@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.}
}