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Although the scheduling problem of the uplink transmission in the IEEE 802.16 broadband wireless access network is extensively discussed, most of the results are limited to the quality of service (QoS) upon throughput and delay requirement. But as in practice only limited wireless resources are made available, a fairness-based scheduling upon each connection's QoS provides better outcomes. In this study, the authors propose a new fair uplink scheduling for real-time polling service and non-real-time polling service with the proportional sharing of excess bandwidth of the network. To implement the proposed fair scheduling that satisfies the delay requirement and full bandwidth utilisation, the authors introduce the rate control algorithm. With the proposed scheduling, we guarantee the fairness, delay requirement and full bandwidth utilisation which are not fully achieved in the existing results.