On Multiple-Access Systems with Queue-Length Dependent Service Quality
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It is commonly observed that higher workload lowers job performance. We model the workload as a queueing process and study the information-theoretic limits of reliable communication through a system with queue-length dependent service quality. The goal is to investigate a multiple-access setting, where transmitters dispatch encoded symbols over a system that is a superposition of continuous-time GI_k/GI/1 queues, and a noisy server, whose service quality depends on the queue-length and processes symbols in order of arrival. We first determine the capacity of single-user queue-length dependent channels and further characterize the best and worst dispatch and service processes for GI/M/1 and M/GI/1 queues, respectively. Then we determine the multiple-access channel capacity using point processes. In particular, 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 the capacity of a single-user M/GI/1 queue-length dependent system. The speed of convergence bound in the number of users is explicitly given. Further, the best and worst server behaviors of M/GI/1 queues from the single-user case are preserved in the sparse multi-access case.
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