High availability is one of the key characteristics of Infrastructure-as-a-Service (IaaS) cloud. In this paper, we show a scalable method for availability analysis of large scale IaaS cloud using analytic models. To reduce the complexity of analysis and the solution time, we use an interacting Markov chain based approach. The construction and the solution of the Markov chains is facilitated by the use of a high-level Petri net based paradigm known as stochastic reward net (SRN). Overall solution is composed by iteration over individual SRN sub-model solutions. Dependencies among the sub-models are resolved using fixed-point iteration, for which existence of a solution is proved. We compare the solution obtained from the interacting sub-models with a monolithic model and show that errors introduced by decomposition are insignificant. Additionally, we provide closed form solutions of the sub-models and show that our approach can handle very large size IaaS clouds.