g-Good-neighbor conditional diagnosability measures for 3-ary n-cube networks

• The RgRg-connectivity of 3-ary n  -cube networks was determined for n≥3n≥3 and 0≤g≤n−10≤g≤n−1.
• Applying the PMC model and the MM* model, we investigated and measured the g-good-neighbor conditional diagnosability of 3-ary n  -cube networks for n≥4n≥4 and 0≤g≤n−10≤g≤n−1.

The diagnosability of a parallel system is defined as the maximum number of faulty processors or nodes that the system can guarantee to identify. In this study, we investigate the g-good-neighbor conditional diagnosability, which indicates that every fault-free node in a system contains at least g fault-free neighbors. Compared with the conventional diagnosability, g-good-neighbor conditional diagnosability improves accuracy in measuring the reliability of interconnection networks in heterogeneous environments. We apply the PMC and MM* models to study the g-good-neighbor conditional diagnosability of 3-ary n-cube networks, which represent a family of popular parallel systems such as IBM's Blue Gene and Cray T3D. The findings made in this study facilitate accurate reliability measurements in modern parallel systems powered by 3-ary n-cube networks. Specifically, our results show that the g-good-neighbor conditional diagnosability of 3-ary n  -cube is g2(2n−g+1)−1 and g−12(4n−2g+1)−1 when the g value is even and odd, respectively.