Failure Detectors Encapsulate Fairness

Abstract

Failure detectors have long been viewed as abstractions for the synchronism present in distributed system models. However, investigations into the exact amount of synchronism encapsulated by a given failure detector have met with limited success. The reason for this is that traditionally, models of partial synchrony are specified with respect to real time, but failure detectors do not encapsulate real time. Instead, we argue that failure detectors encapsulate the fairness in computation and communication. Fairness is a measure of the number of steps executed by one process relative either to the number of steps taken by another process or relative to the duration for which a message is in transit. We argue that failure detectors are substitutable for the fairness properties (rather than real-time properties) of partially synchronous systems. We propose four fairness-based models of partial synchrony and demonstrate that they are, in fact, the 'weakest system models' to implement the canonical failure detectors from the Chandra-Toueg hierarchy. We also propose a set of fairness-based models which encapsulate the G c parametric failure detectors which eventually and permanently suspect crashed processes, and eventually and permanently trust some fixed set of c correct processes.

Asynchronous failure detectors

“…Therefore, if a failure detector D is the weakest to solve a problem P , then a natural question follows: is the synchronism encoded in the outputs of D the minimal synchronism necessary to solve P in a crashprone partially synchronous system? Work to date suggests that the answer is affirmative for some problems [19,22] and negative for others [6]. To our knowledge, there is no characterization of the problems for which the aforementioned question is answered in the affirmative or in the negative.…”

“…Suppose Weakest Failure Detectors and Partial Synchrony. Failure detectors are often viewed as distributed objects that encode information about the temporal constraints on computation and communication necessary for their implementation; the popular perception is that several failure detectors are substitutable for partial synchrony in distributed systems [19,21,20]. Therefore, if a failure detector D is the weakest to solve a problem P , then a natural question follows: is the synchronism encoded in the outputs of D the minimal synchronism necessary to solve P in a crashprone partially synchronous system?…”

Increasing the Power of the Iterated Immediate Snapshot Model with Failure Detectors

“…For each failure detector class taken separately, this approach requires (a) to associate a specific property P with the considered failure detector class, (b) design an ad hoc simulation of the write_snapshot() operation suited to this failure detector class in order to simulate IIS in ARW and (c) design a specific simulation of the output of the failure detector to simulate ARW in IIS. Interestingly, this approach was the first to show that failure detectors are related to fairness and can be considered as schedulers (see also [20]). …”