Short-term fairness and long-term QoS in the Internet

We consider connection-level models of resource allocation in a simple symmetric three-link network, where files arrive into the network according to a Poisson process and the size of each file is exponentially distributed. For the simple network under consideration, we derive an optimal resource allocation policy which minimizes the steady-state expected number of files in the network. Using this result, we show that, in a heavy traffic regime, the mean file-transfer delay under the proportionally fair policy is at most 1.5 times the delay under the optimal policy. Simulation results indicate that the gap is even smaller.