).
Background: RSRP heat map of the best server at each point. Brighter = stronger signal. Color indicates the serving cell.
UEs: Colored dots = UE position. Ring = TTT progress. White flash = handoff event.
LTE relevance: The value function V(x) is the "optimal RSRP surface." Its gradient ∇V points toward the strongest coverage direction — this is exactly the direction RRC measurements should track. Cell boundaries are the zero sets of V_k(x) - V_j(x) = A3.
Try: Set A3=0 to see maximum-RSRP (greedy) policy with frequent handoffs. Increase TTT to see hysteresis effect preventing ping-pong.