Large-scale computing systems, such as cloud data centers, grid infrastructures, and high-performance computing clusters, are the backbone of modern information technology ecosystems. These systems typically consist of numerous heterogeneous, multi-state computing nodes that exhibit varying performance levels due to component failures, degradation, or dynamic resource allocation. Performability analysis, which integrates both system reliability and performance evaluations to quantify the probability of the system operating at a specified performance level, is critical for ensuring the efficient, reliable, and cost-effective operation of these complex systems. This paper presents a comprehens... More >