Capital model
Where spoke cost meets mesh cost
Each router funds spoke channels to its customers and mesh channels to every other router. Too few routers and each one carries too many customers. Too many and the mesh itself is the burden. R* is the minimum.
Customers (P)
10.0B
Spoke / customer (S)
$1,000
Mesh / link (M)
$1.0M
- R* routers
- 3K
- Capital / router
- $6.3B
- Customers / router
- 3.2M
- Max payment / link
- $250K
- Total system
- $24.2T
2ⁿ: 2K or 4K
Spoke = PS / RMesh = RMTotal = PS/R + RMR* = √(PS/M)
Number of routers (R), powers of two
R* = √(PS / M) · min capital = 2√(PSM) · spoke = mesh at R*
Spoke capital per router falls as 1/R. Mesh capital per router rises as R. The U-curve minimum is where they cross. Payments larger than the max per link settle on-chain.