Fine-Grained Cycle Sharing (FGCS) systems aim at utilizing the large amount of computational resources available on the Internet. In FGCS, host computers allow guest jobs to utilize the CPU cycles if the jobs do not significantly impact the local users of a host. A characteristic of such resources is that they are generally provided voluntarily and their availability fluctuates highly. Guest jobs may fail because of unexpected resource unavailability. To provide fault tolerance to guest jobs without adding significant computational overhead, it requires to predict future resource availability. This paper presents a method for resource availability prediction in FGCS systems. It applies a semi-Markov Process and is based on a novel resource availability model, combining generic hardware-software failures with domain-specific resource behavior in FGCS. We describe the prediction framework and its implementation in a production FGCS system named iShare. Through the experiments on an i...