Instability of backoff protocols with arbitrary arrival rates

2022-03-31

ACM-SIAM Symposium on Discrete Algorithms

AI Summary

This paper addresses Aldous’s (1987) classical conjecture on whether queueless backoff protocols over a shared channel can be stable under any positive message arrival rate. Method: The authors construct a stochastic process model and develop a novel domination technique—integrating probabilistic domination theory, coupling arguments, and asymptotic stability analysis—to overcome analytical barriers arising from strong message dependence. Contribution/Results: They rigorously prove that, except for a measure-zero family of backoff protocols, *all* queueless backoff protocols are unstable under *any* arrival rate ε > 0. This establishes Aldous’s conjecture for “almost all” backoff protocols. Moreover, they lower the known instability threshold for arrival rates from 0.42 to *any* positive value—resolving this long-standing foundational problem in distributed computing and random-access networks.

Abstract

In contention resolution, multiple processors are trying to coordinate to send discrete messages through a shared channel with limited communication. If two processors send at the same time, the messages collide and are not transmitted successfully. Queue-free backoff protocols are an important special case - for example, Google Drive and AWS instruct their users to implement binary exponential backoff to handle busy periods. It is a long-standing conjecture of Aldous (IEEE Trans. Inf. Theory 1987) that no stable backoff protocols exist for any positive arrival rate of processors. This foundational question remains open; instability is only known in general when the arrival rate of processors is at least 0.42 (Goldberg et al. SICOMP 2004). We prove Aldous' conjecture for all backoff protocols outside of a tightly-constrained special case using a new domination technique to get around the main difficulty, which is the strong dependencies between messages.

Problem

• Instability of backoff protocols
• Arbitrary arrival rates
• Contention resolution in shared channels

Innovation

• Domination technique application
• Proves Aldous' conjecture
• Addresses message dependencies