Cloud computing became widespread on IT industry, saving costs of acquisition and maintenance for companies of all sizes, and enabling fair management of resources according to the demand. Stochastic models can enable performance and dependability evaluation of cloud computing systems efficiently, what is needed for proper capacity planning. Distinct models may be combined in a hierarchy to address the huge number of components and levels of interaction among the system parts. Identification of bottlenecks in such composite models might be hard yet, due to the huge amount of input factors and variables which may interfere with the results. This paper proposes a method for bottleneck detection of computational systems represented with hierarchical models, that is remarkably applied in cloud computing systems. This is achieved through the composition of indices computed from lower level models in equations and solution methods of the top level model, for computing the sensitivity indices of all parameters with respect to a global system measure. A unified sensitivity ranking, comprising the composite indices, indicates the parameters with highest impact on output metrics. A case study supports the demonstration of accuracy and utility of our methodology. The study addresses a web service running on a private cloud with auto scaling mechanisms. The methods and algorithms presented here are helpful for decision-making when designing and managing cloud computing infrastructures, regarding incremental and architectural improvements.