Reliability Analysis of the Hypercube Architecture.

This dissertation presents improved techniques for analyzing network-connected (NCF), 2-connected (2CF), task-based (TBF), and subcube (SF) functionality measures in a hypercube multiprocessor with faulty processing elements (PE) and/or communication elements (CE). These measures help study system-level fault tolerance issues and relate to various application modes in the hypercube. Solutions discussed in the text fall into probabilistic and deterministic models. The probabilistic measure assumes a stochastic graph of the hypercube where PE\u27s and/or CE\u27s may fail with certain probabilities, while the deterministic model considers that some system components are already failed and aims to determine the system functionality. For probabilistic model, MIL-HDBK-217F is used to predict PE and CE failure rates for an Intel iPSC system. First, a technique called CAREL is presented. A proof of its correctness is included in an appendix. Using the shelling ordering concept, CAREL is shown to solve the exact probabilistic NCF measure for a hypercube in time polynomial in the number of spanning trees. However, this number increases exponentially in the hypercube dimension. This dissertation, then, aims to more efficiently obtain lower and upper bounds on the measures. Algorithms, presented in the text, generate tighter bounds than had been obtained previously and run in time polynomial in the cube dimension. The proposed algorithms for probabilistic 2CF measure consider PE and/or CE failures. In attempting to evaluate deterministic measures, a hybrid method for fault tolerant broadcasting in the hypercube is proposed. This method combines the favorable features of redundant and non-redundant techniques. A generalized result on the deterministic TBF measure for the hypercube is then described. Two distributed algorithms are proposed to identify the largest operational subcubes in a hypercube C\sb{n} with faulty PE\u27s. Method 1, called LOS1, requires a list of faulty components and utilizes the CMB operator of CAREL to solve the problem. In case the number of unavailable nodes (faulty or busy) increases, an alternative distributed approach, called LOS2, processes m available nodes in O(mn) time. The proposed techniques are simple and efficient

Algorithm Based Fault Tolerance in Massively Parallel Systems

An A complex computer system consists of billions of transistors, miles of wires, and many interactions with an unpredictable environment. Correct results must be produced despite faults that dynamically occur in some of these components. Many techniques have been developed for fault tolerant computation. General purpose methods are independent of the application, yet incur an overhead cost which may be unacceptable for massively parallel systems. Algorithm-specific methods, which can operate at lower cost, are a developing alternative [1, 72]. This paper first reviews the general-purpose approach and then focuses on the algorithm-specific method, with an eye toward massively parallel processors. Algorithm-based fault tolerance has the attraction of low overhead; furthermore it addresses both the detection and also the correction problems. The principle is to build low-cost checking and correcting mechanism based exclusively on the redundancies inherent in the system

Analysis and design of algorithm-based fault-tolerant systems

An important consideration in the design of high performance multiprocessor systems is to ensure the correctness of the results computed in the presence of transient and intermittent failures. Concurrent error detection and correction have been applied to such systems in order to achieve reliability. Algorithm Based Fault Tolerance (ABFT) was suggested as a cost-effective concurrent error detection scheme. The research was motivated by the complexity involved in the analysis and design of ABFT systems. To that end, a matrix-based model was developed and, based on that, algorithms for both the design and analysis of ABFT systems are formulated. These algorithms are less complex than the existing ones. In order to reduce the complexity further, a hierarchical approach is developed for the analysis of large systems

Semantics of Non-Deterministic Repairable Fault Trees

Fault Tree Analysis is a popular technique used to support the design of critical systems. In a prior work, fault tree semantics have been developed for Non-Deterministic Dynamic FaultTrees that introduces non-determinism to the recovery actions to solve the problem of spare races and improve system reliability. However the existing work only deals with permanent faults. The focus of the thesis work is extending the formalism of NonDeterministic Dynamic Fault Trees to support the notion of repair and develop semantics for Non-Deterministic Repairable Fault Trees to achieve higher availability of system. It includes formalizing the gate semantics and adapting the algorithms for analyzing the fault tree. Furthermore, the thesis work also adapts the minimization algorithms to produce a more compact version of the Recovery Automaton with fewer state