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.

翻译：我们研究一种受闪电网络支付执行方式启发的图随机过程，闪电网络是比特币上主要的第二层解决方案。首先，当底层图为完全图时，我们证明了支付失败发生时间的上下界几乎紧致，该界是节点数和边容量的函数。其次，我们展示了此类随机过程与边介数中心性度量的关联，并证明了任意图中支付失败时间的上下界，该界是边介数和容量的函数。最后，通过对包括真实闪电网络快照在内的多类图进行广泛模拟，验证了我们的理论结果。