Heavy-Traffic Delay Minimization in Bandwidth-Sharing Networks

Bandwidth-sharing networks as considered by Massoulie & Roberts provide a natural modeling framework for describing the dynamic flow-level interaction among elastic data transfers. Although valuable stability results have been obtained, crucial performance metrics such as flow-level delays and throughputs in these models have remained intractable in all but a few special cases. In particular, it is not well understood to what extent flow-level delays and throughputs achieved by standard bandwidth-sharing mechanisms such as alpha-fair strategies leave potential room for improvement. In order to gain a better understanding of the latter issue, we set out to determine the scheduling policies that minimize the mean delay in some simple linear bandwidth-sharing networks. While admittedly simple, linear networks provide a useful model for flows that traverse several links and experience bandwidth contention from independent cross-traffic. Even for linear topologies it is rarely possible however to explicitly identify optimal policies except in a few limited cases with exponentially distributed flow sizes. Rather than aiming for strictly optimal policies, we therefore focus on a class of relatively simple priority-type strategies that only separate large flows from small ones. To benchmark the performance of these strategies, we compare them with proportional fair as the prototypical alpha-fair policy, and establish that the mean delay may be reduced by an arbitrarily large factor when the load is sufficiently high. In addition, we show the above strategies to be asymptotically optimal for flow size distributions with bounded support. Numerical experiments reveal that even at fairly moderate load values the performance gains can be significant.