Scheduling packets with end-to-end deadline constraints in multihop networks is an important problem that has been notoriously difficult to tackle. Recently, there has been progress on this problem in the worst-case traffic setting, with the objective of maximizing the number of packets delivered within their deadlines. Specifically, the proposed algorithms were shown to achieve $\Omega(1/\log(L))$ fraction of the optimal objective value if the minimum link capacity in the network is $C_{\min}=\Omega(\log (L))$, where $L$ is the maximum length of a packet's route in the network (which is bounded by the packet's maximum deadline). However, such guarantees can be quite pessimistic due to the strict worst-case traffic assumption and may not accurately reflect real-world settings. In this work, we aim to address this limitation by exploring whether it is possible to design algorithms that achieve a constant fraction of the optimal value while relaxing the worst-case traffic assumption. We provide a positive answer by demonstrating that in stochastic traffic settings, such as i.i.d. packet arrivals, near-optimal, $(1-\epsilon)$-approximation algorithms can be designed if $C_{\min} = \Omega\big(\frac{\log (L/\epsilon) } {\epsilon^2}\big)$. To the best of our knowledge, this is the first result that shows this problem can be solved near-optimally under nontrivial assumptions on traffic and link capacity. We further present extended simulations using real network traces with non-stationary traffic, which demonstrate that our algorithms outperform worst-case-based algorithms in practical settings.

翻译：具有端到端截止时间约束的多跳网络中的数据包调度是一个重要且公认难以处理的问题。近期，针对最坏情况下的流量设置，该问题的研究取得了进展，其目标是最大化在截止时间内成功传输的数据包数量。具体而言，已有算法被证明能够在网络最小链路容量 $C_{\min}=\Omega(\log (L))$ 的条件下达到最优目标值的 $\Omega(1/\log(L))$ 比例，其中 $L$ 是网络中数据包路由的最大长度（受数据包最大截止时间限制）。然而，由于严格的最坏情况流量假设，此类保证可能过于悲观，无法准确反映实际场景。本研究旨在通过探索是否存在一种算法，在放松最坏情况流量假设的同时仍能保证达到最优值的恒定比例，从而解决这一局限性。我们提供了肯定的答案：在随机流量场景下（如独立同分布的数据包到达），若 $C_{\min} = \Omega\big(\frac{\log (L/\epsilon) } {\epsilon^2}\big)$，则可设计出近最优的 $(1-\epsilon)$ 近似算法。据我们所知，这是首次证明在非平凡的流量与链路容量假设下，该问题可被近最优求解。我们进一步利用非平稳流量的真实网络轨迹进行了扩展仿真，结果表明，在实际场景中，我们的算法优于基于最坏情况的算法。