Capital

Full mesh, sweet spot

Optimal router count minimizes capital per hub. The U-curve bottoms where spoke cost equals mesh cost.

Customers (P)10.0BSpoke / customer (S)$3,000Mesh / link (M)$1.0M

R* routers: 5K
Capital / router at R*: $11.0B
Customers / router: 1.8M
Max payment / link: $250K
Total system capital: $76.8T

Spoke = PS / R
Mesh = RM
Total = PS/R + RM
R* = √(PS/M)

R* = √(PS / M) · min capital = 2√(PSM) · spoke = mesh at R*

Each hub keeps spoke channels to its customers and a payment channel to every other hub. Spoke capital per hub falls as R grows (fewer customers each). Mesh capital per hub rises as R grows (more links each). Payments larger than max per link settle on-chain.