The Hierarchical Scheduling Framework (HSF) has been introduced as a design-time framework enabling compositional schedulability analysis of embedded software systems with real-time properties. However, supporting resource sharing in HSF is a major challenge, since it increases the amount of CPU resources required to guarantee schedulability of the hard real time tasks, and it decreases the composability at the system level. In this paper, we focus on a compositional framework called the bounded-delay resource open environment (BROE) server, and we identify key parameters of this framework that have a great effect on how the framework will utilize CPU resources. In addition, we show how to select optimal values for these parameters in order to reduce the required CPU resource