An analytical model for computing hypercube availability

Abstract

An analytical model is presented for computing the availability of an n-dimensional hypercube. The model computes the probability of j connected working nodes in a hypercube by multiplying two probabilistic terms. The first term is the probability of x connected nodes (x>or=j) working out of 2/sup n/ fully connected nodes. This is obtained from the numerical solution of the well-known machine repairman model, modified to capture imperfect coverage and imprecise repair. The second term, which is the probability of having j connected nodes in a hypercube, is computed from an approximate model of the hypercube. The approximate model, in turn, is based on a decomposition principle, where an n-cube connectivity is computed from a two-cube base model using a recursive equation. The availability model studied in this paper is known as task-based availability, where a system remains operational as long as a task can be executed on the system. Analytical results from n-dimensional cubes are given for various task requirements. The model is validated by comparing the analytical results with those from simulation.<>