Cyclic dependencies in Modular Performance Analysis

The Modular Performance Analysis based on Real-Time Calculus (MPA-RTC), developed by Thiele et al., is an abstraction for the analysis of component-based real-time systems. The formalism uses an abstract stream model to characterize both workload and availability of computation and communication resources. Components can then be viewed as stream transformers. The Real-Time Calculus has been used successfully on systems where dependencies between components, via either workload or resource streams, are acyclic. For systems with cyclic dependencies the foundations and performance of the formalism are less well understood. In this paper, we develop a general operational semantics underlying the Real-Time Calculus, and use this to show that the behavior of systems with cyclic dependencies can be analyzed by fixpoint iterations. We characterize conditions under which such iterations give safe results, and also show how precise the results can be.