We consider a single-unicast networking scenario where a sender streams a flow at a fixed rate to a receiver across a multi-hop network, possibly using multiple paths. Transmission over a link incurs a traffic-dependent link delay. We optimize network delay concerning two popular metrics, namely maximum delay and average delay. Well-known pessimistic results state that a flow cannot simultaneously achieve a maximum delay and an average delay both within bounded-ratio gaps to optimal. Instead, we pose an optimistic note on the fundamental compatibility of the two delay metrics. Specifically, we design two polynomial-time solutions each of which can deliver $(1-\epsilon)$ -fraction of the flow with maximum delay and average delay simultaneously within $(1/\epsilon)$ -ratio gap to optimal, for any $\epsilon \in (0,1)$ . We prove that the ratio $(1/\epsilon)$ is at least near-tight. Moreover, our solutions can be extended to the multiple-unicast setting. In this setting, the two delay metrics of our solutions are both within a bounded-ratio gap of $(R/(R_{\min }\cdot \epsilon))$ to optimal, where $R$ (resp. $R_{\min }$ ) is the aggregate (resp. minimum) flow rate requirement of all sender-receiver pairs. Hence we pose a similar optimistic note. Simulations based on real-world continent-scale network topology show that the empirical delay gaps observed under practical settings can be much smaller than their theoretical counterparts. In addition, our solutions can achieve over 10% reduction on the maximum delay and average delay simultaneously, only in the cost of losing 3% traffic, as compared to a conceivable delay-aware baseline without traffic loss. Our results can be of particular interest to delay-centric networking applications that can tolerate a small fraction of traffic loss, including cloud video conferencing that recently attracts substantial attention.

中文翻译：

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网络延迟优化的两个指标的故事

我们考虑一种单单播网络场景，其中发送方通过多跳网络以可能的固定速率将流流传输到接收器，并可能使用多个路径。通过链路传输会导致流量依赖的链路延迟。我们针对两个流行的指标优化网络延迟，即最大延迟和平均延迟。众所周知的悲观结果表明，流不能同时在最大比例间隙内达到最大延迟和平均延迟。相反，我们对两个延迟指标的基本兼容性持乐观态度。具体来说，我们设计了两个多项式时间解，每个解都可以提供 $（1- \ epsilon）$ 分流同时在最大延迟和平均延迟范围内 $（1 / \ε）$ -比率差距达到最佳，适用于任何 $ \ epsilon \ in（0,1）$ 。我们证明比率 $（1 / \ε）$ 至少是紧密的 此外，我们的解决方案可以扩展到多单播设置。在这种情况下，我们解决方案的两个延迟指标均在 $（R /（R _ {\ min} \ cdot \ epsilon））$ 达到最佳状态 $ R $ （分别 $ R _ {\ min} $ ）是所有发送方对接收方的总流量（最小流量）要求。因此，我们提出了类似的乐观看法。基于现实世界的大陆规模网络拓扑的仿真表明，在实际设置下观察到的经验性延迟差距可能比理论上的差距小得多。另外，与可想象的没有流量损失的延迟感知基准相比，我们的解决方案可以同时将最大延迟和平均延迟降低10％以上，仅以损失3％的流量为代价。对于以延迟为中心的网络应用程序，它可以忍受一小部分流量损失，其中包括最近引起极大关注的云视频会议，我们的结果可能会特别令人感兴趣。