Robust dimensioning of proportionally fair networks

The notion of proportional fairness has recently gained considerable interest as a potential means for a fair allocation of bandwidth between the end nodes of demands in the networks carrying elastic traffic. The issue of proportionally fair allocation of bandwidth for the nominal state of the network has been studied before, both in the capacitated (link capacities given) and the uncapacitated (link capacities are also subject to optimisation) cases. In the presented paper, we address a more complicated uncapacitated problem - optimisation of link capacities for a proportionally fair network robust to failures. We formulate a relevant optimisation problem and propose efficient solution algorithms. Efficiency of the algorithms is illustrated with numerical examples including large networks. The design approach is applicable to IP/MPLS networks based on leased transmission capacity