Investigation of the robustness of star graph networks

The star interconnection network has been known as an attractive alternative to n-cube for interconnecting a large number of processors. It possesses many nice properties, such as vertex/edge symmetry, recursiveness, sublogarithmic degree and diameter, and maximal fault tolerance, which are all desirable when building an interconnection topology for a parallel and distributed system. Investigation of the robustness of the star network architecture is essential since the star network has the potential of use in critical applications. In this study, three different reliability measures are proposed to investigate the robustness of the star network. First, a constrained two-terminal reliability measure referred to as Distance Reliability (DR) between the source node u and the destination node I with the shortest distance, in an n-dimensional star network, Sn, is introduced to assess the robustness of the star network. A combinatorial analysis on DR especially for u having a single cycle is performed under different failure models (node, link, combined node/link failure). Lower bounds on the special case of the DR: antipode reliability, are derived, compared with n-cube, and shown to be more fault-tolerant than n-cube. The degradation of a container in a Sn having at least one operational optimal path between u and I is also examined to measure the system effectiveness in the presence of failures under different failure models. The values of MTTF to each transition state are calculated and compared with similar size containers in n-cube. Meanwhile, an upper bound under the probability fault model and an approximation under the fixed partitioning approach on the ( n-1)-star reliability are derived, and proved to be similarly accurate and close to the simulations results. Conservative comparisons between similar size star networks and n-cubes show that the star network is more robust than n-cube in terms of ( n-1)-network reliability

A UNIFIED TASK-BASED DEPENDABILITY MODEL FOR HYPERCUBE COMPUTERS

A unified analytical model for computing the task-based dependability (TBD) of hypercube architectures is presented in this paper. The TBD study considers a hypercube operational as long as a task can be executed on the system. The technique is unified in that it can compute both reliability and availability for two types of task requirements-I-connected model and subcube model. The I-connected TBD assumes that a connected group of at least I working nodes is required for task execution. The subcube TBD needs at least an m-cube in an n-cube, m less-than-or-equal-to n, for task execution. We compute the dependability of a hypercube by multiplying two probabilistic terms. The first term is the probability that x nodes (x greater-than-or-equal-to I or x greater-than-or-equal-to 2m) are working in an n-cube at time t. This probability can be obtained easily for a repairable or nonrepairable system. The second term is the conditional probability that the hypercube can satisfy any one of the two task requirements from x working nodes. This term, defined as the "task connection probability," gives the probability that j-connected nodes (j greater-than-or-equal-to I) or an m-cube can be obtained from the x working nodes. Two recursive models are proposed for the two types of task requirements to find the connection probability. The subcube requirement is also extended to find multiple subcubes for analyzing multitask dependability. Analytical results are provided for the two TBD schemes and are validated through extensive simulation.X1115sciescopu

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