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Optical burst switching (OBS) is a promising switching technology for next-generation Internet backbone networks. One of the design challenges is how to provide fair bandwidth allocation in OBS networks; the schemes proposed for general store-and-forward IP switching networks can not be used because of the non-buffering and un-fully utilized bandwidth characteristics of OBS networks. We propose a rate fairness preemption (RFP) scheme to achieve approximately weighted max-min fair bandwidth allocation in OBS networks. We present an analysis of the burst loss probability in RFP-based OBS networks. The analysis and simulation results show that the RFP scheme provides fair bandwidth allocation in OBS networks.