A Time-Optimal Self-Stabilizing Synchronizer Using A Phase Clock

• Published in: IEEE transactions on dependable and secure computing Vol. 4; no. 3; pp. 180 - 190
• Main Authors: Awerbuch, B., Kutten, S., Mansour, Y., Patt-Shamir, B., Varghese, G.
• Format: Journal Article
• Language: English
• Published: Washington IEEE 01.07.2007; IEEE Computer Society
• Subjects: Algorithm design and analysis; Algorithms; Availability; Clocks; Clocks & watches; Communication; Computational modeling; Computer engineering; Computer networks; Computer science; Computer Systems Organization; COMPUTER-COMMUNICATION NETWORKS; Counting circuits; Digital Object Identifier; DISCRETE MATHEMATICS; Distributed algorithms; Distributed computing; Distributed networks; Graph Theory; Mathematical analysis; Mathematical models; Mathematics; Mathematics of Computing; Networks; Peer to peer computing; Pulse counters; Pulse generation; Reliability; Software engineering; Studies; Synchronization; Synchronizers; Synchronous; Theory
• ISSN: 1545-5971; 1941-0018
• DOI: 10.1109/TDSC.2007.1007

A synchronizer with a phase counter (sometimes called asynchronous phase clock) is an asynchronous distributed algorithm, where each node maintains a local "pulse counter" that simulates the global clock in a synchronous network. In this paper, we present a time-optimal self-stabilizing scheme for such a synchronizer, assuming unbounded counters. We give a simple rule by which each node can compute its pulse number as a function of its neighbors' pulse numbers. We also show that some of the popular correction functions for phase clock synchronization are not self-stabilizing in asynchronous networks. Using our rule, the counters stabilize in time bounded by the diameter of the network, without invoking global operations. We argue that the use of unbounded counters can be justified by the availability of memory for counters that are large enough to be practically unbounded and by the existence of reset protocols that can be used to restart the counters in some rare cases where faults will make this necessary.