The Weakest Failure Detector for Solving Wait-Free, Eventually Bounded-Fair Dining Philosophers

This dissertation explores the necessary and sufficient conditions to solve a variant of the dining philosophers problem. This dining variant is defined by three properties: wait-freedom, eventual weak exclusion, and eventual bounded fairness. Wait-freedom guarantees that every correct hungry process eventually enters its critical section, regardless of process crashes. Eventual weak exclusion guarantees that every execution has an infinite suffix during which no two live neighbors execute overlapping critical sections. Eventual bounded fairness guarantees that there exists a fairness bound k such that every execution has an infinite suffix during which no correct hungry process is overtaken more than k times by any neighbor. This dining variant (WF-EBF dining for short) is important for synchronization tasks where eventual safety (i.e., eventual weak exclusion) is sufficient for correctness (e.g., duty-cycle scheduling, self-stabilizing daemons, and contention managers). Unfortunately, it is known that wait-free dining is unsolvable in asynchronous message-passing systems subject to crash faults. To circumvent this impossibility result, it is necessary to assume the existence of bounds on timing properties, such as relative process speeds and message delivery time. As such, it is of interest to characterize the necessary and sufficient timing assumptions to solve WF-EBF dining. We focus on implicit timing assumptions, which can be encapsulated by failure detectors. Failure detectors can be viewed as distributed oracles that can be queried for potentially unreliable information about crash faults. The weakest detector D for WF-EBF dining means that D is both necessary and sufficient. Necessity means that every failure detector that solves WF-EBF dining is at least as strong as D. Sufficiency means that there exists at least one algorithm that solves WF-EBF dining using D. As such, our research goal is to characterize the weakest failure detector to solve WF-EBF dining. We prove that the eventually perfect failure detector 3P is the weakest failure detector for solving WF-EBF dining. 3P eventually suspects crashed processes permanently, but may make mistakes by wrongfully suspecting correct processes finitely many times during any execution. As such, 3P eventually stops suspecting correct processes

Fairness Properties of the Trusting Failure Detector

In 1985 it was shown by Fischer et al. that consensus, a fundamental problem in distributed computing, was impossible in asynchronous distributed systems in the presence of even just one process failure. This result prompted a search for alternative system models that were capable of solving such problems and culminated in the development of two helpful constructs: partially synchronous system models and failure detectors. Partially synchronous system models seek to solve the problem of identifying process crashes by constraining the real-time behavior of the underlying system. In the resulting models, crashed processes can be detected indirectly through the use of timeouts. Failure detectors, on the other hand, address process crashes by directly providing (potentially inaccurate) information on failures. As a result, failure detectors were viewed as abstractions of real-time information. Pike et al. proposed a different perspective on failure detectors; as abstracting fairness properties. Fairness in a system imposes bounds on the relative frequencies of communication and execution between processes in a system, and it was shown that four frequently-used failure detectors from the Chandra-Toueg hierarchy (P, ♢P, S, ♢S) encapsulate these fairness properties. This discovery suggests that failure detectors may be better understood as abstractions of fairness rather than real-time properties as well as demonstrates the possibility to communicate results between systems augmented with failure detectors and partially synchronous system models. In this thesis, we will be discussing an extension of the Pike et al. result to the trusting failure detector. The trusting failure detector is the weakest failure detector to implement the problem of fault-tolerant mutual exclusion: a fundamental primitive for distributed computing

The weakest failure detector for wait-free dining under eventual weak exclusion

Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect per-formance. Previous work showed that the eventually perfect failure detector (3P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that 3P is also necessary, and thus 3P is the weakest oracle to solve this problem. Our reduction also establishes that any such din-ing solution can be made eventually fair. Finally, the reduc-tion itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T) is necessary (but not sufficient) to solve the problem o

A Prescription for Partial Synchrony

Algorithms in message-passing distributed systems often require partial synchrony to tolerate crash failures. Informally, partial synchrony refers to systems where timing bounds on communication and computation may exist, but the knowledge of such bounds is limited. Traditionally, the foundation for the theory of partial synchrony has been real time: a time base measured by counting events external to the system, like the vibrations of Cesium atoms or piezoelectric crystals. Unfortunately, algorithms that are correct relative to many real-time based models of partial synchrony may not behave correctly in empirical distributed systems. For example, a set of popular theoretical models, which we call M_*, assume (eventual) upper bounds on message delay and relative process speeds, regardless of message size and absolute process speeds. Empirical systems with bounded channel capacity and bandwidth cannot realize such assumptions either natively, or through algorithmic constructions. Consequently, empirical deployment of the many M_*-based algorithms risks anomalous behavior. As a result, we argue that real time is the wrong basis for such a theory. Instead, the appropriate foundation for partial synchrony is fairness: a time base measured by counting events internal to the system, like the steps executed by the processes. By way of example, we redefine M_* models with fairness-based bounds and provide algorithmic techniques to implement fairness-based M_* models on a significant subset of the empirical systems. The proposed techniques use failure detectors — system services that provide hints about process crashes — as intermediaries that preserve the fairness constraints native to empirical systems. In effect, algorithms that are correct in M_* models are now proved correct in such empirical systems as well. Demonstrating our results requires solving three open problems. (1) We propose the first unified mathematical framework based on Timed I/O Automata to specify empirical systems, partially synchronous systems, and algorithms that execute within the aforementioned systems. (2) We show that crash tolerance capabilities of popular distributed systems can be denominated exclusively through fairness constraints. (3) We specify exemplar system models that identify the set of weakest system models to implement popular failure detectors

Failure detectors encapsulate fairness

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[subscript c] parametric failure detectors which eventually and permanently suspect crashed processes, and eventually and permanently trust some fixed set of c correct processes.National Science Foundation (U.S.) (Grant CCF-0964696)National Science Foundation (U.S.) (Grant CCF-0937274)Texas Higher Education Coordinating Board (grant NHARP 000512-0130-2007)National Science Foundation (U.S.) (NSF Science and Technology Center, grant agreement CCF-0939370

The weakest failure detector for wait-free dining under eventual weak exclusion

ABSTRACT Dining philosophers is a classic scheduling problem for local mutual exclusion on arbitrary conflict graphs. We establish necessary conditions to solve wait-free dining under eventual weak exclusion in message-passing systems with crash faults. Wait-free dining ensures that every correct hungry process eventually eats. Eventual weak exclusion permits finitely many scheduling mistakes, but eventually no live neighbors eat simultaneously; this exclusion criterion models scenarios where scheduling mistakes are recoverable or only affect performance. Previous work showed that the eventually perfect failure detector (3P) is sufficient to solve wait-free dining under eventual weak exclusion; we prove that 3P is also necessary, and thus 3P is the weakest oracle to solve this problem. Our reduction also establishes that any such dining solution can be made eventually fair. Finally, the reduction itself may be of more general interest; when applied to wait-free perpetual weak exclusion, our reduction produces an alternative proof that the more powerful trusting oracle (T ) is necessary (but not sufficient) to solve the problem of Fault-Tolerant Mutual Exclusion (FTME)

A Prescription for Partial Synchrony

Algorithms in message-passing distributed systems often require partial synchrony to tolerate crash failures. Informally, partial synchrony refers to systems where timing bounds on communication and computation may exist, but the knowledge of such bounds is limited. Traditionally, the foundation for the theory of partial synchrony has been real time: a time base measured by counting events external to the system, like the vibrations of Cesium atoms or piezoelectric crystals. Unfortunately, algorithms that are correct relative to many real-time based models of partial synchrony may not behave correctly in empirical distributed systems. For example, a set of popular theoretical models, which we call M_*, assume (eventual) upper bounds on message delay and relative process speeds, regardless of message size and absolute process speeds. Empirical systems with bounded channel capacity and bandwidth cannot realize such assumptions either natively, or through algorithmic constructions. Consequently, empirical deployment of the many M_*-based algorithms risks anomalous behavior. As a result, we argue that real time is the wrong basis for such a theory. Instead, the appropriate foundation for partial synchrony is fairness: a time base measured by counting events internal to the system, like the steps executed by the processes. By way of example, we redefine M_* models with fairness-based bounds and provide algorithmic techniques to implement fairness-based M_* models on a significant subset of the empirical systems. The proposed techniques use failure detectors — system services that provide hints about process crashes — as intermediaries that preserve the fairness constraints native to empirical systems. In effect, algorithms that are correct in M_* models are now proved correct in such empirical systems as well. Demonstrating our results requires solving three open problems. (1) We propose the first unified mathematical framework based on Timed I/O Automata to specify empirical systems, partially synchronous systems, and algorithms that execute within the aforementioned systems. (2) We show that crash tolerance capabilities of popular distributed systems can be denominated exclusively through fairness constraints. (3) We specify exemplar system models that identify the set of weakest system models to implement popular failure detectors

The Weakest Failure Detector to Solve Mutual Exclusion

Mutual exclusion is not solvable in an asynchronous message-passing system where processes are subject to crash failures. Delporte-Gallet et. al. determined the weakest failure detector to solve this problem when a majority of processes are correct. Here we identify the weakest failure detector to solve mutual exclusion in any environment, i.e., regardless of the number of faulty processes. We also show a relation between mutual exclusion and consensus, arguably the two most fundamental problems in distributed computing. Specifically, we show that a failure detector that solves mutual exclusion is sufficient to solve non-uniform consensus but not necessarily uniform consensus

Dining philosophers with masking tolerance to crash faults

We examine the tolerance of dining philosopher algorithms subject to process crash faults in arbitrary conflict graphs. This classic problem is unsolvable in asynchronous message-passing systems subject to even a single crash fault. By contrast, dining can be solved in synchronous systems capable of implementing the perfect failure detector P (from the Chandra-Toueg hierarchy). We show that dining is also solvable in weaker timing models using a combination of the trusting detector T and the strong detector S; Our approach extends and composes two currents of previous research. First, we define a parametric generalization of Lynch’s classic algorithm for hierarchical resource allocation. Our construction converts any mutual exclusion algorithm into a valid dining algorithm. Second, we consider the fault-tolerant mutual exclusion algorithm (FTME) of Delporte-Gallet, et al., which uses T and the strong detector S to mask crash faults in any environment. We instantiate our dining construction with FTME, and prove that the resulting dining algorithm guarantees masking tolerance to crash faults. Our contribution (1) defines a new construction for transforming mutual exclusion algorithms into dining algorithms, and (2) demonstrates a better upper-bound on the fault-detection capabilities necessary to mask crash faults in dining philosophers