Self-stabilizing mutual exclusion using unfair distributed scheduler

Abstract

A self-stabilizing algorithm, regardless of the initial system state, converges infinite time to a set of states that satisfy a legitimacy predicate without the need for explicit exception handler of backward recovery. Mutual exclusion is fundamental in the area of distributed computing, by serializing the accesses to a common shared resource. All existing probabilistic self-stabilizing mutual exclusion algorithms designed to work under an unfair distributed scheduler suffer from the following common drawback: Once stabilized, there exists no upper bound of time between two executions of the critical section at a given node. We present the first probabilistic self-stabilizing algorithm that guarantees such a bound (O(n/sup 3/), where n is the network size) while working using an unfair distributed scheduler. As the scheduling adversary gets weaker the bound gets better. Our algorithm works in an anonymous unidirectional ring of any size and has a O(n/sup 3/) expected stabilization time.