  Payment channel networks (PCNs) have emerged as a scalability solution for
blockchains built on the concept of a payment channel: a setting that allows
two nodes to safely transact between themselves in high frequencies based on
pre-committed peer-to-peer balances. Transaction requests in these networks may
be declined because of unavailability of funds due to temporary uneven
distribution of the channel balances. In this paper, we investigate how to
alleviate unnecessary payment blockage via proper prioritization of the
transaction execution order. Specifically, we consider the scheduling problem
in PCNs: as transactions continuously arrive on both sides of a channel, nodes
need to decide which ones to process and when in order to maximize their
objective, which in our case is the channel throughput. We introduce a
stochastic model to capture the dynamics of a payment channel under random
arrivals, and propose that channels can hold incoming transactions in buffers
up to some deadline in order to enable more elaborate processing decisions. We
describe a policy that maximizes the channel success rate/throughput for
uniform transaction requests of fixed amounts, both in the presence and absence
of buffering capabilities, and formally prove its optimality. We also develop a
discrete event simulator of a payment channel, and evaluate different heuristic
scheduling policies in the more general heterogeneous amounts case, with the
results showing superiority of the heuristic extension of our policy in this
case as well. Our work opens the way for more formal research on improving PCN
performance via joint consideration of routing and scheduling decisions.
