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Worldwide interoperability for microwave access (WiMAX) is a promising technology for last-mile Internet access, particularly in the areas where wired infrastructures are not available. In a WiMAX network, call admission control (CAC) is deployed to effectively control different traffic loads and prevent the network from being overloaded. In this paper, we propose a framework of a 2-D CAC to accommodate various features of WiMAX networks. Specifically, we decompose the 2-D uplink and downlink WiMAX CAC problem into two independent 1-D CAC problems and formulate the 1-D CAC optimization, in which the demands of service providers and subscribers are jointly taken into account. To solve the optimization problem, we develop a utility- and fairness-constrained optimal revenue policy, as well as its corresponding approximation algorithm. Simulation results are presented to demonstrate the effectiveness of the proposed WiMAX CAC approach.