Reliability Analysis of Subsystem in Balanced Hypercubes

The probability that a multiprocessor computer system has faults arises as the cardinality of the system grows. The subsystem reliability in a system, defined as the probability that there exists a fault-free subsystem of a specified cardinality when the system has faults. In this paper, we derive an upper bound and a lower bound on the probability of a (n - 1)-dimensional subgraph being fault-free in a n-dimensional balanced hypercube under the probabilistic fault model. Numerical simulations indicate that these two analytical results we get are in good consistency, especially when the value of node reliability goes low.