On the relationship between absolute and relative fairness bounds

The fairness of scheduling disciplines used in communication networks has frequently been evaluated using one of two fairness measures: the absolute fairness bound (AFB) and the relative fairness bound (RFB). We present a tight bounded relationship between these measures of fairness. The bounds established are exactly reached in the case of many real scheduling disciplines, thus leading to an easy conversion between these two measures. In the case of latency-rate (LR) servers, this also leads to an easy determination of the upper bound on the latency of a flow from the more tractable relative fairness bound of the scheduler. Our results also indicate that in many real contexts, the two measures of fairness approach each other as the number of flows increases, confirming the RFB as an adequate measure of fairness.