Scheduling With Time Discounts

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.