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Queueing Delay Minimization in Overloaded Networks via Rate Control

We study the pattern of queueing delay minimization in overloaded networks using link rate control. We show that serving packets with maximum link rates does not minimize queueing delay when networks are on overload. To understand this counter-intuitive observation and identify the optimal solution, we characterize the packet queueing delay explicitly through a fluid queue model, which enables us to characterize the sufficient and necessary condition for a policy to be delay-optimal for single-hop networks. We show that setting the link rates to be proportional to the packet arrival rates minimizes both average and maximum delay among all sources simultaneously. We further prove that a queue-proportional rate control policy, agnostic of packet arrival rates, asymptotically achieves optimal delay performance given any initial state of queue backlog. We evaluate our policies over single-hop networks with different network settings, and demonstrate its superiority compared to the policies that work well in networks not overloaded.