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This paper addresses the inherent unreliability and instability of worker nodes in large-scale donation-based distributed infrastructures such as peer-to-peer and grid systems. We present adaptive scheduling techniques that can mitigate this uncertainty and significantly outperform current approaches. In this work, we consider nodes that execute tasks via donated computational resources and may behave erratically or maliciously. We present a model in which reliability is not a binary property, but a statistical one based on a node's prior performance and behavior. We use this model to construct several reputation-based scheduling algorithms that employ estimated reliability ratings of worker nodes for efficient task allocation. Our scheduling algorithms are designed to adapt to changing system conditions, as well as nonstationary node reliability. Through simulation, we demonstrate that our algorithms can significantly improve throughput while maintaining a very high success rate of task completion. Our results suggest that reputation-based scheduling can handle a wide variety of worker populations, including nonstationary behavior, with overhead that scales well with system size. We also show that our adaptation mechanism allows the application designer fine-grain control over the desired performance metrics.