Failure detectors in homonymous distributed systems (with an application to consensus)

Abstract

ABSTRACT

This paper is on homonymous distributed systems where processes are prone to crash failures and have no
initial knowledge of the system membership (‘‘homonymous’’ means that several processes may have the same identifier). New classes of failure detectors suited to these systems are first defined. Among them, the classes HΩ and HΣ are introduced that are the homonymous counterparts of the Classes Ω and Σ, respectively. (Recall that the pair ⟨Ω, Σ⟩ defines the weakest failure detector to solve consensus.) Then, the paper shows how HΩ and HΣ can be implemented in homonymous systems without membership knowledge (under different synchrony requirements). Finally, two algorithms are presented that use these failure detectors to solve consensus in homonymous asynchronous systems where there is no initial knowledge of the membership. One algorithm solves consensus with ⟨HΩ, HΣ⟩, while the other uses only
HΩ, but needs a majority of correct processes.
Observe that the systems with unique identifiers and anonymous systems are extreme cases of
homonymous systems from which follows that all these results also apply to these systems. Interestingly, the new failure detector class HΩ can be implemented with partial synchrony (i.e., all messages sent after some bounded time GST will be received after at most an unknown bounded latency δ), while the analogous class AΩ defined for anonymous systems cannot be implemented (even in synchronous systems). Hence, the paper provides the first consensus algorithm for anonymous systems with this model of partial synchrony and a majority of correct processes.