Extending response-time analysis for the automatic synthesis of functional graphs into fixed-priority distributed systems

In this paper, we extend traditional response time analysis to a functional data flow graph (functional graph for brevity) mapped into a set of tasks. Different tasks synchronization semantics can be considered, depending on the way tasks synchronize on inputs consumed and outputs produced by functions in the functional graph. We study three different synchronization semantics and we give the appropriate response time analysis for functional graphs mapped into a set of preemptible fixed-priority tasks distributed over a priority-based network. Our response time analysis extension is needed to integrate response time constraints in an automatic approach for tasks synthesis. In this paper, for each semantics, the corresponding analysis is integrated in a tasks synthesis approach based on mathematical programming. Each semantics is evaluated against the minimum response time that can be obtained running task synthesis over a set of synthetic functional graphs. Finally, different sematics are considered and evaluated for an automotive case study.