In this paper, we analyze the performance of a peer-to-peer (P2P) distributed storage architecture based on a layered overlay scheme, where some nodes provide their disk capacities for hosting data fragments generated by other active users. This system has been introduced and studied, by means of simulations, in a previous paper, where the use of randomized network coding has been proposed as an appealing alternative to classical erasure coding to generate the required redundancy in a distributed storage system. In fact, the proposed network coding-based scheme provides proactive network maintenance to guarantee sufficient resource redundancy: this leads to a reduction of maintenance complexity and to a larger amount of free disk space on storage nodes. In the current paper, we provide a preliminary analytical framework that encompasses the use of a few characteristic parameters of the considered distributed storage system, such as the resource availability and the available free disk space portion. Our results show a good agreement between analysis and simulations, thus confirming the effectiveness of our network coding-based approach.