We present a performance analysis technique for distributed real-time systems in a setting where certain components are modeled in a purely functional manner, while the remaining components require additional modeling of state information. The functional models can be efficiently analyzed but have restricted expressiveness. On the other hand, state-based models are more expressive and offer a richer set of analyzable properties but are computationally more expensive to analyze. We show that by appropriately composing these two classes of models it is possible to leverage on their respective advantages. To this end, we propose an interface between components that are modeled using Real-Time Calculus [Chakraborty, K¡§unzli and Thiele, DATE 2003] and those that are modeled using Event Count Automata [Chakraborty, Phan and Thiagarajan, RTSS 2005]. The resulting modeling technique is as expressive as Event Count Automata, but is amenable to more effficient analysis. We illustrate these advantages using a number of examples and a detailed case study.