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lief, parallel downloading is far from being optimal in terms of reducing the download time. Its performance is very much dependent upon the heterogeneity in service capacities in the network and upon the degree of competi- tion in the network. In a network consisting of many het- erogeneous sources (as in current P2P networks), we are better off keeping fewer connections so that not every user gets stuck in the bad sources. Overall, from Figures 4, it is evident that the random periodic switching generally performs the best. Although it may not compete with parallel downloading in the case where all sources offer the same service capacity with very light competition, those conditions are not practical in most cases. For all other situations with realistic heterogeneity, competition among peers, as well as with temporal correlations in each path, the random periodic switching gives the most stable and optimal performance in the sense that its download time is minimal, robust with respect to network config- urations, and consistent for different users in a random environment.

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