Dynamics of heterogeneous peer-to-peer networks

The most tractable models of population dynamics in peer-to-peer file sharing systems apply to a single class of peers with homogeneous network access parameters. When upload bandwidths are heterogeneous, reciprocity mechanisms lead to non-uniform download rates and a more complex multi-class dynamics. We consider first a model where mutual download bandwidths are allocated in proportion to the upload speed, plus a uniformly distributed server component. For an ordinary differential equation model of the multi-class peer populations, we characterize the equilibrium and establish its global stability, invoking results from monotone systems. We also analyze a partial differential equation model that tracks download progress of the populations; we establish the local asymptotic stability of the equilibrium. Finally, we extend the ODE model to include a mix of proportional and uniform bandwidth allocation, which better describes the mechanisms of BitTorrent systems; again we characterize equilibrium configurations and give a partial result on local stability.

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