Resilient Packet Ring (RPR) is a more promising solution to the bottleneck of metropolitan-area networks (MANs). The ring network architecture and associated protocol has been standardized by the IEEE 802.17 working group in 2004. To achieve high bandwidth utilization, optimum spatial reuse and fairness simultaneously, a policy of fair bandwidth assignment must be implemented in current RPR network. The existing fairness mechanisms suffer from severe oscillations under certain conditions, such as unbalanced traffic scenario and noticeable time delay. With our proposed fairness algorithm, the system performance of the three-node unbalanced traffic scenario, where the traffic loads are fixed, can be sustained by simply adjusting the compensating factor with respect to the time delay. In this paper, the time delay is constant, we investigate how this compensating factor should be adjusted with respect to the degree of unbalance. Furthermore, we study a four-node scenario, each node-to-node pair has different time-delay as well as unbalance degree. The simulation results show that the system performance remains excellent with the guidelines summarized.