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As online service providers utilize cloud computing to host their services, they are challenged by evaluating the quality of experience and designing redirection strategies in this complicated environment. We propose a hierarchical modeling approach that can easily combine all components of this environment. Identifying interactions among the components is the key to construct such models. In this particular environment, we first construct four sub-models: an outbound bandwidth model, a cloud computing availability model, a latency model and a cloud computing response time model. Then we use a redirection strategy graph to glue them together. We also introduce an all-in-one barometer to ease the evaluation. The numeric results show that our model serves as a very useful analytical tool for online service providers to evaluate cloud computing providers and design redirection strategies.