Why Self-Stabilizing Systems Break: The Missing Theory of Composition
In Search of a Compositional Theory of Self-Stabilization
A frustrated search for a compositional theory of self-stabilization leads to a 2017 control theory paper on parametric assume-guarantee contracts. The author tries to adapt its small gain theorem to a retry storm model but finds it ignores memory—backlog from previous rounds—and misreads stability. A linear analysis reveals the true per-round multiplier is 1.19, above one, so disturbances grow rather than decay.
The small gain theorem reads only the coupling and ignores the memory. When we take the memory into account, the real per-round multiplier becomes 1.19, which is above one, so almost any disturbance grows rather than decays.