It is nowadays common to use a grid middleware to access distributed resources in order to solve large problems. Many middleware can be found in the literature. Whereas they all rely on the use of resource brokers (also sometimes called agents) to schedule jobs, and servers to execute them, they do not share the same structure. Many rely on a simple design, e.g., a star graph (one agent managing several servers); and the most scalable ones rely on a hierarchy of agents. To the best of our knowledge, very few studies have been conducted on the modelization and performance prediction of such middleware. In this paper, we present a model for hierarchical middleware, i.e., based on a tree structure. Then, we compare our model predictions with real executions on the DIET middleware, and provide a few hints on how to attain the best performance.