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Supporting quality of service (QoS) while fulfilling high efficiency of bandwidth utilization is challenging in wireless mesh networks. To deal with this issue, hybrid medium access control (MAC) protocols are effective candidates because they can achieve QoS support and better resource sharing at the same time. However, in multi-hop communication environments, hybrid MAC protocols suffer from interference and low bandwidth efficiency. To solve these problems, in this paper, we propose a distributed interference-aware admission control algorithm (DIACA) with soft resource allocation for hybrid MAC protocols suitable for IEEE 802.11 wireless mesh networks; a scheme for providing QoS improvement for real-time sessions (RTSNs) while enhancing the efficiency of bandwidth utilization. The proposed DIACA possesses a function for interference probing, making each node recognize their interfering counterparts. Further, through support of interference detection, concurrent transmissions can be achieved by letting non-interfering nodes transmit data simultaneously along a route which improves the efficiency of spatial reuse of bandwidth. In addition, the DIACA can implement soft resource allocation for RTSNs having delay requirements but loose (or low) throughput demands. By using soft resource allocation, a transmission opportunity can be shared by different RTSNs with low data rates and each of the RTSNs can obtain satisfactory QoS. Simulation results indicate that the proposed admission control algorithm can significantly enhance the bandwidth utilization of wireless channel and can improve QoS for RTSNs.