Fairness issues in peer-to-peer networks

This paper considers the issue of fairness arising from peer-to-peer networks. Various concepts of fairness are proposed. In particular, it is shown that the issue of having a perfectly fair solution is related to a generalization of the Perron-Frobenius Theorem. The fairness issue also leads questions whether there exist distributed feedback control algorithms that converge to the desired optimal or feasible states. These control algorithms possess the following characteristics. First of all, the controllers are numerous and are highly distributed. Secondly, controls are based on limited feedback information. Finally, network parameters are mostly unknown; hence these controllers should be robust. A class of controllers satisfying these characteristics is presented and their applicability of the fairness problem will be discussed.