Subnetwork reliability of the arrangement graphs under probabilistic fault condition

Abstract

The subnetwork reliability of the interconnection network of a multiprocessor system is an important factor for processing the computing tasks. In order to measure reliability of the arbitrary size subnetwork of the (n,k)-arrangement graph An,k, the probability Rn,km(p) of existing fault-free An−m,k−m subnetworks in An,k under the probabilistic fault condition is studied for m≥1. An upper bound and a lower bound of Rn,km(p) are derived, and a heuristic algorithm based on the Monte Carlo simulation to calculate Rn,km(p) is proposed. Experimental results show that the upper and lower bounds of Rn,km(p) are in accordance with the results of the heuristic algorithm when the upper and lower bounds are close; otherwise, the results of the heuristic algorithm are relatively accurate. Under the consideration that high accuracy requirement and large size of An,k may greatly reduce the evaluation efficiency when the heuristic algorithm is used, the back propagation neural network model for evaluating Rn,km(p) is constructed, and the experiments on the generated data indicate that the constructed model has certain advantages in balancing accuracy and efficiency.