Theory Meets Practice: Assessment of Decomposition-Based Approximation in 2D Markov Models for Server Cluster Resilience

Markov models are widely used to analyze complex stochastic systems, particularly in modeling of server cluster resilience, where they provide valuable insights into key performance metrics such as unavailability and blocking probability. However, their applicability to large-scale systems is often constrained by the state space explosion problem, leading researchers to employ decomposition-based approximation techniques to improve computational efficiency. Some commonly used approaches involve nearly-completely decomposable (NCD) Markov models, where processes operating at significantly different time scales are treated separately. This work critically examines the assumption that a large difference in time scales between system components guarantees a small approximation error. Using two examples from the context of server cluster resilience, we demonstrate that simplifications in NCD Markov models can lead to substantial inaccuracies. While decomposition-based methods offer large computational savings, their accuracy depends on specific structural conditions, rather than just the separation of time scales. Our findings emphasize the importance of carefully validating approximation assumptions and model structures to ensure reliable performance evaluation in large-scale stochastic systems.