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As a flexible and cost effective solution for a scalable Internet-access network, we have studied the Wireless Internet-access Mesh NETwork (WIMNET) that is composed of multiple access points (APs). WIMNET utilizes multi-hop communications between APs to provide access to the Internet through a gateway (GW) from associated hosts, which becomes increasingly vulnerable to problems of the available bandwidth degradation and the network latency. As a result, real-time applications such as Voice-over-IP (VoIP) and video conferences are hard in WIMNET. In this paper, we propose a traffic control method with consumed bandwidth estimation to afford real-time applications in WIMNET. After the consumed bandwidth by the requesting applications is estimated, the least priority application is repeatedly dropped at GW using the leaky bucket traffic shaping, until it does not exceed the available bandwidth in WIMNET. The effectiveness of our proposal is verified through simulations using the QualNet simulator.