Robustness of reliability bounds for (n,k)-star networks

Abstract

The sub-network reliability, SNR for short, of a network is the probability that a healthy sub-network of a certain scale is operational in the network when faults occurs. It is surprisingly found that some networks’ SNR are different even though they have the same cardinality of processors. Hereby, we conduct comparative analysis for a pair of distinct topologies of $(n,k)$-star networks $S_{n,k}$ with same cardinality of processors to assess the robustness of their SNR bounds. We demonstrate analytically that SNR in $S_{n,k}$ is proportional to $n$ when sub-networks are of the same cardinality of processors. This study presents a theoretical framework for selecting the more reliable topology among $S_{n,k}$s of the same cardinality of processors. We also conduct numerical simulations to verify our theoretical findings.