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This paper defines an end-to-end QoS functional model for mobile WiMAX systems and investigate several technical issues. Our main contribution is to analyze the end-to-end QoS variations in mobile WiMAX systems according to the QoS functions. We discuss the strong and weak points of QoS related functions, which can be affected by the network architecture, and propose the design examples of a service class mapping function. To evaluate the end-to-end QoS, we implemented an end-to-end performance analysis simulator of mobile WiMAX using OPNET. Simulation results show that the uplink application layer throughput is about 70 percent of the uplink physical layer throughput.