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

We present a randomizedself-stabilizing leaderelection protocol and a randomizedself-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. Therefore, 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 selfstabilization of a randomized distributed system: de nition of a probabilistic space and de nition of the self-stabilization of a randomized protocol. We also propose a new technique of scheduler management through a self-stabilizing protocols composition (cross-over composition). Roughly speaking, we force all computations to have some fairness property under any scheduler, even under an unfair one.

• Type: Journal
• Year: 2007
• Where: DC
• Authors: Joffroy Beauquier, Maria Gradinariu, Colette Johnen
• Keywords: DC 2001, DC 2007, Distributed System, Randomizedself-stabilizing Leaderelection Protocol, Token Circulation Protocol