Abstract
Compared with existing payment systems, Bitcoin’s throughput is low. Designed to address Bitcoin’s scalability challenge, the Lightning Network (LN) is a protocol allowing two parties to secure bitcoin payments and escrow holdings between them. In a lightning channel, each party commits collateral towards future payments to the counterparty and payments are cryptographically secured updates of collaterals. The network of channels increases transaction speed and reduces blockchain congestion. This paper (i) identifies conditions for two parties to optimally establish a channel, (ii) finds explicit formulas for channel costs, (iii) obtains the optimal collaterals and savings entailed, and (iv) derives the implied reduction in congestion of the blockchain. Unidirectional channels costs grow with the square-root of payment rates, while symmetric bidirectional channels with their cubic root. Asymmetric bidirectional channels are akin to unidirectional when payment rates are significantly different, otherwise to symmetric bidirectional.