A Tale of Two Metrics in Network Delay Optimization

We consider the scenario where a source streams a flow at fixed rate to a receiver across a network, possibly using multiple paths. Transmission over a link incurs a delay modeled as a non-negative, non-decreasing and differentiable function of the link aggregated transmission rate. This setting models various practical network communication scenarios. We study network delay optimization concerning two popular metrics, namely maximum delay and average delay experienced by the flow. A well-known pessimistic result says that a flow cannot simultaneously achieve optimal maximum delay and optimal average delay, or even within constant-ratio gaps to the two optimums. In this paper, we pose an optimistic note on the fundamental compatibility of the two delay metrics. Specifically, we design two polynomial-time solutions to deliver (1 -ε) fraction of the flow with maximum delay and average delay simultaneously within 1/ε to the optimums for any ε ∈ (0,1). Hence, the two delay metrics are “largely” compatible. The ratio 1/ε is independent to the network size and link delay function, and we show that it is tight or near-tight. Simulations based on real-world continent-scale network topology verify our theoretical findings. Note that the proposed delay gap 1/ε, upon sacrificing ε fraction of the flow rate, is guaranteed even under the worst theoretical case setting. Our simulation results show that the empirical delay gaps observed under practical settings can be much smaller than 1/ε. Our results are 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.