Inspired by the emerging Cloud Computing challenge, in this paper we provide a comprehensive framework for modeling and managing time bound constraints in data-intensive Grid and Cloud infrastructures, along with its experimental assessment and analysis. We provide both conceptual and theoretical contributions of the proposed framework, along with a heuristic scheme, called RGDTExec, that solves all possible instances of the problem underlying the proposed framework by exploiting a suitable greedy algorithm, called RGDTExecRun. As we demonstrate throughout the paper, the framework keeps several aspects of research innovations that are beneficial in a wide range of application scenarios.