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The IEEE 802.16 standard defines MAC and physical layers for WiMAX networks, but it does not provide any recommendation for the scheduling algorithm that regulates resource assignment for both uplink and downlink. Focusing on the point-to-multipoint mode, where the base station decides about resource allocations in both uplink and downlink, this paper proposes a scheduling algorithm to support UGS and BE traffic classes, where the UGS service is based on a token bucket scheme. An analytical study has been performed to validate the simulator. Simulation runs have permitted to prove the goodness of the proposed scheduler as a comparison with a reference scheduler developed by the NIST Institute.