Instability of backoff protocols with arbitrary arrival rates

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 (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., 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.