The Resilient Packet Ring (RPR) IEEE 802.17 is a new Medium Access Control (MAC) protocol for high-speed ring networks. In order to achieve fairness among nodes, a fairness algorithm is employed at each RPR node. In this paper, we develop an analytical model for fair rate calculation in the standard RPR Aggressive fairness algorithm in parking lot scenario. Our approach is to model the fair rate calculation by a non-linear discrete-time low-pass filter. We verify our model by simulation results and analyze the convergence of the fairness algorithm. Further, the effect of various parameters on convergence time is investigated.