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When a spread spectrum contention-based feedback channel is employed, it has been shown that most of the multiuser diversity gain can be maintained without any delay constraint. To address the delay in sending packets, we investigate how a spread spectrum contention-based feedback channel affects the delay and throughput performance. Using large deviations techniques, we show that most of the multiuser diversity gain can be maintained while satisfying a delay constraint in which the probability that the maximum delay of any bits in any usersiquest queues is less than a specified value. In addition, we show that the spectral efficiency improves as the number of users increases while maintaining a fixed normalized maximum delay (which is defined as the ratio of the maximum delay and the number of users) as the number of users increases.