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In this paper, we address the performance of downlink packet delivery under differentiated rate scheduling, where the base station supports different arrival rates to different subsets of users. To reduce the uplink feedback load, the user whose downlink channel gain is larger than a threshold is allowed to send its channel-state information with an access probability through a spread-spectrum-based contention channel. Under this framework, we show that the differentiated rates can be supported among the subsets by adjusting their access probabilities according to their arrival rates. Using large deviation techniques (LDTs), we show that the throughput can be maintained if the performance degradations in the delay and the queue length are allowed for the low-arrival-rate user subset. However, the queue-length performance degradation of the low-rate subset is less severe compared with that of the delay performance. In addition, our simulation results show that the delay performance estimation from LDT analysis is valid even for a delay that is not too large, although it is developed under the assumption of large delay asymptote.