This paper tackles the challenging task of developing a simple and accurate analytical model for performance evaluation of WiMAX networks. The need for accurate and fast-computing tools is of primary importance to face complex and exhaustive dimensioning issues for this promising access technology. In this paper, we present a generic Markovian model developed for three usual scheduling policies (slot sharing fairness, throughput fairness and opportunistic scheduling) that provides closed-form expressions for all the required performance parameters at a click speed. This model is compared in depth with realistic simulations that show its accuracy and robustness regarding the different modeling assumptions. Finally, the speed of our analytical tool allows us to carry on dimensioning studies that require several thousands of evaluations, which would not be tractable with any simulation tool.