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 κₛ(CCN(n))=(s+1)(n+1)-s(s+3)/2 for n≥ 3 and 0≤ s≤ n-2. Subsequently, we demonstrate that the s-ED under the PMC model is tₛ(CCN(n))=(s+1)(n+1)-s(s+3)/2+s for n≥ 3 and 1≤ s≤ n-2. Similarly, under the MM* model, the s-ED is tₛ(CCN(n))=(s+1)(n+1)-s(s+3)/2+s for n≥ 6 and 1≤ s≤ 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 $CCN(n)$.