This paper focus on the deployment of grid infrastructures, more specifically Problem Solving Environments (PSE) for numerical applications on the grid. Even if the deployment of such an architecture is forced by physical constraints (firewall, access permission, 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 the modeling approach in this case are multiple: evaluate a virtual deployment before an actual deployment, provide a decision builder tool (i.e., designed to compare different architectures or buy new resource), take into account the platform scalability. Using this modeling, 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 this modeling by applying this results to an existing hierarchical PSE called DIET.