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The emerging broadband wireless access technology based on IEEE 802.16 is one of the most promising solutions to provide ubiquitous wireless access to the broadband service at low cost. This paper proposes an efficient uplink bandwidth request-allocation algorithm for real-time services in Mobile WiMAX networks based on IEEE 802.16e. In order to minimize bandwidth wastage without degrading quality of service (QoS), we introduce a notion of target delay and propose dual feedback architecture. The proposed algorithm calculates the amount of bandwidth request such that the delay is regulated around the desired level to minimize delay violation and delay jitter for real-time services. Also, it can increase utilization of wireless channel by making use of dual feedback, where the bandwidth request is adjusted based on the information about the backlogged amount of traffic in the queue and the rate mismatch between packet arrival and service rates. Due to the target delay and dual feedback, the proposed scheme can control delay and allocate bandwidth efficiently while satisfying QoS requirement. The stability of the proposed algorithm is analyzed from a control-theoretic viewpoint, and a simple design guideline is derived based on this analysis. By implementing the algorithm in OPNET simulator, its performance is evaluated in terms of queue regulation, optimal bandwidth allocation, delay controllability, and robustness to traffic characteristics.