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Critical to the successful deployment of grid systems is their ability to guarantee efficient meta-scheduling, namely optimal allocation of jobs across a pool of sites with diverse local scheduling policies. The centralized nature of current meta-scheduling solutions is not well suited for the envisioned increasing scale and dynamicity of next-generation grids, the success of which relies on the development of fully distributed, flexible and autonomic systems tailored to very large sets of highly volatile and heterogeneous resources. In this respect, we introduce a fully distributed grid meta-scheduling scheme that effectively addresses the concerns regarding the scalability and adaptability of future grid systems. Our approach employs a lightweight protocol, called A RiA, that is based on peer-to-peer communication between grid nodes, and makes use of dynamic rescheduling to consider and adapt to changes in the availability of resources. Extensive evaluation by means of an in depth simulation study highlighted the effectiveness of the proposed solution in improving the overall performance in terms of job completion time and load-balancing.