@article{Zukerman2008fair,
author = {M. Zukerman and M. Mammadov and L. Tan and I. Ouveysi
and L. L. H. Andrew},
title = {To be fair or efficient or a bit of both},
journal = {Computers and Operations Research},
volume = {35},
number = {12},
pages = {3787-3806},
month = {Dec.},
year = {2008},
abstract = {Introducing a new concept of
(\alpha,\beta)-fairness, which allows for a bounded fairness
compromise, so that a source is allocated a rate neither less than
0\leq \alpha \leq 1,
nor more than \beta \geq
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
(\alpha,\beta)-fairness constraints. This leads to what we call an
efficiency¨Cfairness 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.}
}