Exploiting Synchronicity for Immediate Feedback in Self-Stabilizing PIF Algorithms

A distributed algorithm, run by distributed processes, satisfies mutual exclusion if at most one process is granted a privilege to access the critical section in each execution step (safety), and each process is privileged infinitely often in each execution (fairness). The design of mutual exclusion algorithms is, in particular, impacted to satisfy the fairness property. In this work, we focus on a class of synchronous systems, where processes rarely request a privilege, that the fairness property is satisfied anyway if the process selection is fast enough. We also consider that systems of this class have to satisfy self-stabilization, which ensures that a system eventually achieves its desired behavior, and does not leave it voluntarily, regardless of the system´s initial behavior. We present a self-stabilizing synchronous Propagation of Information with Feedback (PIF) algorithm for trees. The algorithm exploits the synchronous environment to provide immediate feedback of requesting processes, which in turn guarantees fast selection of unique processes to be granted privileges.