Capacity of Systems with Queue-Length Dependent Service Quality

TL;DR

This paper investigates the maximum reliable information processing capacity of queue-dependent systems, analyzing how queue dynamics influence system throughput and reliability in various operational scenarios.

Contribution

It introduces an information-theoretic capacity framework for queue-length dependent systems and characterizes optimal and worst-case input distributions in discrete-time models.

Findings

Memoryless arrivals minimize capacity in single-arrival systems.

Burstiness in arrivals reduces system capacity.

Capacity is characterized by queue parameters and process distributions.

Abstract

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.