Capacity of systems with queue-length dependent service quality

We study the information-theoretic limit of reliable information processing by a server with queue-length dependent quality of service. We define the capacity for such a system as the number of bits reliably processed per unit time, and characterize it in terms of queuing system parameters. We also characterize the distributions of the arrival and service processes that maximize and minimize the capacity of such systems, observing a minimum around the memoryless distribution. The problem is theoretically motivated by an effort to incorporate the notion of reliability in queueing systems, and is applicable in contexts of multimedia communication, crowdsourcing, and stream computing.