Title: Optimizing Scheduling in Queueing Systems Amidst Uncertain and Dynamic Holding Costs

Abstract

In the context of content moderation on social media, the penalty for postponing the review of a post is tied to its view trajectory—a factor that is both unpredictable and unknown beforehand. Driven by this scenario of uncertain and time-varying holding costs, we analyze a queueing framework where job states transition according to a Markov chain, incurring instantaneous costs that depend on the current state. Our analysis reveals that when such dynamic and uncertain costs are present, two standard algorithmic heuristics—the instantaneous-cost ($c\mu$-rule) and the expected-remaining-cost ($c\mu/\theta$-rule)—fail to achieve optimality.

To address this limitation, we model each job as a Markovian ski-rental problem. This perspective allows us to devise a novel index-based algorithm named Opportunity-adjusted Remaining Cost (OaRC). OaRC is designed to adapt to the potential benefits of serving jobs later, taking into account the resolution of uncertainty over time. We prove that the suboptimality gap of OaRC scales as $\tilde{O}(\sqrt{N})$, with $N$ representing the system size. This scaling indicates that OaRC becomes asymptotically optimal for overloaded systems as $N$ approaches infinity. Furthermore, this performance bound remains independent of the size of the state space, a significant advantage when job states include extensive contextual data.

We validate our theoretical findings through a comprehensive simulation study utilizing two distinct holding cost patterns observed in social media content moderation: online advertisements and user-generated content. Results from simulations using both synthetic and real-world datasets confirm that OaRC consistently surpasses current industry practices, which rely on the two aforementioned canonical algorithmic principles.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC