Fast and Fair Randomized Wait-Free Locks

TL;DR

This paper introduces a randomized wait-free lock mechanism that guarantees fairness and bounded step complexity, even under arbitrary delays, by leveraging probabilistic success guarantees based on known contention bounds.

Contribution

It proposes a novel randomized lock algorithm with strong fairness and efficiency guarantees, accommodating arbitrary process delays and providing probabilistic success bounds.

Findings

Achieves fairness with probability at least 1/(appa L)

Ensures step complexity of O(appa^2 L^2 T) per attempt

Expected retries to success are bounded by O(appa^3 L^3 T)

Abstract

We present a randomized approach for wait-free locks with strong bounds on time and fairness in a context in which any process can be arbitrarily delayed. Our approach supports a tryLock operation that is given a set of locks, and code to run when all the locks are acquired. A tryLock operation, or attempt, may fail if there is contention on the locks, in which case the code is not run. Given an upper bound $\kappa$ known to the algorithm on the point contention of any lock, and an upper bound $L$ on the number of locks in a tryLock's set, a tryLock will succeed in acquiring its locks and running the code with probability at least $1/(\kappa L)$. It is thus fair. Furthermore, if the maximum step complexity for the code in any lock is $T$, the attempt will take $O(\kappa^2 L^2 T)$ steps, regardless of whether it succeeds or fails. The attempts are independent, thus if the tryLock is repeatedly retried on failure, it will succeed in $O(\kappa^3 L^3 T)$ expected steps, and with high probability in not much more.