The use of many distributed, heterogeneous resources as a large collective resource offers great potential and has become an increasingly popular idea. A key issue for these Grid platforms is middleware scalability and how middleware services can best be mapped to the resource platform structure. Optimizing deployment is a difficult problem with no existing general solutions. In this paper we address a simpler sub-problem: how to carry out an adapted deployment on a cluster with hundreds of nodes? Efficient use of clusters alone or as part of the Grid is an important issue. In this paper we present an approach for automatically determining an optimal deployment for hierarchically distributed middleware services on clusters where the goal is to optimize steady-state request throughput. We prove that a complete spanning d-ary tree provides an optimal deployment and we present an algorithm to construct this optimal tree. We use a distributed Problem Solving Environment called DIET to test our approach. We define a performance model for each component of DIET and validate these models in a real-world cluster environment. Additional experiments demonstrate that our approach selects a deployment that performs better than other reasonable deployments.