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The integration of WiMAX networks with EPON networks combine the large bandwidth availability in optical access networks with the mobility provided by wireless technologies. In this integration, a WiMAX bandwidth scheduler that takes into account the variability of the channel capacity provided by the EPON scheduler is quite important, since the granted bandwidth must be sufficient to support the QoS of WiMAX connections. This paper evaluates the performance of a standard-compliant WiMAX uplink scheduler designed to the ONU-BS. The evaluation is conducted using integrated simulators for the WiMAX and for the EPON components. Simulation results show that the proposed scheduler is able to provide QoS to the subscriber stations.