EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS Euro. Trans. Telecomms. 2005; 16:241–251 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/ett.1050 Resilient dimensioning of proportionally fair networks Michal Pio ´ro 1;2 *, Eligijus Kubilinskas 1 and Pa ˚l Nilsson 1 1 Department of Communication Systems, Lund University, PO Box 118, SE-22100 Lund, Sweden 2 Institute of Telecommunications, Warsaw University of Technology, Nowowiejska15/19, 00-665 Warsaw, Poland SUMMARY 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. Copyright # 2005 AEIT. 1. INTRODUCTION The issue of economical and at the same time fair alloca- tion of bandwidth in networks carrying elastic traffic, both from the network operator and the user viewpoints, has been studied in References [1–5, 13]. Elastic traffic can be regarded as greedy, that is, capable of consuming all capacity available to it (perhaps within some limit). At the same time it is capable of adapting to a decreased band- width (of course at the expense of impairing the appli- cation performance, although preserving its basic function). It is commonly known that packet data net- works, as for example the Internet, are mainly devoted to carry traffic that can be regarded as elastic. Increasing growth of the throughput-demanding real-time multimedia applications over Internet that require quality of service (QoS) guarantees, raises a need of sophisticated bandwidth allocation schemes, giving greater user satisfaction and, at the same time, increased economical profit for network providers. For such a scheme, two basic aspects taken into account are: (i) fair bandwidth allocation and (ii) robust- ness (i.e. resilience) to failures. While among all allocation schemes, throughput maximisation (TM) is the most profitable from the network operator’s point of view (although possibly quite unfair for some customers), two alternatives exist that make the allocation more fair. These are the max-min fairness (MMF), [1, 9, 13] and the propor- tional fairness (PF), [5, 13] allocation methods. Comparing the two principles, MMF, though guaranteeing maximal fairness, suffers from poor total network throughput, whereas PF seems to be a good compromise between TM and MMF. The requirement of network robustness to link failures leads to allocation of flows which assures that the maxi- mum possible total flow is realised in the network under any of the assumed failure situations. A failure situation is defined as a situation when one or more links are completely or partially broken. Previously considered fair network designs [10, 13, 14], referred to as the nominal case fair designs, did not take robustness into account. Received 23 August 2004 Copyright # 2005 AEIT Accepted 31 August 2004 * Correspondence to: Michal Pio ´ro, Department of Communication Systems, Lund University, PO Box 118, SE-22100 Lund, Sweden. E-mail: mpp@telecom.lth.se Contract/grant sponsor: Swedish Research Council; contract/grant number: 621-2003-2767.