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The IEEE 802.16 provides a reservation-based MAC protocol for high speed broadband wireless services. A subscriber station (SS) which wishes to transmit data transmits a bandwidth request message to its base station (BS) to reserve the resource. However, if the bandwidth request message is transmitted by a contention-based scheme, the collision probability of the bandwidth request message may be increased as the number of contending subscriber stations increases. In worst case, the BS cannot allocate the bandwidth to stations due to the failure of the bandwidth request procedure although the BS has enough bandwidth. In this paper, we propose an efficient bandwidth request scheme that appropriately uses a contention-based scheme and a contention-free scheme according to the network condition for non-real-time services such as nrtPS and BE. The proposed scheme determines when the contention-free based bandwidth request scheme can be used, and it allocates more bandwidth to SSs than the contention-based scheme. We implemented the IEEE 802.16 MAC protocol and the proposed scheme in the ns-2 simulator, and evaluated the performance. The simulation results show that the proposed scheme can allocate more bandwidth to nrtPS and BE flows without any influence to UGS and rtPS flows. The simulation results also show that the proposed scheme shows improved performance compared with existing contention-based schemes.