Reliability analysis of complete cubic networks based on extra conditional fault

Abstract

The reliability of multiprocessor systems is now a crucial concern in parallel computing. In fact, thanks to rapid and consistent technological advances in networking hardware and software, multiprocessor (core) systems have been successfully implemented. Consequently, there is a notable importance in examining the structures of interprocess communication, with a particular focus on investigating the fault tolerance and fault diagnosability of these structures to build a functionally efficient system. This paper investigates the $s$-extra connectivity ($s$-EC) and $s$-extra diagnosability ($s$-ED) of the complete cubic network $CCN(n)$. Specifically, we initially demonstrate that the $s$-EC of $CCN(n)$ is $\kappa_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}$ for $n\geq 3$ and $0\leq s\leq n-2$. Subsequently, we demonstrate that the $s$-ED under the PMC model is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 3$ and $1\leq s\leq n-2$. Similarly, under the MM* model, the $s$-ED is $t_s(CCN(n))=(s+1)(n+1)-\frac{s(s+3)}{2}+s$ for $n\geq 6$ and $1\leq s\leq \frac{n-2}{4}$. Finally, we conduct simulation experiments, and the results indicate that the $s$-EC consistently surpasses other known connectivities, including classical connectivity and $s$-component connectivity. Additionally, the $s$-ED consistently outperforms classical diagnosability and $s$-component diagnosability of $CCN(n)$.