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IEEE 802.16 standard defines the air interface specifications for broadband access in wireless metropolitan area networks. Although the medium access control signaling has been well-defined in the IEEE 802.16 specifications, resource management and scheduling, which are crucial components to guarantee quality of service performances, still remain as open issues. In this paper, we propose adaptive queue-aware uplink bandwidth allocation and rate control mechanisms in a subscriber station for polling service in IEEE 802.16 broadband wireless networks. While the bandwidth allocation mechanism adaptively allocates bandwidth for polling service in the presence of higher priority unsolicited grant service, the rate control mechanism dynamically limits the transmission rate for the connections under polling service. Both of these schemes exploit the queue status information to guarantee the desired quality of service (QoS) performance for polling service. We present a queuing analytical framework to analyze the proposed resource management model from which various performance measures for polling service in both steady and transient states can be obtained. We also analyze the performance of best-effort service in the presence of unsolicited grant service and polling service. The proposed analytical model would be useful for performance evaluation and engineering of radio resource management alternatives in a subscriber station so that the desired quality of service performances for polling service can be achieved. Analytical results are validated by simulations and typical numerical results are presented.