[论文解读] Constant RMR Recoverable Mutex under System-wide Crashes

Dhoked, Sahil, Golab, Wojciech+1 more|arXiv (Cornell University)|Jan 1, 2023

Distributed systems and fault tolerance被引用 2

一句话总结

本文提出两种新型的可恢复互斥锁（RME），适用于缓存一致性（CC）和分布式共享内存（DSM）模型下的系统级崩溃场景。仅使用标准原子指令（CAS、FAS），算法在最坏情况下的RMR复杂度为O(1)，每个进程仅需常数空间，同时支持动态创建的线程。关键贡献在于证明了系统级崩溃与单个进程崩溃模型在RMR复杂度上的可证明分离：系统级崩溃可实现常数RMR性能，而单个崩溃模型的下限为Ω(log n / log log n)。

ABSTRACT

Recoverable mutual exclusion (RME) is a fault-tolerant variation of Dijkstra’s classic mutual exclusion (ME) problem that allows processes to fail by crashing as long as they recover eventually. A growing body of literature on this topic, starting with the problem formulation by Golab and Ramaraju (PODC'16), examines the cost of solving the RME problem, which is quantified by counting the expensive shared memory operations called remote memory references (RMRs), under a variety of conditions. Published results show that the RMR complexity of RME algorithms, among other factors, depends crucially on the failure model used: individual process versus system-wide. Recent work by Golab and Hendler (PODC'18) also suggests that explicit failure detection can be helpful in attaining constant RMR solutions to the RME problem in the system-wide failure model. Follow-up work by Jayanti, Jayanti, and Joshi (SPAA'23) shows that such a solution exists even without employing a failure detector, albeit this solution uses a more complex algorithmic approach. In this work, we dive deeper into the study of RMR-optimal RME algorithms for the system-wide failure model, and present contributions along multiple directions. First, we introduce the notion of withdrawing from a lock acquisition rather than resetting the lock. We use this notion to design a withdrawable RME algorithm with optimal O(1) RMR complexity for both cache-coherent (CC) and distributed shared memory (DSM) models in a modular way without using an explicit failure detector. In some sense, our technique marries the simplicity of Golab and Hendler’s algorithm with Jayanti, Jayanti and Joshi’s weaker system model. Second, we present a variation of our algorithm that supports fully dynamic process participation (i.e., both joining and leaving) in the CC model, while maintaining its constant RMR complexity. We show experimentally that our algorithm is substantially faster than Jayanti, Jayanti, and Joshi’s algorithm despite having stronger correctness properties. Finally, we establish an impossibility result for fully dynamic RME algorithms with bounded RMR complexity in the DSM model that are adaptive with respect to space, and provide a wait-free withdraw section.

研究动机与目标

• 设计适用于缓存一致性（CC）和分布式共享内存（DSM）模型的RME锁，以容忍因断电等原因导致所有进程同时崩溃的系统级崩溃情况。
• 在CC和DSM模型中均实现O(1)最坏情况下的RMR复杂度，超越单个崩溃模型中的已知下限。
• 支持任意命名的动态创建线程在运行时加入协议，无需预先分配。
• 确保有界恢复与有界退出特性，实现崩溃后高效且可预测的重启。
• 在最坏情况RMR复杂度方面，证明系统级崩溃模型与单个崩溃模型之间的理论分离。

提出的方法

• 设计一种两阶段RME协议，使用三阶段锁（Lock[0]、Lock[1]、Lock[2]）来管理临界区访问与恢复状态。
• 使用序列号（Seq）与状态追踪（Sp、Sq、CSowner、Stop）协调进程状态，确保恢复期间的互斥性。
• 使用原子操作——CAS与FAS——实现锁的获取与释放，确保在系统级崩溃下仍保持正确性。
• 引入恢复机制：进程在重启后调用ℓ.recoverp()，根据其最后状态返回IN REM或IN CS。
• 使用包含每进程28个程序计数器状态的状态机，追踪进度并确保崩溃后正确恢复。
• 使用三阶段锁抽象（Lock[i].try、Lock[i].exit、Lock[i].recover）协调访问，确保有界恢复与有界退出。

实验结果

研究问题

• RQ1 在CC与DSM模型中，系统级崩溃下是否可实现RME锁的O(1)最坏情况RMR复杂度？
• RQ2 是否可设计一种RME锁，支持无需预分配的动态创建线程，同时保持常数空间与RMR复杂度？
• RQ3 在已知单个崩溃模型下限的前提下，系统级崩溃模型是否可实现优于单个崩溃模型的RMR复杂度？
• RQ4 在系统级崩溃模型中，是否可实现有界恢复与有界退出，同时保持O(1) RMR复杂度？
• RQ5 系统级崩溃的何种结构性特性，使得其在RMR复杂度上与单个崩溃模型实现分离？

主要发现

• 第一个算法在CC模型中实现了O(1)最坏情况下的RMR复杂度，每个进程仅需O(1)空间，并支持动态线程加入。
• 第二个算法将第一个算法扩展至CC与DSM模型，同样在相同空间与动态加入约束下实现了O(1)最坏情况下的RMR复杂度。
• 该工作首次在标准硬件支持（CAS、FAS）下，于CC与DSM模型中均实现了O(1)最坏情况下的RMR复杂度。
• 研究建立了理论分离：系统级崩溃可实现O(1) RMR，而单个崩溃模型的下限为Ω(log n / log log n) RMR。
• 协议确保临界区重入（CSR）、互斥性、无饥饿性、有界恢复与有界退出。
• 通过形式化归纳不变式，验证了所有配置下的正确性，包括崩溃与重启场景。