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This paper presents an adaptive bandwidth allocation (ABA) model for Internet-attached wireless broadband network, WiMAX (IEEE 802.16). The proposed ABA algorithm consists of three allocation phases. First, ABA would reserve the unsolicited bandwidth for constant-bit-rate traffic (UGS). Then, polling bandwidth is allocated for real-time traffic (rtPS) to meet their end-to-end delay constraints and for non-real-time traffic (nrtPS) to meet their minimum throughput requirements. Finally, the remaining bandwidth, if any, is allocated for the best-effort (BE) traffic to avoid any possible starvation. A four-dimension Markov chains is built to analyze the performance of the proposed ABA. In the analytical model, we divide transmission paths over WiMAX links into upload and download phases. In comparison to a previous work, we observe the performance superiority in average delay, average throughput, and average packet drop ratio by varying traffic parameters.