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The IEEE 802.16 standard is considered to be one of the most promising technologies. Bandwidth reservation is employed to provide quality of service (QoS)-guaranteeing services. A request/grant scheme is defined in the IEEE 802.16 standard. There are two types of bandwidth request (BR) mechanisms, i.e., unicast polling and contention resolution, which are defined in the standard. As specified, connections belonging to scheduling classes of extended real-time polling service, non-real-time polling service, and best effort have options to make BRs via both mechanisms, depending on the scheduling decision made by the base station (BS). However, most research assumes that only one of them is available and do not take both of them into account. A comprehensive study of both mechanisms is critical for the BS to make an appropriate decision for those connections to achieve better system performance. To the best of our knowledge, this is the first attempt to analyze this issue. There are two major contributions presented in this paper. First, a comprehensive study of both BR mechanisms in terms of bandwidth utilization and delay is provided. Additionally, we propose two practical performance objectives: When the expected delay or target bandwidth utilization is given, how does the BS make a scheduling decision such that the performance of the other metric (either delay or bandwidth utilization) is optimized? As our second contribution, we proposed two scheduling algorithms to find the combination of both mechanisms to meet our objectives. The simulation results show that our scheduling algorithms can always help the BS make a scheduling decision to reach better system performance.