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With the development of wireless communication technologies, future networks will most likely be heterogeneous, consist of both wired and wireless links. However, current active queue management (AQM) schemes, which are originally designed for wired networks, could cause performance degradation of Transmission Control Protocol (TCP) flows over wired-cum-wireless networks. Thus, to deal with these problems, we propose a new rate-based AQM scheme (NRAQM). NRAQM scheme uses a new marking/dropping module and a timer updating module for packets dropping/marking and dropping/marking probability updating, which are different from other existing AQM schemes. The objectives of our proposed scheme are to stabilize networks with low end-to-end delay, and high link utilization regardless the dynamics of wired-cum-wireless networks conditions. Simulation results show that our proposed scheme outperforms the existing AQM schemes over wired-cum-wireless networks.