Network Optimization Problems Subject to Max-Min Fair Flow Allocation

• Published in: IEEE communications letters Vol. 17; no. 7; pp. 1463 - 1466
• Main Authors: Amaldi, E., Capone, A., Coniglio, S., Gianoli, L. G.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2013; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Access methods and protocols, osi model; Applied sciences; Bandwidth; bandwidth sharing; Exact sciences and technology; Linear programming; Max-min fairness; Operations research; Optimization; Organization and planning of networks (techniques and equipments); Resource management; Routing; Studies; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Teletraffic; Throughput; Traffic control; traffic engineering; Transmission and modulation (techniques and equipments); utility-based routing; Vectors; Utility function; Resource allocation; Network architecture; Equity; Optimization; Topological structure; bandwidth sharing; Traffic flow; traffic engineering; Traffic control; Max-min fairness; Availability; Maximin problem; Flow rate regulation; Control system; Transmission protocol; Teletraffic; Mixed integer programming; Routing; Resource sharing; Bandwidth allocation; Reference model; Computation time; Traffic management; Distributed control; Resource management; utility-based routing
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2013.060513.130351

We propose a novel way to consider the max-min fairness (MMF) paradigm in traffic engineering. Since MMF appears as a reference model for a fair capacity allocation when the traffic flows are elastic and rates are adapted based on resource availability, we consider it as a requirement due to the way resources are shared by the distributed rate control scheme (like that of the transport protocol), rather than the routing objective. In particular, we define the traffic engineering problem where, given a network topology with link capacities and a set of elastic traffic demands to route, we must select a single path for each demand so as to maximize a network utility function, assuming an MMF bandwidth allocation. We propose a compact mixed-integer linear programming formulation as well as a restricted path formulation. We show with computational experiments that the exact formulation can be solved in a reasonable amount of computing time for medium-size networks and that the restricted path model provides solutions of comparable quality much faster.