In June 2004, the IEEE approved a new standard for Resilient Packet Rings (RPR). The standard is maintained in the 802 LAN/MAN Standards Committee, and is designated the standard number 802.17. In this paper, we analyze and discuss performance aspects of the Resilient Packet Ring fairness mechanism. We explain that, if the ring is not configured correctly, the fairness mechanism fails to stabilize at a fair division of bandwidth between the active nodes. We present a novel addition to the fairness algorithm, and show that with this modification, RPR reaches a stable state with more optimal parameter settings. We also show that our proposed modification gives shorter convergence time for the Resilient Packet Ring fairness algorithm.