On the performance of Beauquier and Debas’ self-stabilizing algorithm for mutual exclusion

In [Dij74] Dijkstra introduced the notion of self-stabilizing algorithms and presented an algorithm with three states for the problem of mutual exclusion on a ring of processors. In [BD95] a similar three state algorithm with an upper bound of 5 3 4n2 + O(n) and a lower bound of 1 8n2 − O(n) were presented for its stabilization time. For this later algorithm we prove an upper bound of 1 1 2n2 + O(n), and show a lower bound of n2 − O(n).