This document presents a scalable, stochastic model-driven approach for analyzing the availability of large-scale infrastructure-as-a-service (IaaS) clouds, which addresses the common issue of component failures potentially violating service level agreements (SLAs). It introduces an interacting Markov chain-based methodology to simplify the analysis of these complex systems, demonstrating that this approach can handle large-scale cloud environments while maintaining accuracy. The findings suggest that cloud service providers can enhance design, development, testing, and operational strategies using the proposed modeling frameworks.