Nowadays, multimedia applications are expected to be an important traffic source in wireless networks. Such sources usually have stringent delay requirements and in many cases they should be delivered exactly as they were generated. In this paper, we propose a novel polling based uplink packet scheduling policy for rtPS/ertPS (real-time Polling Service/extended real-time Polling Service) traffic to support real-time applications, with strict delay requirements, such as VBR (Variable Bit Rate) traffic in IEEE 802.16e BWA (Broadband Wireless Access) systems. The proposed transmit-permission policy can derive sufficient conditions such that all the rtPS/ertPS sources satisfy their time constraints to provide deterministic QoS (Quality of Service) guarantees. In addition to theoretical analysis, simulations are conducted to evaluate the performance of the proposed scheme. As it turns out, our design provides a good quality performance in the IEEE 802.16e BWA systems.