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In a desktop grid model, the job (computational task) is submitted for execution in the resource only when the resource is idle. There is no guarantee that the job which has started to execute in a resource will complete its execution without any disruption from user activity (such as a keyboard stroke or mouse move) if the desktop machines are used for other purposes. This problem becomes more challenging in a Peer-to-Peer (P2P) model for a desktop grid where there is no central server that decides to allocate a job to a particular resource. This paper describes a P2P desktop grid framework that utilizes resource availability prediction. We improve the functionality of the system by submitting the jobs on machines that have a higher probability of being available at a given time. We benchmark our framework and provide an analysis of our results.