@article{Zukerman2005Efficiency,
    author = {M. Zukerman and L. Tan and H. Wang and I. Ouveysi},
    title = {Efficiency-fairness tradeoff in telecommunications networks},
    journal = {IEEE Communications Letters},
    volume = {9},
    number = {7},
    pages = {643-645},
    month = {Jul.},
    year = {2005},
    abstract = {Introducing the concept of $\alpha$-fairness, which allows for a bounded fairness compromise, so that no source is allocated less than a fraction $\alpha$ of its fair share, this letter studies tradeoffs between efficiency (utilization, throughput or revenue) and fairness in a general telecommunications network with relation to any fairness criterion. We formulate a linear program that finds the optimal bandwidth allocation by maximizing efficiency subject to $\alpha$-fairness constraints. This leads to what we call an efficiency-fairness curve, which shows the benefit in efficiency as a function of the extent to which fairness is compromised.}
}