The concept of fairness: Definitions and use in bandwidth allocation applied to satellite environment

Starting from the literature in the field, the article has discussed and formalized the concept of fairness, as well as reporting on specific evaluation indexes. Fairness indexes have been computed for some resource allocation methods applied to satellite systems taken in the literature, giving numerical examples on which to comment. The analysis has shown that the fairness concept has different meanings and, consequently, must be measured through different indexes. Allocation algorithms may be fair concerning one index and unfair concerning another one (the case of NBS is evident from this viewpoint). This aspect underlines the importance of having a precise definition of fairness within a scientific work to avoid ambiguities. In summary, the MMF and Jain fairness indexes\´ results are in agreement concerning the order when the fading factor varies and the bandwidth is fixed (meaning given bandwidth C, if β\´ > β", I_JF|_β\´,C > I_JF|_β",C and I_MMF|_β\´,C > I_MMF|_β",C), but the slopes of the curves provided by the two indexes are different, also from the concavity viewpoint, and IJF increases and decreases less quickly by varying bandwidth. Moreover, the MMF index neglects the bandwidth distribution among stations, while the Jain fairness index measures the degree of bandwidth distribution. The PF index has a different aim: it not only considers the amount of provided bandwidth and the channel status concerning fading but also weights the bandwidth use and the possible user revenue through a utility function. Because the objectives are different, the results provided by allocation schemes that take PF as a reference (also implicitly) provide different results from the algorithms that have inspiration from MMF and/or Jain fairness.