2025/11/20 by Abedesselam, Taki E. M., Giacomelli, Fabio, Pasquale, Francesco +1
#FOS: Computer and information sciences #FOS: Mathematics #Networking and Internet Architecture (cs.NI) #Probability (math.PR)
paper · doi:10.48550/arxiv.2511.16376
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.