In this paper, we present a novel stochastic analyzing model for e2e virtualized cloud services using hierarchical Quasi-Birth Death structures (QBDs). We divide the overall virtualized cloud services into three sub-hierarchies, and then, analyze each individual sub-hierarchy using QBDs. Our approach reduces the complexity of performance analysis. Our results are useful to prevent the cloud center from entering unsafe operation, and also reveal practical insights into load balancing and capacity planning for virtualized computing environments.