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Managing geographically dispersed deployments of complex multitier applications involves dealing with the substantial effects of network latency. However, the effects of network latency on an application's end-to-end performance can be far from obvious, thus making it difficult to predict the true impact of infrastructure changes such as network upgrades or server relocation on the users of an application. In this paper, we propose a new metric to quantify this impact called the link gradient. We develop a novel noise-resistant, nonintrusive technique to measure the link gradients in running systems without requiring knowledge of the system structure by using a combination of run-time delay injection and spectral analysis. We evaluate the intrusiveness and accuracy of our approach using micro-benchmarks and a deployment of two benchmark multitier Web applications on PlanetLab. Using these results, we show that link gradients can be used to accurately predict the impact of network latency changes on the end-to-end responsiveness of individual application transactions, even in new application configurations and without requiring a dedicated test environment.