Network Function Virtualization (NFV) is changing the way networks are managed, by providing more scalability and flexibility. However, to meet stringent real-time constraints, some network functions have to be hosted close to end users, which incites Network Operators (NOs) to install well di-mensioned data centers at the edge of the network. In this framework, the contributions of this paper are twofold. First, we proposed an analytical model for the blocking analysis in a multidimensional cloud system, which was validated using discrete events' simulations. Second, we conducted a comparative analysis of the most popular placement's strategies. The proposed model, as well as the comparative study, reveal practical insights into the performance evaluation of resource allocation and capacity planning for distributed edge cloud with limited capacities.