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A peer-to-peer (P2P) technology is applied for various systems because it enables to construct a system with high scalability and robustness. We have proposed a distributed cooperative storage system that can construct huge storage space by providing it on a P2P network. The storage system is based on an overlay network construction, and its hash space is created in an application layer. Each peer manages the certain range of the hash space, and an object is stored to suitable peers by using a hash value from the object.In the general P2P network, objects are replicated over many peers to achieve high availability. Some replicated methods have been proposed: objects are randomly assigned, assigned on a route path, or assigned to peers that the number of them is fixed by a network neighborhood depending on a distributed hash table. However, they are not so suitable since the scale of the network is not considered in these methods. Therefore, we propose distributed interval trees for setting the number suitably, and the availability is described with simulation.