  To analyze complex and heterogeneous real-time embedded systems, recent works
have proposed interface techniques between real-time calculus (RTC) and timed
automata (TA), in order to take advantage of the strengths of each technique
for analyzing various components. But the time to analyze a state-based
component modeled by TA may be prohibitively high, due to the state space
explosion problem. In this paper, we propose a framework of granularity-based
interfacing to speed up the analysis of a TA modeled component. First, we
abstract fine models to work with event streams at coarse granularity. We
perform analysis of the component at multiple coarse granularities and then
based on RTC theory, we derive lower and upper bounds on arrival patterns of
the fine output streams using the causality closure algorithm. Our framework
can help to achieve tradeoffs between precision and analysis time.
