  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.
