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Resilient packet ring (RPR) is a new kind of metropolitan area network technology which has a fast automatic protection switching ability. Fairness algorithm is a key technology of RPR. Current fairness algorithms cannot get high bandwidth utilization and suffer from permanent oscillations under unbalanced conditions. A new fairness algorithm based on deficit round robin (FBDRR) is presented. Its ideal model, based on the GPS (generalized processor sharing) scheduling algorithm, is proved to be RIAS (ring ingress aggregated with spatial reuse) fair. Analysis and simulations prove that FBDRR can solve the oscillation problems, allocate bandwidth fairly and converge very quickly.