Abstract
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.
Highlights
It is well known that the study of a multiprocessor computer system has been an important research area in the field of parallel and distribute systems
A fundamental measure of reliability evaluation is the network reliability [11], defined as the probability that all nodes in the system are available and connected
Others are terminal reliability [12], defined as the probability that given two nodes are available and connected, task-based dependability [13], [14], defined as probability that some minimum number of connected nodes are operational for the execution of a task, and subsystem reliability [15], defined as the probability that a subsystem of a certain cardinality is operational in the system
Summary
It is well known that the study of a multiprocessor computer system has been an important research area in the field of parallel and distribute systems. A typical method to evaluating subsystem reliability is to decompose the system into some smaller subsystems using a graph theory model where nodes and/or edges are postulated to fail independently with a given probability. Chang and Bhuyan [15] put forward a new combinatorial reliability model, the probability fault model, to evaluate the subcube reliability of hypercubes. There are many results related to the subsystem reliability under the probability fault model besides the hypercube network. Inspired by the above results, in this paper, we analyze the subsystem reliability of the balanced hypercube under the probabilistic fault model. The n-dimensional balanced hypercube, denoted by BHn, has 22n nodes, each labeled by a string
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