To be fair or efficient or a bit of both

  • Authors:
  • Moshe Zukerman;Musa Mammadov;Liansheng Tan;Iradj Ouveysi;Lachlan L. H. Andrew

  • Affiliations:
  • ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Electrical and Electronic Engineering (EEE) Department, The University of Melbourne, Vic. 3010, Australia;School of Information Technology and Mathematical Sciences, University of Ballarat, Vic. 3353, Australia;Computer Science Department, Central China Normal University, Wuhan 430079, PR China;ARC Special Research Centre for Ultra-Broadband Information Networks (CUBIN), Electrical and Electronic Engineering (EEE) Department, The University of Melbourne, Vic. 3010, Australia;Department of Computer Science, Caltech, Pasadena, CA 91125, USA

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2008

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Abstract

Introducing a new concept of (@a,@b)-fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0==1, times its fair share, this paper provides a framework to optimize efficiency (utilization, throughput or revenue) subject to fairness constraints in a general telecommunications network for an arbitrary fairness criterion and cost functions. We formulate a non-linear program (NLP) that finds the optimal bandwidth allocation by maximizing efficiency subject to (@a,@b)-fairness constraints. This leads to what we call an efficiency-fairness function, which shows the benefit in efficiency as a function of the extent to which fairness is compromised. To solve the NLP we use two algorithms. The first is a well-known branch-and-bound-based algorithm called Lipschitz Global Optimization and the second is a recently developed algorithm called Algorithm for Global Optimization Problems (AGOP). We demonstrate the applicability of the framework to a range of examples from sharing a single link to efficiency fairness issues associated with serving customers in remote communities.