  Consider the problem of a multi-user multiple access channel. While several
multi-user coding techniques exist, in practical scenarios, not all users can
be scheduled simultaneously. Thus, a key problem is which users to schedule in
a given time slot. Under realistic approach for time dependency of the channel,
we adopt a distributed scheduling algorithm in which each user, in the
beginning of each slot, estimates his channel gain and compares it to a
threshold, and if exceeding it the user can transmit. In this work we are
interested in the expected capacity of the system and the delay and quality of
service of the data accumulated at the users under this scheduling scheme.
First we derive the expected capacity under scheduling (distributed and
centralized) for this time dependent environment and show that its scaling law
is $O(\sigma_g\sqrt{2\log K}+\mu_g)$, were $\sigma_g, \mu_g$ are the good
channel parameters (assuming Gaussian capacity approximation, e.g., under MIMO)
and $K$ is the number of users. Then we turn to the performance analysis of
such system while assuming the users are not necessarily fully backlogged, and
focus specifically on the queueing problem and the strong dependence between
the queues which leave no alternative but to turn to approximate models for
this system. We 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 further utilize this finding to
suggest a much simpler approximate model, which accurately describes the system
behavior when the number of queues is large. The system performance as
predicted by the approximate models shows excellent agreement with simulation
results.
