Understanding the Benefit of Being Patient in Payment Channel Networks

Scaling blockchain efficiency is crucial to its widespread usage in which the payment channel is one of the most prominent approaches. With payment channels and the network they construct, two users can move some transactions off-chain in a predetermined duration to avoid expensive and time-consuming on-chain settlements. Existing work is devoted to designing high-throughput payment channel networks (PCNs) or efficient PCN routing policies to reduce the fee. In this paper, we investigate the PCN routing from a different perspective by answering whether the routing fee of transactions can be saved by being a bit more patient. The key idea is to reorder the processing sequence of atomic transactions, other than to handle each of them separately and immediately. We present two mechanisms, one is periodic transaction processing assisted by a PCN broker and the other is purely strategic waiting. In the former, all the incoming transactions in a short time interval are processed collectively. We formulate an optimization model to minimize their total routing fee and derive the optimal permutation of processing transactions as well as the routing policy for each of them. A Shapley value based scheme is presented to redistribute the benefit of reordering among the transactions efficiently and fairly. In the latter, we model the waiting time of a strategic transaction on a single payment channel as the first passage time problem in queueing theory when the transaction value is higher than the edge capacity upon its arrival. By capturing the capacity dynamics, we are able to calculate the recursive expression of waiting for time distribution that is useful to gauge a user's cost of patience. Experimental results manifest that our cost redistribution mechanism can effectively save routing fees for all the transactions, and the waiting time distribution coincides with the model well.