Randomized self-stabilizing and space optimal leader election under arbitrary scheduler on rings

Abstract

We present a randomized self-stabilizing leader election protocol and a randomized self-stabilizing token circulation protocol under an arbitrary scheduler on anonymous and unidirectional rings of any size. These protocols are space optimal. We also give a formal and complete proof of these protocols. To this end, we develop a complete model for probabilistic self-stabilizing distributed systems which clearly separates the non deterministic behavior of the scheduler from the randomized behavior of the protocol. This framework includes all the necessary tools for proving the self- stabilization of a randomized distributed system: definition of a probabilistic space and definition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocol composition (cross-over composition). Roughly speaking, we force all computations to have a fairness property under any scheduler, even under an unfair one.