Modeling Parallel Real-time Tasks with Di-Graphs

Multiframe, generalised multiframe and di-graph task models have been proposed to cope with the increasing complexity of real-time applications. However, these models have been designed for single processor systems and cannot express the potential intra-task parallelism of many modern real-time applications. In this paper, we extend the di-graph model to support parallel tasks. We propose a sufficient feasibility test for partitioned scheduling of a set of di-graph tasks on an identical core platform. Based on this test, we also propose a set of heuristics for parallelising and partitioning a set of di-graph tasks and for assigning the core frequency. Thus, our frequency selection algorithm can be used to reduce the energy consumption of a system. A set of synthetic experiments are presented that emphasise the effectiveness of our model against other less expressive models proposed in the literature.