Self-stabilizing token circulation on asynchronous uniform unidirectional rings

In [2], J. Beauquier, M. Gradinariu and C. Johnen presented a probabilistic self-stabilizing token circulation algorithm for asynchronous uniform unidirectional rings. This paper provides an improvement on this algorithm. It also computes the (message) complexity of the stabilization period of the original algorithm, which is &THgr;(<italic>N</italic><supscrpt>3</supscrpt>), and the improved version, which is &THgr;(<italic>N</italic><supscrpt>2</supscrpt> log <italic>N</italic>), where <italic>N</italic> is the number of processes plus the number of messages in transit. Such algorithms are mostly used for mutual exclusion.