Almost two-state self-stabilizing algorithm for token rings

A self-stabilizing distributed system is a network of processors, which, regardless of its initial global state, will achieve the desired state in a finite number of steps. There are two main performance issues in the design of a self-stabilizing system: the stabilization time and memory requirements (the number of states required by each process). We first show that the probabilistic two-state algorithm for asynchronous, unidirectional token rings stabilizes only in systems where k, the upper bound for the ratio of the speeds of any two processes, exists, but is unknown, and neither the convergence time nor token circulation delay of this algorithm can be bounded. Then we present an almost two-state self-stabilizing algorithm for unidirectional token rings. The processes move synchronously and k is known. The algorithm requires each process in the ring to have two states; one process, called the exceptional process, needs an additional integer variable of size O(n), where n is the number of nodes in the ring; the algorithm stabilizes in O(n) time and achieves an O(kn) token circulation delay.