Stability of a Random Multiple Access Channel with "Success-Failure" Feedback

TL;DR

This paper analyzes a decentralized multiple access system with a unique binary feedback, demonstrating that for rates below 1/e, a randomized protocol can stabilize the system, extending understanding of feedback's role in stability.

Contribution

It introduces a new stability result for a system with binary feedback, showing stabilization with a doubly randomized protocol for rates below 1/e.

Findings

Stability achieved for input rates < 1/e with a randomized protocol.

Binary feedback system can be stabilized similarly to ternary feedback systems.

Discussion of related problems and formulation of hypotheses.

Abstract

We consider a model of a decentralized multiple access system with a non-standard binary feedback where the empty and collision situations cannot be distinguished. We show that, like in the case of a ternary feedback, for any input rate \lambda < 1/e, there exists a "doubly randomized" adaptive transmission protocol which stabilizes the behavior of the system. We discuss also a number of related problems and formulate some hypotheses.