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In cases when system load approaches capacity (>;90% of capacity), scarce radio resources are wasted when a scheduler serves video packets that exceed a required latency, as the decoder will ultimately discard any such packets. In this paper, we introduce a combination of a packet-dropping policy with a modified Greedy-based scheduler to guarantee meeting maximum latency requirements under heavy load conditions, whilst optimising the system goodput for the WiMAX real-time Polling service (rtPS) class. Results of the comparison with existing schedulers show that they all can successfully guarantee the required maximum latency after they have been extended by the same packet- dropping policy, with average latency values well below the required maximum latency. The proposed channel- and delay-aware scheduler results in the lowest number of packet drops. Results also show that mobility does not have significant impact on the system performance across the schedulers compared to the number of users in the cell.