A fundamental relationship between fairness and optimum throughput in TDMA protocols

A general relationship is established between fairness and throughput in TDMA protocols. We prove the fundamental result that, under quite general conditions, fairness and optimum throughput imply each other in TDMA protocols, in the sense that if one of them holds then the other is automatically guaranteed to hold. The result has the important practical consequence that in cases when packet loss is characterized by a loss function, satisfying certain natural properties, it is enough to guarantee fairness to automatically obtain a guaranteed maximum throughput. Or, conversely, maximum throughput will automatically lead to fairness