Reaching approximate agreement with mixed-mode faults

In a fault-tolerant distributed system, different non-faulty processes may arrive at different values for a given system parameter. To resolve this disagreement, processes must exchange and vote upon their respective local values. Faulty processes may attempt to inhibit agreement by acting in a malicious or “Byzantine” manner. Approximate agreement defines one form of agreement in which the voted values obtained by the non-faulty processes need not be identical. Instead, they need only agree to within a predefined tolerance. Approximate agreement can be achieved by a sequence of convergent voting rounds, in which the range of values held by non-faulty processes is reduced in each round. Historically, each new convergent voting algorithm has been accompanied by ad-hoc proofs of its convergence rate and fault-tolerance, using an overly conservative fault model in which all faults exhibit worst-case Byzantine behavior. This paper presents a general method to quickly determine convergence rate and fault-tolerance for any member of a broad family of convergent voting algorithms. This method is developed under a realistic mixed-mode fault model comprised of asymmetric, symmetric, and benign fault modes. These results are employed to more accurately analyze the properties of several existing voting algorithms, to derive a sub-family of optimal mixed-mode voting algorithms, and to quickly determine the properties of proposed new voting algorithms     

Stability and Performance of List Scheduling With External Process Delays

Non-preemptive static priority list scheduling is a simple, low-overhead approach to scheduling precedence-constrained tasks in real-time multiprocessor systems. However, it is vulnerable to anomalous timing behavior caused by variations in task durations. Specifically, reducing the duration of one task can delay the starting time of another task. This phenomenon, called Scheduling Instability, can make it difficult or impossible to guarantee real-time deadlines. Several heuristic solutions to handle scheduling instability have been reported. This paper addresses three main limitations in the state of the art in schedule stabilization. First, each stabilization technique only applies to a narrowly defined class of systems. To alleviate this constraint, we present an Extended Scheduling Model encompassing a wide range of assumptions about the scheduling environment, and address the stability problem under this model. Second, existing stabilization methods are heuristics based on a partial understanding of the causes of instability. We therefore derive a set of General Instability Conditions which are both necessary and sufficient for instability to occur. Third, solutions to scheduling instability range from trivial constraints on the run-time dispatcher through complex transformations of the precedence graph. We present scheduling simulation results comparing the average performance of several inherently stable run-time dispatchers of widely varying levels of complexity. Results show that for representative real-time workloads, simple low-overhead dispatchers perform nearly as well as a complex minimally stabilized dispatcher. Thus, complex schedule stabilization methods may be unnecessary, or even detrimental, due to their high computational overhead.     

Unified approach to synchronous and asynchronous approximateagreement in the presence of hybrid faults

An important problem in fault-tolerant distributed computer systems is maintaining agreement between nonfaulty processes in the presence of undiagnosed faults. Approximate agreement defines a condition in which it is not necessary for the agreed values to be numerically identical. Rather, processes need only agree with each other to within a predefined numerical tolerance. Convergent voting algorithms which achieve approximate agreement have been studied in the context of two classes of systems, synchronous and asynchronous. Studies have also addressed both completely connected and partially connected systems. Together, the two properties of synchrony and connectivity yield 4 different voting domains. In all studies to date, each voting domain has been treated as a separate problem. This paper: shows that for at least one broad family of voting algorithms, the 4 domains are special cases of a more general convergent voting problem; analyzes convergent voting under the 3-mode hybrid fault model of Thambidurai and Park; and presents a set of unifying relations applicable to all 4 voting domains. These relations are used to specify voting algorithms which optimize fault-tolerance, convergence rate, or computational overhead in any given voting domain. The task of designing a voting algorithm for a particular fault-tolerant system is thus greatly simplified