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The provision of QoS control is a key of the successful deployment of multimidia networks. Buffer management plays an important role in QoS control. Therefore, this paper proposes a novel QoS buffer management algorithm named GREEN (Global Random Early Estimation for Nipping), which extends the concepts of ERD (early random drop) and RED (random early detection). Specifically, GREEN enhances the concept of “Random” to “Global Random” by globally considering the random probability function. It also enhances the concept of “Early” to “Early Estimation” by early estimating the network status. For performance evaluation, except compared with RED, extensive simulation cases are performed to probe the characteristics of GREEN.