This paper proposes a stochastic fluid flow model to compute the transfer time distribution of resources in peer-to-peer file sharing applications. The amount of bytes transferred among peers is represented by a continuous quantity (the fluid level) whose flow rate is modulated by a set of discrete states representing the concurrent upload and download operations on the peers participating to the transfer. A transient solution of the model is then performed to compute the probability that a peer can download a given resource in less than t units of time as a function of several system parameters. In particular, the impact of file popularity, bandwidth characteristics, concurrent downloads and uploads, cooperation level among peers, and user behavior are included in our model specification. We also provide numerical results aiming at proving the potentialities of the approach we adopted as well as to investigate interesting issues related to the effect of incentive mechanisms on the user cooperation.
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