Probabilistic self-stabilization
Information Processing Letters
The Theory of Weak Stabilization
WSS '01 Proceedings of the 5th International Workshop on Self-Stabilizing Systems
Weak vs. Self vs. Probabilistic Stabilization
ICDCS '08 Proceedings of the 2008 The 28th International Conference on Distributed Computing Systems
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Motivation. Roughly speaking, a weakly stabilizing system $\cal S$ executed under a probabilistic scheduler ρ is probabilistically self-stabilizing, in the sense that any execution eventually reaches a legitimate execution with probability 1 [1-3]. Here ρ is a set of Markov chains, one of which is selected for $\cal S$ by an adversary to generate as its evolution an infinite activation sequence to execute $\cal S$. The performance measure is the worst case expected convergence time $\tau_{{\cal S},M}$ when $\cal S$ is executed under a Markov chain M∈ρ. Let $\tau_{{\cal S},\rho} = \sup_{M \in \rho} \tau_{{\cal S},M}$. Then $\cal S$ can be "comfortably" used as a probabilistically self-stabilizing system under ρ only if $\tau_{{\cal S},\rho} ρ such that $\tau_{{\cal S},\rho} = \infty$, despite that $\tau_{{\cal S},M} M∈ρ. Somewhat interesting is that, for some $\cal S$, there is a randomised version ${\cal S}^*$ of $\cal S$ such that $\tau_{{\cal S}^*,\rho}