  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 in a discrete-time setting.
For arrival processes with at most one arrival per time slot, we observed a
minimum around the memoryless distribution. We also studied the case of
multiple arrivals per time slot, and observed that burstiness in arrival has
adverse effects on the system. The problem is theoretically motivated by an
effort to incorporate the notion of reliability in queueing systems, and is
applicable in the contexts of crowdsourcing, multimedia communication, and
stream computing.
