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In wireless networks, the definition of fair resource allocation is ambiguous because the wireless channel condition is not constant over time and location. Two main ways to define fair resource allocation are: by number of allocated service time units per user, temporal fairness, or the number of transmitted bytes per user, throughput fairness. In wireless broadband networks i.e., IEEE 802.16e Mobile WiMAX, the quality of services level offered by service providers is associated with the price paid. Similar to a traditional cellular phone system, the users may be required to pay air-time charges. The throughput fairness is favorable to customers with a poor channel condition or those at a far distance. Slot fairness will be preferred by the customers near the base stations and with good channel condition. In this paper, we define the Generalized Weighted Fairness (GWF) criterion that allows carriers to implement either of the two fairness criteria applying into a Mobile WiMAX environment. In addition, we show how a scheduling algorithm can use the GWF criterion to achieve a general weighted fair resource allocation in IEEE 802.16e Mobile WiMAX networks. We use Deficit Round Robin with Fragmentation (DRRF) as an example of scheduling algorithm. Numerical and simulation results are presented to demonstrate the effect of the GWF.