在未知包价值的情况下,实现带截止时间的在线包调度,提升网络服务质量。
Online Packet Scheduling with Deadlines and Learning
- 基于部分反馈的带宽学习机制,将调度问题转化为睡眠老虎机模型。
- 在2-有界截止时间场景下,确定性算法达到最优竞争比,优于经典黄金分割比。
- 当包类型有限时,突破传统竞争比上限,实现更优性能,适合实际网络系统。
网络路由器在保证服务质量(QoS)时,必须在每个时钟周期决定发送哪个即将过期的信息包,而包的价值直到处理后才能得知。我们将其建模为带部分反馈的在线包调度(OPSD)问题:包在每个时钟周期到达,具有不同截止时间,但权重仅在执行后观察到。在权重服从随机假设的前提下,研究了带老虎机反馈的不同变体。建立了该设定与睡眠老虎机问题的联系,将学习目标设为α-遗憾最小化。在不同松弛度条件下,分别设计了可证明α-遗憾上界为$ ilde{oldsymbol{O}}(oldsymbol{ ext{sqrt}}(KT))$的算法,与标准老虎机设置的下界匹配。在实际相关的2-有界截止时间实例中,我们的确定性算法实现了理论上最紧的竞争比。值得注意的是,当不同包类型数$Koldsymbol{ ext{≥2}}$为有限时,能够打破长期存在的$Φ=\frac{1+\sqrt{5}}{2}$竞争比壁垒,达到范围在$[\sqrt{2}, Φ)$内的更优竞争比$θ_K$。
原文摘要 · Abstract (English)
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 $[\sqrt{2}, Φ)$.
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