Self-stabilizing ring orientation

Abstract

A self-stabilizing system is a distributed system which can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of an outside intervention. A ring is a distributed system in which all processors are connected in a ring. A ring is oriented if all processors in the ring agree on common right and left directions. A protocol is uniform if all processors use the same program.

In this paper we answer the following question: Does a uniform self stabilizing protocol for ring orientation exist? We begin the presentation by answering this question negatively for deterministic protocols. Then we present a randomized uniform self stabilizing protocol for ring orientation. When the protocol stabilizes all processors agree upon a “right” (privileged) direction. The protocol works for a ring of any size and even tolerates dynamic additions and removals of processors as long as the ring topology is preserved. The number of states of each processor is O(1), and its stabilization time is O(n ²), where n is the number of processors in the system.

Partially supported by Technion VPR Funds - Japan TS Research Fund and B. & G. Greenberg Research Fund (Ottawa).

Partially supported by a Gutwirth fellowship.