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The authors consider connection-level models of resource allocation in the Internet, where files arrive into the network according to a Poisson process and the size of each file is exponentially distributed. For a simple symmetric three-link star network, they derive the optimal resource allocation policy which minimizes the expected number of files waiting in the system. The performance of the optimal policy is then compared with the performance of the widely-studied proportionally-fair resource allocation policy. They show that the expected number of files under proportional fairness is at most 1:5 times more than the expected number under the optimal policy in a heavy-traffic regime.
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