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We propose an analytic model using WiMAX as backhaul support for WiFi traffic and evaluate the system performance. One unique feature is that the WiFi traffic completely reflects the realistic user behavior. A WiFi user may be overflowed to its overlaid WiMAX cell when it is rejected at the WiFi cell; the WiFi user may also work for some time duration in the WiFi cell and then make a vertical handoff to its overlaid WiMAX cell when it needs to move from its current WiFi cell (e.g., office) to its target WiFi cell (e.g., airport). Further, the target WiFi cell may be located at another place in the same WiMAX cell, or at a different WiMAX cell. We use Markov processes to model the dynamics of the WiMAX traffic and WiFi traffic including the overflowed WiFi traffic, the vertical handoff WiFi traffic, the horizontal handoff WiFi traffic, and the take-back WiFi traffic. We derive various traffic arrival rates and performance metrics. Numerical results are provided for further quantitative evaluation.