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IEEE 802.16e is a broadband wireless access technology that provides high-speed data transmission whilst offering Quality of Service (QoS). To preserve the network QoS, the IEEE 802.16e Medium Access Control (MAC) layer of IEEE 802.16e classifies and categorizes data into different service types according to the requirements of the connections QoS. However, intra-class bandwidth assignment within the same service class in the IEEE 802.16e bandwidth request and granting process is a challenging issue because all the service flows have the same QoS parameters. Thus, QoS parameters could not be considered as factors in resource distribution. This paper proposes a new bandwidth assignment policy for the real-time polling service (rtPS) class for IEEE 802.16e networks, with the aim of resolving the intra-class issue during the bandwidth request and granting process. The proposed solution conforms to the IEEE 802.16 standard and it could easily be integrated into a QoS control module of the MAC common layer at a base station (BS). Extensive simulations were carried out using the Qualnet network simulator on performance metrics like end-to-end delay, jitter and throughput. The results showed that the proposed solution improves the end-to-end delay and jitter for rtPS traffic compared with strict priority + first-come first-served policy, which is typically used by many other researchers. [ABSTRACT FROM AUTHOR]