Although the medium access control (MAC) signaling has been well-defined in the IEEE 802.16 specifications, resource management and scheduling, which are crucial components to guarantee QoS performances, still remain as open issues. In this paper, we propose a scheme for queue-aware uplink bandwidth allocation in a subscriber station (SS) for polling services (real-time and non-real-time) in IEEE 802.16 broadband wireless networks. The proposed scheme adaptively allocates bandwidth in order to control queue length at a target level so that the requirements for delay and PDU dropping probability can be met. We present a queueing analytical framework to analyze the proposed scheme from which various QoS performance measures can be obtained. The proposed analytical model is validated by simulations and typical numerical results are presented