Service time optimal self-stabilizing token circulation protocol on anonymous undirectional rings

We present a self-stabilizing token circulation protocol on unidirectional anonymous rings. This protocol requires no processor identifiers or distinguished processor (i.e. all processors perform the same algorithm). The protocol is randomized and 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 designed to work under unfair distributed schedulers have the same drawback: once stabilized, 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 the token once. The protocol can be used to implement fair distributed mutual exclusion in any ring topology network.