A UNIFIED TASK-BASED DEPENDABILITY MODEL FOR HYPERCUBE COMPUTERS

Abstract

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.