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Many organizations have chosen to host Internet applications at Internet data centers (IDCs) located near network access points of the Internet to take advantage of their high availability, large network bandwidths and low network latencies. Current IDCs provide for a dedicated and static allocation of resources to each hosted application. Unfortunately, workloads for these sites are highly variable, leading to poor resource utilization, poor application performance, or both. In this paper, we develop a framework for QoS-driven dynamic resource allocation in IDCs. Termed QuID (quality of service infrastructure on demand), the framework's contributions are threefold. First, we develop a simple adaptive algorithm to reduce the average number of servers used by an application while satisfying its QoS objectives. Second, we develop an optimal off-line algorithm that bounds the advantage of any dynamic policy and provides a benchmark for performance evaluation. Finally, we perform an extensive simulation study using traces from large-scale E-commerce and search-engine sites. We explore the gains of the QuID algorithms as a function of the system parameters (such as server migration time), algorithm parameters (such as control time scale), and workload characteristics (such as peak-to-mean ratio and autocorrelation function of the request rate).