Queueing Delay Minimization in Overloaded Networks via Rate Control

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rate-proportional</i> policies. We further generalize the rate-proportional policies to <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">queue-proportional</i> 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.