Aldous's instability conjecture for backoff protocols

Consider a multiple-access channel in discrete time with Poisson arrivals of mean birth rate $\lambda>0$. A backoff protocol is specified by a send sequence $\overline{p}=(p_0,p_1,p_2,\ldots)$, where a message that has experienced $k$ collisions sends at each subsequent step with probability $p_k$ and remains silent with probability $1-p_k$. Aldous's conjecture. No backoff process is stable for any birth rate $\lambda>0$. This conjecture generalizes Aldous's result that binary exponential backoff is unstable for every positive birth rate. The paper proves the conjecture, so the claim is solved.