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To be fair or efficient or a bit of both

Authors
Journal
Computers & Operations Research
0305-0548
Publisher
Elsevier
Publication Date
Volume
35
Issue
12
Identifiers
DOI: 10.1016/j.cor.2007.02.007
Keywords
  • Non-Linear Programming
  • Utility Optimization
  • Fairness
  • Efficiency–Fairness Tradeoff
  • Bandwidth Allocation
Disciplines
  • Communication
  • Computer Science

Abstract

Abstract Introducing a new concept of ( α , β ) -fairness, which allows for a bounded fairness compromise, so that a source is allocated a rate neither less than 0 ⩽ α ⩽ 1 , nor more than β ⩾ 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 ( α , β ) -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.

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