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Payment channel is a class of techniques designed to solve the scalability problem of blockchain. By establishing channels off the blockchain to form payment channel networks (PCNs), users can make instant payments without interacting with the blockchain, avoiding the problems of long transaction consensus delays and high transaction fees. Recently, the optimization of PCNs has mainly focused on improving the network throughput via multi-path routing. However, the transaction's atomicity comes at a non-trivial cost for transaction completion latency that affects user experience in deadline-sensitive applications of PCNs. In this paper, we propose a new and systematic framework DPCN to consider the deadlines of transactions for payment channel networks while improving the success ratio of transactions. DPCN is enabled via a synergy of three components: (1) deadline-based dynamic transaction split mechanism that splits the transaction according to current network status and the transaction's deadline; (2) deadline-aware transaction scheduling that prioritizes near-deadline transactions; (3) deadline-aware transaction congestion avoidance algorithm, which uses a path window to balance transactions with different deadlines. Our extensive experiments show that compared with existing methods, DPCN can well meet the needs of transactions with different deadlines and ensure a higher success ratio for transactions in the payment channel networks.