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In this paper, a packet scheduling algorithm for non-real-time service is considered, with a soft QoS requirements, which allows for degrading the QoS level, e.g., typically the packet delay, whenever necessary, in mobile broadband wireless internet access systems. This is designed to optimally trade off system throughput and delay performance, depending on soft QoS requirements, as opposed to most existing packet scheduling algorithms for non-real-time service, which are simply designed to maximize the system throughput without a delay constraint in any sense. The proposed adaptive exponential scheduling algorithm intentionally introduces additional delay to some users under bad channel conditions, allowing for serving users only under good channel conditions, as long as the resulting QoS degradation is acceptable for non-real-time service users. The results from system-level simulation demonstrate that the system capacity can be significantly increased, over existing algorithms, by as much as 65%, using the adaptive exponential scheduling algorithm, and satisfying the given QoS level requirements.