The Instability of all Backoff Protocols

2026-02-24

AI Summary

This study addresses a long-standing open problem in distributed systems: whether there exists a backoff protocol that remains stable under any positive packet arrival rate. Focusing on uncoordinated users sharing a common channel with random retransmissions, the authors model the stability of a general backoff sequence $\overline{p} = (p_0, p_1, \ldots)$ under the Kelly Poisson arrival framework. Employing rigorous probabilistic and stochastic process techniques, they provide a formal disproof by demonstrating that no such stable protocol exists. In particular, they establish for the first time the validity of Aldous’s 1987 conjecture, proving that all backoff protocols—including binary exponential backoff—are unstable under any positive arrival rate. This result reveals a fundamental theoretical limitation inherent in the design of multiple-access protocols.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

In this paper we prove Aldous's conjecture from 1987 that there is no backoff protocol that is stable for any positive arrival rate. The setting is a communication channel for coordinating requests for a shared resource. Each user who wants to access the resource makes a request by sending a message to the channel. The users don't have any way to communicate with each other, except by sending messages to the channel. The operation of the channel proceeds in discrete time steps. If exactly one message is sent to the channel during a time step then this message succeeds (and leaves the system). If multiple messages are sent during a time step then these messages collide. Each of the users that sent these messages therefore waits a random amount of time before re-sending. A backoff protocol is a randomised algorithm for determining how long to wait -- the waiting time is a function of how many collisions a message has had. Specifically, a backoff protocol is described by a send sequence $\overline{p} = (p_0,p_1,p_2,\ldots)$. If a message has had $k$ collisions before a time step then, with probability $p_k$, it sends during that time step, whereas with probability $1-p_k$ it is silent (waiting for later). The most famous backoff protocol is binary exponential backoff, where $p_k = 2^{-k}$. Under Kelly's model, in which the number of new messages that arrive in the system at each time step is given by a Poisson random variable with mean $λ$, Aldous proved that binary exponential backoff is unstable for any positive $λ$. He conjectured that the same is true for any backoff protocol. We prove this conjecture.

Problem

• backoff protocol
• stability
• Aldous's conjecture
• collision
• shared communication channel

Innovation

• backoff protocol
• stability
• Aldous's conjecture
• Poisson arrivals
• collision resolution