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.
['Moshe Zukerman', 'Musa Mammadov', 'Liansheng Tan', 'Iradj Ouveysi', 'Lachlan L. H. Andrew']
To be fair or efficient or a bit of both