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.