Nowdays, several streaming servers are available to provide a variety of multimedia applications such as Video on Demand in cloud computing environments. These environments have the business potential because of the pay-per-use model, as well as the advantages of easy scalability and, up-to-date of the packages and programs. This paper uses hierarchical modeling and different sensitivity analysis techniques to determine the parameters that cause the greatest impact on the availability of a Video on Demand. The results show that distinct approaches provide similar results regarding the sensitivity ranking, with specific exceptions. A combined evaluation indicates that system availability may be improved effectively by focusing on a reduced set of factors that produce large variation on the measure of interest.