Performance, Scalability, and Semantics of Concurrent FIFO Queues

Abstract

Abstract. We introduce the notion of a k-FIFO queue which may dequeue elements out of FIFO order up to a constant k ≥ 0. Retrieving the oldest element from the queue may require up to k + 1 dequeue operations (bounded fairness), which may return elements not younger than the k + 1 oldest elements in the queue (bounded age) or nothing even if there are elements in the queue. A k-FIFO queue is starvation-free for finite k where k + 1 is what we call the worst-case semantical deviation (WCSD) of the queue from a regular FIFO queue. The WCSD bounds the actual semantical deviation (ASD) of a k-FIFO queue from a regular FIFO queue when applied to a given workload. Intuitively, the ASD keeps track of the number of dequeue operations necessary to return oldest elements and the age of dequeued elements. We show that a number of existing concurrent algorithms implement k-FIFO queues whose WCSD are determined by configurable constants independent from any workload. We then introduce so-called Scal queues, which implement k-FIFO queues with generally larger, workloaddependent as well as unbounded WCSD. Since ASD cannot be obtained without prohibitive overhead we have developed a tool that computes lower bounds on ASD from time-stamped runs. Our micro-and macrobenchmarks on a state-ofthe-art 40-core multiprocessor machine show that Scal queues, as an immediate consequence of their weaker WCSD, outperform and outscale existing implementations at the expense of moderately increased lower bounds on ASD.

Quantitative relaxation of concurrent data structures

“…The relaxation framework generalizes previous work on so-called semantical deviation and k-FIFO queues [10,12] which correspond to restricted out-of-order k-FIFO queues here.…”

“…Our relaxed stack implementation is closely related to the very recent efficient lockfree implementation of a relaxed k-FIFO queue [11] (by some of us and a third coauthor), but the change from queue to stack semantics imposes a significant difference as well. The k-FIFO queue [11] is in turn related to implementations of relaxed FIFO queues such as the Random Dequeue and Segment Queue [2] as well as Scal queues [10,12]. Both the Random Dequeue Queue and the Segment Queue implement the restricted out-of-order relaxation.…”

Verifying a Quantitative Relaxation of Linearizability via Refinement

“…Our algorithm can directly handle the implementation model M impl , the standard (not quasi) specification model M spec , and the quasi factor QF , thereby completely avoiding the user's intervention. We have evaluated our new algorithm on a set of models of standard and quasi linearizable concurrent data structures [1,12,17], including queues, stacks, quasi queues, quasi stacks, and quasi priority queues. For each data structure, there can be several variants, each of which has a slightly different implementation.…”

“…Despite the advantages of quasi linearizability and its rising popularity (e.g., [9,12,17]), such relaxed consistency property is difficult to test and verify. Inspit of being an important property of concurrent data structures, there does not yet exist any effective way of formally verifying this relaxed correctness condition.…”

“…Realizing that a more relaxed correctness condition than linearizability suffices in many applications, Afek et al [1] have defined a new notion called quasi linearizability. Quasi linearizability is a quantitative relaxation of linearizability [9,12,17] to allow for more flexibility in how the data structures are implemented. While preserving the basic intuition of linearizability, quasi linearizability relaxes the semantics of the data structures to achieve increased runtime performance.…”