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The rising complexity of distributed server applications in Internet data centers has made the tasks of modeling and analyzing their behavior increasingly difficult. This article presents Modellus, a novel system for automated modeling of complex web-based data center applications using methods from queuing theory, data mining, and machine learning. Modellus uses queuing theory and statistical methods to automatically derive models to predict the resource usage of an application and the workload it triggers; these models can be composed to capture multiple dependencies between interacting applications. Model accuracy is maintained by fast, distributed testing, automated relearning of models when they change, and methods to bound prediction errors in composite models. We have implemented a prototype of Modellus, deployed it on a data center testbed, and evaluated its efficacy for modeling and analysis of several distributed multitier web applications. Our results show that this feature-based modeling technique is able to make predictions across several data center tiers, and maintain predictive accuracy (typically 95% or better) in the face of significant shifts in workload composition; we also demonstrate practical applications of the Modellus system to prediction and provisioning of real-world data center applications.