Leader Election in Anonymous Rings: Franklin Goes Probabilistic

We present a probabilistic leader election algorithm for anonymous, bidirectional, asynchronous rings. It is based on an algorithm from Franklin, augmented with random identity selection, hop counters to detect identity clashes, and round numbers modulo 2. As a result, the algorithm is finite-state, so that various model checking techniques can be employed to verify its correctness, that is, eventually a unique leader is elected with probability one. We also sketch a formal correctness proof of the algorithm for rings with arbitrary size

Self-Stabilization in the Distributed Systems of Finite State Machines

The notion of self-stabilization was first proposed by Dijkstra in 1974 in his classic paper. The paper defines a system as self-stabilizing if, starting at any, possibly illegitimate, state the system can automatically adjust itself to eventually converge to a legitimate state in finite amount of time and once in a legitimate state it will remain so unless it incurs a subsequent transient fault. Dijkstra limited his attention to a ring of finite-state machines and provided its solution for self-stabilization. In the years following his introduction, very few papers were published in this area. Once his proposal was recognized as a milestone in work on fault tolerance, the notion propagated among the researchers rapidly and many researchers in the distributed systems diverted their attention to it. The investigation and use of self-stabilization as an approach to fault-tolerant behavior under a model of transient failures for distributed systems is now undergoing a renaissance. A good number of works pertaining to self-stabilization in the distributed systems were proposed in the yesteryears most of which are very recent. This report surveys all previous works available in the literature of self-stabilizing systems

Self-Stabilizing Algorithms for Synchronous Unidirectional Rings (Extended Summary)

In this work we investigate the notion of built-in faulttolerant (i.e. self-stabilizing) computations on a synchronous uniform unidirectional ring network. Our main result is a protocol-compiler that transforms any selfstabilizing protocol P for a (synchronous or asynchronous) bidirectional ring to a self-stabilizing protocol P 0 which runs on the synchronous unidirectional ring. P 0 requires O(SLE (n)+S(n)) space and has expected stabilization time O(TLE (n) + n 2 + nT (n)), where S(n) (T (n)) is the space (time) performance of P and SLE (n) (TLE (n)) is the space (time) performance of a self-stabilizing leader-election protocol on a bidirectional ring. As subroutines, we also solve the problems of leader election and round-robin token management in our setting. 1 Introduction The design of efficient distributed algorithms for unidirectional networks has proven to be a difficult task. There are only a few known protocols, e.g., [15, 31, 2, 25, 16, 28] and most of them do no..

Abstract Chapter 1 Self-Stabilizing Algorithms for Synchronous Unidirectional Rings

In this work we investigate the notion of built-in faulttolerant (i.e. self-stabilizing) computations on a synchronous uniform unidirectional ring network. Our main result is a protocol-compiler that transforms any selfstabilizing protocol P for a (synchronous or asynchronous) bidirectional ring to a self-stabilizing protocol P 0 which runs on the synchronous unidirectional ring. P 0 requires O(SLE (n)+S(n)) space and has expected stabilization time O(TLE (n) +n 2 +nT (n)), where S(n) (T(n)) is the space (time) performance of P and SLE (n) (TLE (n)) is the space (time) performance of a self-stabilizing leader-election protocol on a bidirectional ring. As subroutines, we also solve the problems of leader election and round-robin token management in our setting.