Computational grids are emerging as the new generation computing paradigm for tackling large scale hard problems in a wide range of scientific fields. Grids are highly complex distributed systems (involving multiple organizations with different goals and policies) which aim at providing computing services without the users need to know the location and features of the required resources. While the current and previous research efforts have been mainly concentrated on architectures and protocols, this paper deals with quantitative methods for grid resource management. In particular, three main issues are considered: performance forecasting, local scheduling (i.e., job scheduling within a single administrative domain) and distributed mechanisms for coordinating grid resources within several administrative domains. For each such a topic, the current literature is reviewed and new research avenues are highlighted.
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