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 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

A Universal Approach to Queuing With Distortion Control

Abstract—An efficient buffer-management algorithm is developed for queues that handle distortion-tolerant data under finite memory limitations. We avoid overflows and realize significant performance gains through the use of multiresolution source codes. These codes enable us to reduce the fidelity of signal descriptions in a controlled progressive manner. The proposed approach is universal, i.e., it works without knowledge of queue arrival and departure statistics. More strongly, we show that its performance is sample-path optimal, i.e., it achieves an average distortion equal to the best achievable by any algorithm, including those designed with full noncausal knowledge of queue arrival and service times. Index Terms—Buffer management, congestion control, multimedia communications, multiresolution source coding, queuing analysis, successive refinement, transcoding. I

IEEE TRANSACTION ON AUTOMATIC CONTROL 1 A Universal Approach to Queuing with Distortion Control

An efficient buffer-management algorithm is developed for queues that handle distortion-tolerant data under finite memory limitations. We avoid overflows and realize significant performance gains through the use of multiresolution source codes. These codes enable us to reduce the fidelity of signal descriptions in a controlled, progressive, manner. The proposed approach is universal, i.e., it works without knowledge of queue arrival and departure statistics. More strongly, we show that its performance is sample-path optimal, i.e., it achieves an average distortion equal to the best achievable by any algorithm, including those designed with full non-causal knowledge of queue arrival and service times. Index Terms — buffer management, congestion control, multimedia communications, multiresolution source coding, queuing analysis, successive refinement, transcoding. I