We study a \emph{financial} version of the classic online problem of scheduling weighted packets with deadlines. The main novelty is that, while previous works assume packets have \emph{fixed} weights throughout their lifetime, this work considers packets with \emph{time-decaying} values. Such considerations naturally arise and have wide applications in financial environments, where the present value of future actions may be discounted. We analyze the competitive ratio guarantees of scheduling algorithms under a range of discount rates encompassing the ``traditional'' undiscounted case where weights are fixed (i.e., a discount rate of 1), the fully discounted ``myopic'' case (i.e., a rate of 0), and those in between. We show how existing methods from the literature perform suboptimally in the more general discounted setting. Notably, we devise a novel memoryless deterministic algorithm, and prove that it guarantees the best possible competitive ratio attainable by deterministic algorithms for discount factors up to $\approx 0.77$. Moreover, we develop a randomized algorithm and prove that it outperforms the best possible deterministic algorithm, for any discount rate. While we highlight the relevance of our framework and results to blockchain transaction scheduling in particular, our approach and analysis techniques are general and may be of independent interest.

翻译：我们研究经典在线加权数据包截止时间调度问题的一个**金融**版本。主要创新在于，先前工作假设数据包在其生命周期内具有**固定**权重，而本研究考虑具有**时间衰减**价值的数据包。此类考量在金融环境中自然产生且具有广泛应用，其中未来行为的现值可能需要折现。我们分析了调度算法在一系列折现率下的竞争比保证，涵盖权重固定的"传统"无折现情况（即折现率为1）、完全折现的"短视"情况（即折现率为0）以及介于两者之间的情形。我们展示了现有文献方法在更一般的折现设置中如何表现次优。值得注意的是，我们设计了一种新颖的无记忆确定性算法，并证明对于约0.77以下的折现因子，它能保证确定性算法可达到的最佳竞争比。此外，我们开发了一种随机算法，并证明对于任意折现率，其性能均优于最佳确定性算法。虽然我们特别强调了研究框架和结果与区块链交易调度的相关性，但我们的方法和分析技术具有普适性，可能具有独立的研究价值。