As a flexible and cost-efficient scalable Internet access network, we studied architectures, protocols, and design optimizations of the Wireless Internet-access Mesh NETwork (WIMNET). WIMNET is composed of multiple access points (APs) connected through multihop wireless communications on IEEE 802.11 standards. The increasing popularity of real-time applications such as IP-phones and IP-TV means that they should be supported in WIMNET. However, the contention resolution mechanism using a random backoff-time in the CSMA/CA protocol of 802.11 standards is not sufficient for handling real-time traffic in multihop wireless communications. In this paper, we propose a Fixed Backoff-time Switching (FBS) method for the CSMA/CA protocol to improve the real-time traffic performance in WIMNET by giving the necessary activation chances to each link. We implement our proposal on the QualNet simulator, and verify its effectiveness through simulations on three network topologies with four scenarios.