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The mobile WiMax system is based on IEEE 802.16e, which defines radio interface supporting several classes of Internet Protocol applications and services. While the mobile WiMax system is being deployed, IEEE 802.16m TG is developing an amendment to the IEEE 802.16e to greatly improve the system performance, and it is focusing not only on the PHY and MAC performance but also on a level of end-to-end performance improvement that includes the scope of the network and application to embrace the strong market request and interest. To evaluate the mobile WiMax system capacity and performance, all the aspects of performance evaluation - from air link to application - are required. For the network and application-level capacity and performance analysis, we first provide an overview of mobile WiMAX systems, especially of the OFDMA/TDD systems of IEEE 802.16e and then describe subscriber and application profiles that include traffic-mix ratio, data-session attempts for applications, diurnal-application traffic distribution, and the application-traffic model. Afterward, the simulation results of network- traffic characteristics and demand estimation are provided. Finally, in the last section, we provide simulation results of end-to-end application performance evaluation using the examples of VoIP and a TCP/IP performance-enhancement method that can be implemented in the mobile WiMAX MAC or MAC/IP cross layer.