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Applications utilizing Grid computing infrastructure usually require resources allocation (e.g., bandwidth and CPU) to satisfy their quality of service (QoS) requirements. Given the dynamic nature of grid computing, QoS support and adaptation must be a high priority to successfully support those applications. In this paper, we present an adaptive resources provisioning scheme that optimizes the resources utilization while satisfying the required QoS. More specifically, it minimizes the request blocking probability and, thus, maximizes the revenues of the infrastructure provider.