Safe Register Token Transfer in a Ring

TL;DR

This paper presents protocols for implementing a self-stabilizing token ring using safe registers that may produce undefined values during concurrent access, enabling reliable token transfer with minimal register use.

Contribution

It introduces quasi-atomic communication protocols constructed from safe registers, facilitating self-stabilizing token rings with reduced register complexity.

Findings

Protocols for quasi-atomic communication from safe registers.

Implementation of self-stabilizing token ring using these protocols.

Reduction of register use to O(log N) between neighbors.

Abstract

A token ring is an arrangement of N processors that take turns engaging in an activity which must be controlled. A token confers the right to engage in the controlled activity. Processors communicate with neighbors in the ring to obtain and release a token. The communication mechanism investigated in this paper is the safe register abstraction, which may arbitrarily corrupt a value that a processor reads when the operation reading a register is concurrent with an write operation on that register by a neighboring processor. The main results are simple protocols for quasi-atomic communication, constructed from safe registers. A quasi-atomic register behaves atomically except that a special undefined value may be returned in the case of concurrent read and write operations. Under certain conditions that constrain the number of writes and registers, quasi-atomic protocols are adequate substitutes for atomic protocols. The paper demonstrates how quasi-atomic protocols can be used to implement a self-stabilizing token ring, either by using two safe registers between neighboring processors or by using O(lg N) safe registers between neighbors, which lowers read complexity.