In this paper, we describe a Markov chain based approach for the performance and availability analysis of cloud provided services. We use infrastructure-asa-service as an example of a cloud based service, where service availability and provisioning response delays are key service level agreements (SLAs) to users while cost reductions are important to service providers. In order to reduce complexity, we divide the overall model into multiple interacting Markov sub-models and then obtain the overall solution by iteration over sub-model solutions. This results in a high fidelity model that is scalable. We summarize our modeling approach and outline future avenues of research.