The peer-to-peer (P2P) paradigm have emerged as a cheap, scalable, self-repairing and fault-tolerant storage solution. This solution relies on erasure codes to generate additional redundant fragments of each "block of data" in order to increase the reliability and availability and overcome the churn. When the amount of unreachable fragments attains a predefined threshold, due to permanent departures or long disconnections of peers, a recovery process is initiated to compensate the missing fragments, requiring multiple fragments of data of a given "block" to be downloaded in parallel for an enhanced service. Recent modeling efforts that address the availability and the durability of data have assumed the recovery process to follow an exponential distribution, an assumption made mainly in the absence of studies characterizing the "real" distribution of the recovery process. This work aims at filling this gap and better understanding the behavior of these systems through simulation while taking into consideration the heterogeneity of peers, the underlying network topologies, the propagation delays and the transport protocol. To that end, the distributed storage protocol is implemented in the NS-2 network simulator. This paper describes a realistic simulation model that captures the behavior of P2P storage systems. We provide some experiments results that show how modeling the availability and durability can be impacted by the recovery times distribution which is impacted in turn by the characteristics of the the network and the context.