High-performance Network Over Coax, or HINOC for short, is a broadband access technology that can achieve bidirectional transmission for high-speed Internet service through a coaxial medium. In HINOC access networks, buffer management scheme can improve the fairness of buffer usage among different output ports and the overall loss performance. To provide different services to multiple priority classes while reducing the overall packet loss rate and ensuring fairness among the output ports, this study proposes a QoS optimization method for access networks. A backpressure-based queue threshold control scheme is used to minimize the weighted average packet loss rate among multiple priorities. A theoretical analysis is performed to examine the performance of the proposed scheme, and optimal system parameters are provided. Software simulation shows that the proposed method can improve the average packet loss rate by about 20% to 40% compared with existing buffer management schemes. Besides, FPGA evaluation reveals that the proposed method can be implemented in practical hardware and performs well in access networks.