Feedback Increases the Capacity of Queues with Bounded Service Times

TL;DR

This paper proves that full feedback always enhances the capacity of queues with bounded service times, extending previous hypotheses and providing a clear structural condition for feedback benefits.

Contribution

It establishes that bounded support of service times guarantees capacity increase with full feedback, generalizing prior results and analyzing a broader feedback framework.

Findings

Full feedback increases queue capacity with bounded service times.

Bounded support of service times is a sufficient condition for feedback benefits.

Analysis of generalized feedback mechanisms extends previous models.

Abstract

In the "Bits Through Queues" paper, it was hypothesized that full feedback always increases the capacity of first-in-first-out queues, except when the service time distribution is memoryless. More recently, a non-explicit sufficient condition under which feedback increases capacity was provided, along with simple examples of service times meeting this condition. While this condition yields examples where feedback is beneficial, it does not offer explicit structural properties of such service times. In this paper, we show that full feedback increases capacity whenever the service time has bounded support. This is achieved by investigating a generalized notion of feedback, with full feedback and weak feedback as particular cases.