On the performance of Dijkstra's third self-stabilizing algorithm for mutual exclusion

In [7] Dijkstra introduced the notion of self-stabilizing algorithms, and presented three such algorithms for the problem of mutual exclusion on a ring of processors. The third algorithm is the most interesting of these three, but is rather non intuitive. In [8] a proof of its correctness was presented, but the question of determining its worst case complexity - that is, providing an upper bound on the number of moves of this algorithm until it stabilizes - remained open. In this paper we solve this question, and prove an upper bound of O(n(2)) (n being the size of the ring) for this algorithm's complexity. This complexity applies to a centralized as well as to a distributed scheduler.