Service Time Optimal Self-Stabilizing Token Circulation Protocol on Anonymous Unidrectional Rings

We present a self-stabilizing token circulation protocol on unidirectional anonymous rings. This protocol does not required processor identifiers, no distinguished processor (i.e. all processors perform the same algorithm). The protocol is a randomized self-stabilizing, meaning that starting from an arbitrary configuration (in response to an arbitrary perturbation modifying the memory state), it reaches (with probability 1) a legitimate configuration (i.e. a configuration with only one token in the network). All previous randomized self-stabilizing token circulation protocols design to work under unfair distributed schedulers have the same drawback. Once stabilized, the service time is slow (in the best case, it is bounded by 2N where N is the ring size). Once stabilized, our protocol provides an optimal service: after N computation steps, each processor has obtained one time the token. The protocol can be used to implement a fair distributed mutual exclusion in any ring topology network.