We develop link rate control policies to minimize the queueing delay of packets in overloaded networks. We show that increasing link rates does not guarantee delay reduction during overload. We consider a fluid queueing model that facilitates explicit characterization of the queueing delay of packets, and establish explicit conditions on link rates that can minimize the average and maximum queueing delay in both single-hop and multi-stage (switching) networks. These min-delay conditions require maintaining an identical ratio between the ingress and egress rates of different nodes at the same layer of the network. We term the policies that follow these conditions rate-proportional policies. We further generalize the rate-proportional policies to queue-proportional policies, which minimize the queueing delay asymptotically based on the time-varying queue length while remaining agnostic of packet arrival rates. We validate that the proposed policies lead to minimum queueing delay under various network topologies and settings, compared with benchmarks including the backpressure policy that maximizes network throughput and the max-link-rate policy that fully utilizes bandwidth. We further remark that the explicit min-delay policy design in multi-stage networks facilitates co-optimization with other metrics, such as minimizing total bandwidth, balancing link utilization and node buffer usage. This demonstrates the wider utility of our main results in data center network optimization in practice.

翻译：本文提出了链路速率控制策略以最小化过载网络中数据包的排队时延。研究表明，在过载状态下提高链路速率并不能保证降低时延。我们采用流体排队模型，该模型能显式刻画数据包的排队时延特征，并建立了单跳网络与多级（交换）网络中分别使平均排队时延和最大排队时延最小化的链路速率显式条件。这些最小化时延条件要求网络同一层级中不同节点的入口速率与出口速率保持恒定比例。我们将遵循该条件的策略称为速率比例策略。进一步将速率比例策略推广至队列比例策略，该策略基于时变队列长度渐近实现排队时延最小化，且无需获知数据包到达率。通过与最大化网络吞吐量的背压策略及充分利用带宽的最大链路速率策略等基准方法对比，验证了所提策略在各种网络拓扑与场景下均能实现最小排队时延。此外我们指出，多级网络中显式最小化时延策略的设计可促进与其他指标（如最小化总带宽、均衡链路利用率与节点缓存占用）的协同优化，这展示了本文主要结果在数据中心网络优化实践中的广泛适用性。