Chain or Channel? Payment Optimization with Heterogeneous Flow
45 Pages Posted: 23 Jan 2025
Date Written: December 06, 2024
Abstract
Payment-channel networks (PCNs) such as the Lightning Network enable offchain payments secured by the channels' balances as alternatives to on-chain transactions. This paper solves the optimal channel management problem for two agents who pay each other arbitrarily distributed amounts. Agents optimally choose the channel's size and whether to make each payment on-chain or on-channel, depending on their current balance. With unidirectional flows, payments below some balancedependent chain amount happen on-channel while others on-chain. As the balance falls below the reserve level, payments are always made on-channel if feasible. Below the refill level, the channel is reset to its initial state. Symmetric bidirectional flows entail distinct chain thresholds and reset levels for both directions, but channels may last indefinitely. Asymmetric flows lead to a more complex optimal policies, in which both, either, or no party resets the channel. The paper characterizes optimal channels and payment policies, describing an algorithm to obtain them, given payments' frequency and distribution.
Keywords: payments, lightning network, point processes, stochastic control
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