An Adaptive Approach to Recoverable Mutual Exclusion

Abstract

Mutual exclusion is one of the most commonly used techniques to handle contention in concurrent systems. Traditionally, mutual exclusion algorithms have been designed under the assumption that a process does not fail while acquiring/releasing a lock or while executing its critical section. However, failures do occur in real life, potentially leaving the lock in an inconsistent state. This gives rise to the problem of recoverable mutual exclusion (RME) that involves designing a mutual exclusion (ME) algorithm that can tolerate failures, while maintaining safety and liveness properties.In this work, we present a framework that transforms any algorithm that solves the RME problem into an algorithm that can also simultaneously adapt to (a) the number of processes competing for the lock, as well as (b) the number of failures that have occurred in the recent past, while maintaining the correctness and performance properties of the underlying RME algorithm. Additionally, the algorithm constructed as a result of this transformation adds certain desirable properties like fairness (a variation of FCFS) and bounded recovery.We further extend our framework by presenting a novel memory reclamation algorithm to bound the worst-case space complexity of the RME algorithm. The memory reclamation techniques maintain the fairness, performance and correctness properties of our transformation. The technique is general enough that is may also be employed to bound the space of other RME algorithms.One of the important measures of performance of any ME algorithm, including an RME algorithm, is the number of remote memory references (RMRs) made by a process-for acquiring and releasing a lock as well as recovering the lock structure after a failure.Assume that the worst-case RMR complexity of a critical section request in the underlying RME algorithm is ( ), where denotes the number of processes in the system. Then, our framework yields an RME algorithm for which the worst-case RMR complexity of a critical section request is given by O (min{ , √ + 1, ( ) }), where denotes the point contention of the request and denotes the number of failures in the recent past of the request.In addition to read and write instructions, our algorithm uses compare-and-swap (CAS) and fetch-and-store (FAS) hardware instructions, both of which are commonly available in most modern processors.

Tight Lower Bound for the RMR Complexity of Recoverable Mutual Exclusion

“…In particular, we show that any -process RME algorithm using only atomic read, write, fetch-and-store, fetch-andincrement, and compare-and-swap operations, has an RMR complexity of Ω(log /log log ) on the CC and DSM model. This lower bound covers all realistic synchronization primitives that have been used in RME algorithms and matches the best upper bounds of algorithms employing swap objects (e.g., [6,7,11]). Algorithms with better RMR complexity than that have only been obtained by either (i) assuming that all failures are systemwide [8], (ii) employing fetch-and-add objects of size (log ) (1) [13], or (iii) using artificially defined synchronization primitives that are not available in actual systems [7,10].…”

“…In particular, we show that any -process RME algorithm using only atomic read, write, fetch-and-store, fetch-andincrement, and compare-and-swap operations, has an RMR complexity of Ω(log /log log ) on the CC and DSM model. This lower bound covers all realistic synchronization primitives that have been used in RME algorithms and matches the best upper bounds of algorithms employing swap objects (e.g., [6,7,11]).…”

“…RME can be solved in constant RMRs with fetch-and-add primitives of size Ω (1) bits [6], so obviously our lower bound cannot be extended to cover such primitives. But it remains an open problem, whether fetch-and-add operations can help, under the standard assumption that objects can store only (log )-bits.…”

“…Recently, Dhoked and Mittal [6] gave an algorithm that adapts to the number of process crashes (in the "recent" past), . In particular, they achieve an RMR complexity of (min{ √…”

Memory Reclamation for Recoverable Mutual Exclusion

“…The RME problem in the current form was formally defined a few years ago by Golab and Ramaraju in [12]. Several algorithms have been proposed to solve this problem [7,10,13,16,17]. However, in order to ensure that the problem of RME is also of practical interest, and not just a theoretical one, memory reclamation poses as a major obstacle in several RME algorithms.…”