This paper focuses on the deployment of Grid infrastructures, more specifically Problem Solving Environments (PSE) for numerical applications on the Grid. Although the deployment of such an architecture may be constrained e.g., firewall, right access or security, its efficiency heavily depends on the quality of the mapping between its different components and the Grid resources. This paper proposes a new model based on linear programming to estimate the performance of a deployment of a hierarchical PSE. The advantages of our modeling approach are: evaluate a virtual deployment before a real deployment, provide a decision builder tool (i.e., designed to compare different architectures or add new resources) and take into account the platform scalability. Using our model, it is possible to determine the bottleneck of the platform and thus to know whether a given deployment can be improved or not. We illustrate the model by applying the results to improve performance of an existing hierarchical PSE called DIET.