Payment-failure times for random Lightning paths

TL;DR

This paper analyzes the time until payment failure in the Lightning Network using a random graph process, providing bounds and validating results through simulations on real and synthetic graphs.

Contribution

It establishes tight bounds on payment failure times in Lightning Network models and relates these to edge-betweenness centrality, extending understanding to arbitrary graphs.

Findings

Derived tight bounds for failure times in complete graphs.

Linked failure times to edge-betweenness centrality measures.

Validated theoretical bounds with extensive simulations.

Abstract

We study a random process over graphs inspired by the way payments are executed in the Lightning Network, the main layer-two solution on top of Bitcoin. We first prove almost tight upper and lower bounds on the time it takes for a payment failure to occur, as a function of the number of nodes and the edge capacities, when the underlying graph is complete. Then, we show how such a random process is related to the edge-betweenness centrality measure and we prove upper and lower bounds for arbitrary graphs as a function of edge-betweenness and capacity. Finally, we validate our theoretical results by running extensive simulations over some classes of graphs, including snapshots of the real Lightning Network.