  We consider transmission of packets over queue-length sensitive unreliable
links, where packets are randomly corrupted through a noisy channel whose
transition probabilities are modulated by the queue-length. The goal is to
characterize the capacity of this channel. We particularly consider
multiple-access systems, where transmitters dispatch encoded symbols over a
system that is a superposition of continuous-time $GI_k/GI/1$ queues. A server
receives and processes symbols in order of arrivals with queue-length dependent
noise.
  We first determine the capacity of single-user queue-length dependent
channels. Further, we characterize the best and worst dispatch processes for
$GI/M/1$ queues and the best and worst service processes for $M/GI/1$ queues.
Then, the multiple-access channel capacity is obtained using point processes.
When the number of transmitters is large and each arrival process is sparse,
the superposition of arrivals approaches a Poisson point process. In
characterizing the Poisson approximation, we show that the capacity of the
multiple-access system converges to that of a single-user $M/GI/1$ queue-length
dependent system, and an upper bound on the convergence rate is obtained. This
implies that the best and worst server behaviors of single-user $M/GI/1$ queues
are preserved in the sparse multiple-access case.
