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Wireless Mesh Networks (WMNs) have emerged as a key technology for next generation wireless networks showing rapid progress and inspiring numerous applications. Advanced antenna techniques, scheduling algorithms, admission control and routing schemes have attracted increased research interests aiming to optimize the performance of WMNs and satisfy their vast and diverse traffic requirements. However in such networks, uncontrolled admission of arbitrary large number of data flows can highly increase congestion for the whole network. To overcome this difficulty, the paper proposes a novel Robust Bandwidth Assignment (RBA) algorithm for connection admission control with the objective to efficiently manage the resources and thereby maximize the performance of the network. Connection-level QoS constraints such as handoff connection dropping probability can be guaranteed within a threshold. Multiple service classes are prioritized. This allows us to take admission control decisions for new data flows in a way that we can increase the resource utilization while maintaining the QoS.