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 $5\frac{3}{4}n^2+O(n)$ and a lower bound of $\frac{1}{8}n^2-O(n)$ were presented for its stabilization time. For this later algorithm we prove an upper bound of $1\frac{1}{2}n^2 + O(n)$, and show a lower bound of n2i¾? O(n).