Wait-free scheduling is unsolvable in asynchronous message-passing systems subject to crash faults. Given the practical importance of this problem, we examine its solvability under partial synchrony relative to the eventually perfect failure detector 3P. Specifically, we present a new oracle-based solution to the dining philosophers problem that is wait-free in the presence of arbitrarily many crash faults. Additionally, our solution satisfies eventual k-bounded waiting, which guarantees that every execution has an infinite suffix where no process can overtake any live hungry neighbor more than k consecutive times. Finally, our algorithm uses only bounded space, bounded-capacity channels, and is also quiescent with respect to crashed processes. Among other practical applications, our results support wait-free distributed daemons for fairly scheduling self-stabilizing protocols in the presence of crash faults.

Failure detectors — oracles that provide information about process crashes — are an important abstraction for crash tolerance in distributed systems. The generality of failure-detector theory, while providing great expressiveness, poses significant challenges in developing a robust hierarchy of failure detectors. We address some of these challenges by proposing (1) a variant of failure detectors called asynchronous failure detectors and (2) an associated modeling framework. Unlike the traditional failure-detector framework, our framework eschews real-time completely. We show that asynchronous failure detectors are sufficiently expressive to include several popular failure detectors including, but not limited to, the canonical Chandra-Toueg failure detectors, Σ and other quorum failure detectors, Ω, anti-Ω, Ωk, and Ψk. Additionally, asynchronous failure detectors satisfy many desirable properties: they are self-implementable, guarantee that stronger asynchronous failure-detectors solve harder problems, and ensure that their outputs encode no information other than the set of crashed processes. We introduce the notion of a failure detector being representative for a problem to capture the idea that some problems encode the same information about process crashes as their weakest failure detectors do. We show that a large class of problems, called bounded problems, do not have representative failure detectors. Finally, we use the asynchronous failure-detector framework to show how sufficiently strong AFDs circumvent the impossibility of consensus in asynchronous systems.

Failure detectors — oracles that provide information about process crashes — are an important abstraction for crash tolerance in distributed systems. Although current failuredetector theoryprovidesgreat generality andexpressiveness, it also poses significant challenges in developing a robust hierarchy of failure detectors. We address some of these challenges by proposing a variant of failure detectors called asynchronous failure detectors and an associated modeling framework. Unlike the traditional failure-detector framework, our framework eschews real time completely. We show that asynchronous failure detectors are sufficiently expressive to include several popular failure detectors. Additionally, we show that asynchronous failure detectors satisfy many desirable properties: they are self-implementable, guarantee that stronger asynchronous failure detectors solve more problems, and ensure that their outputs encode no information other than process crashes. We introduce the notion of a failure detector being representative of a problem to capture the idea that some problems encode the same information about process crashes as their weakest failure detectors do. We show that a large class of problems, called finite problems, donothaverepresentativefailure detectors.