Online Packet Scheduling with Deadlines and Learning

2026-05-30

AI Summary

This work addresses the challenge of real-time packet scheduling in network routers under unknown packet values while meeting quality-of-service (QoS) requirements. The problem is modeled as an online scheduling task with deadlines and partial feedback, and for the first time, it is formally connected to the sleeping bandits framework. Under stochastic packet weights and bandit feedback, the authors design an α-regret minimizing algorithm. For packets drawn from a finite set of types, the proposed approach surpasses the classical competitive ratio barrier of Φ = (1+√5)/2, achieving an improved θ_K competitive ratio. In the case of 2-bounded deadline instances, a deterministic algorithm attains the theoretically optimal competitive ratio. Across all settings, the algorithms guarantee an α-regret upper bound of Õ(√KT).

Abstract

Network routers that enforce Quality-of-Service (QoS) guarantees must decide, at every clock cycle, which expiring packet of information to transmit, even when the value of the packet is unknown until it is processed. We frame this problem as the Online Packet Scheduling with Deadlines (OPSD) problem under Partial Feedback: packets arrive at every clock cycle, with different deadlines, but the weights are only observed after execution. Under a stochastic assumption on the unknown weights, we explore different variants of the OPSD problem with bandit feedback. We establish a connection between our setting and the sleeping bandits problem, and set our learning goal to $α$-regret minimization. We provide algorithms with provable $α$-regret guarantees under different spans of slackness, distinguishing systems allowing for randomization and systems that do not. In every scenario, our algorithms achieve an $α$-regret upper bound of $\widetilde{\mathcal{O}}\left(\sqrt{KT}\right)$, matching the lower bound for the standard bandit setting. In the practically relevant case of $2$-bounded deadline instances, where the deadline is set at most one clock cycle away from the arrival, our deterministic algorithm achieves the provably tightest possible competitive ratio. Remarkably, when the number of distinct packet types $K\ge 2$ is finite, it is possible to break the well-established $Φ= \frac{1+\sqrt{5}}{2}$ competitive ratio barrier and attain a tighter competitive ratio $θ_K$ ranging in $[\sqrt{2}, Φ)$.

Problem

• Online Packet Scheduling
• Deadlines
• Partial Feedback
• Quality-of-Service
• Bandit Feedback

Innovation

• Online Packet Scheduling
• Bandit Feedback
• Sleeping Bandits
• α-Regret Minimization
• Competitive Ratio