The increasing shift of various critical services towards Infrastructure-as-a-Service (IaaS) cloud data centers (CDCs) creates a need for analyzing CDCs' availability, which is affected by various factors including repair policy and system parameters. This paper aims to apply analytical modeling and sensitivity analysis techniques to investigate the impact of these factors on the availability of a large-scale IaaS CDC, which (1) consists of active and two kinds of standby physical machines (PMs), (2) allows PM moving among active and two kinds of standby PM pools, and (3) allows active and two kinds of standby PMs to have different mean repair times. Two repair policies are considered: (P1) all pools share a repair station and (P2) each pool uses its own repair station. We develop monolithic availability models for each repair policy by using Stochastic Reward Nets and also develop the corresponding scalable two-level models in order to overcome the monolithic model's limitations, caused by the large-scale feature of a CDC and the complicated interactions among CDC components. We also explore how to apply differential sensitivity analysis technique to conduct parametric sensitivity analysis in the case of interacting submodels. Numerical results of monolithic models and simulation results are used to verify the approximate accuracy of interacting sub-models, which are further applied to examine the sensitivity of the large-scale CDC availability with respect to repair policy and system parameters.