On Multiuser Systems with Queue-Length Dependent Service Quality

Consider the information-theoretic limits of reliable communication in a multiuser setting of transmission through a system with queue-length dependent service quality. Multiple transmitters dispatch encoded symbols using renewal processes over a system that is a superposition of GI-{k}/GI/1 queues, and a noisy server processes symbols in order of arrival with error probability depending on the queue-length. First, the information capacities of the single-user and multiuser continuous-time queue-length dependent system are found. When the number of transmitters is large and each is sparse, the superposition of arrivals approaches a Poisson point process. In characterizing the Poisson approximation, we show that the individual and sum capacities of the multiuser system converges to the capacity of a single-user M/GI/1 queue-length dependent system. The speed of convergence in the number of users is explicitly given. Further, the best and worst server behaviors of M / G I /1 queues from the single-user case are preserved in the multiuser case.