Multimedia traffic on the Internet is rapidly increasing with the advent of broadband networks. However, the Best-Effort (BE) service used with Internet Protocol (IP) networking was never intended to guarantee Quality of Service (QoS) for each user. Therefore, the realization of QoS guarantees has become a very important issue. Previously, we have proposed a queue management scheme, called Dual Metrics Fair Queuing (DMFQ), to improve fairness and to guarantee QoS. DMFQ improves fairness and throughput by considering the amount of instantaneous and historical network resources consumed per flow. In addition, DMFQ has characteristics of high speed and high scalability because it is hardware oriented. However, DMFQ may be unable to adapt to network fluctuations, given that it has static setup parameters. Moreover, DMFQ is unable to support a multiclass environment. In this paper, we propose a new buffer management scheme based on DMFQ that can adapt flexibly to network conditions and can provide classified services. The proposed scheme stabilizes buffer utilization within a fixed range by controlling the buffer threshold, which affects the calculated packet discard probability. Moreover, by applying the proposed scheme to Differentiated Services (DiffServ), we achieve prioritized buffer management.