[Paper Review] Self-Stabilizing Paxos

Peva Blanchard, Shlomi Dolev+2 more|arXiv (Cornell University)|May 18, 2013

Distributed systems and fault tolerance15 references3 citations

TL;DR

This paper presents the first self-stabilizing Paxos algorithm for asynchronous message-passing systems, enabling automatic recovery from arbitrary transient faults without requiring a predefined initial configuration. By integrating a self-stabilizing bounded time-stamp and resilient message handling, the scheme ensures eventual consensus and state machine agreement, achieving practical stabilization where safety and liveness are regained after any transient fault.

ABSTRACT

We present the first self-stabilizing consensus and replicated state machine for asynchronous message passing systems. The scheme does not require that all participants make a certain number of steps prior to reaching a practically infinite execution where the replicated state machine exhibits the desired behavior. In other words, the system reaches a configuration from which it operates according to the specified requirements of the replicated state-machine, for a long enough execution regarding all practical considerations.

Motivation & Objective

• To address the lack of self-stabilization in classical Paxos, which cannot recover from arbitrary transient faults like corrupted time-stamps.
• To design a self-stabilizing consensus and replicated state machine for asynchronous message-passing systems, where no initial configuration consistency is assumed.
• To ensure that the system converges to correct behavior from any arbitrary configuration, guaranteeing eventual safety and liveness after transient faults.
• To overcome limitations of prior self-stabilizing shared-memory consensus by adapting it to message-passing with arbitrary message sets and label values.
• To provide a practical stabilization model where the system reaches a correct, stable configuration for all practical purposes, even after transient faults.

Proposed method

• Integrates a self-stabilizing bounded time-stamp mechanism that ensures consistent ordering of proposals despite arbitrary initial values.
• Uses a two-phase protocol (Phase 1: prepare, Phase 2: accept) with message tagging and state tracking to ensure safety and liveness.
• Employs a dynamic state update mechanism using functions ν^s and ν^t to handle command history and proposal ordering based on received messages.
• Implements a truncation routine to align command sequences with current step values, ensuring consistency across replicas.
• Uses a preemptive decision mechanism where proposers re-enter Phase 1 if their proposal is superseded or if state changes are detected.
• Relies on message filtering and condition checks (C+ and C−) to determine whether to accept or reject incoming proposals based on consistency and ordering.

Experimental results

Research questions

• RQ1 Can a self-stabilizing consensus algorithm be designed for asynchronous message-passing systems, where no initial configuration is assumed?
• RQ2 How can a self-stabilizing bounded time-stamp be composed across multiple proposers to ensure eventual strict ordering of events?
• RQ3 What mechanisms allow the system to recover from arbitrary transient faults, such as corrupted time-stamp values or message inconsistencies?
• RQ4 How can a replicated state machine be implemented in a self-stabilizing manner under message-passing semantics with no initial consistency?
• RQ5 What defines 'practical stabilization' in this context, and how does it differ from classical self-stabilization in real-world systems?

Key findings

• The proposed algorithm achieves practical stabilization, meaning the system reaches a correct, stable configuration from any arbitrary initial state, ensuring safety and liveness for all practical purposes.
• The system recovers from transient faults such as corrupted time-stamp values or message inconsistencies without requiring a restart or predefined initial state.
• The integration of a self-stabilizing bounded time-stamp enables correct ordering of proposals even when initial labels are arbitrary or inconsistent.
• The algorithm ensures that all correct replicas eventually agree on the same sequence of commands, maintaining the safety and liveness properties of Paxos.
• The scheme supports generalized Paxos with dynamic command sequences and handles message reordering and loss through state reconciliation and truncation.
• The correctness is proven under the assumption that transient faults cease after a finite time, guaranteeing eventual convergence to correct behavior.