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Connection admission control and routing are two important mechanisms in the provision of quality of service (QoS) in IEEE 802.16-based wireless mesh networks. In this paper, we intend to develop an optimal model which aims to maximize the total revenue from all carried connections in the mesh network while provide QoS support for each service class. We formulate the problem as a decision process and apply optimization techniques to obtain the optimal policies. Simulation results show that the proposed joint admission control and routing scheme can significantly improve the achieved system revenue, successfully prioritize different service classes, and effectively guarantee the QoS constraints such as new or handoff connection blocking probability.