- Consider a multiple access channel with a large number of users. In most practical scenarios, due to decoding complexity, users are not scheduled together, and only one user may transmit at any given time. In this work, we analyze the delay and QoS of such systems under a specific, opportunistic and distributed scheduling algorithm, in which each user, at the beginning of each slot, estimates its channel gain and transmits only if it is greater than a given threshold. Specifically, we analyze the performance while assuming the users are not necessarily fully backlogged, focusing on the queueing problem and, especially, on the strong dependence between the queues. We first adopt the celebrated model of Ephremides and Zhu to give new results on the convergence of the probability of collision to its average value (as the number of users grows), and hence for the ensuing system performance metrics, such as throughput and delay. We then utilize this finding to suggest a much simpler approximate model, which accurately describes the system behaviour when the number of users is large. The system performance as predicted by the approximate models shows excellent agreement with simulation results.