Symbolic Analysis of Dataflow Graphs (Extended Version)

The synchronous dataflow model is widely used to design embedded stream-processing applications under strict quality-of-service requirements (e.g., buffering memory, throughput, input-output latency). The required analyses can either be performed at compile-time (for design space exploration) or at run-time (for resource management and reconfigurable systems). However, they may cause a huge run-time overhead or make design space exploration unacceptably slow due to their exponential time complexity.In this paper, we argue that symbolic analyses are more appropriate since they express the system performance as a function of parameters (i.e., input and output rates, execution times). Such functions can be quickly evaluated for each different configuration or checked w.r.t. different quality-of-service requirements. We provide symbolic analyses for computing the maximal throughput of acyclic graphs, the minimum required buffers for which as soon as possible scheduling achieves this throughput, and finally the corresponding input-output latency of the graph. The paper firstinvestigates these problems for a simple graph made of a single parametric edge. The results are then extended to general acyclic graphs using linear approximation techniques. We assess the proposed analyses experimentally on both synthetic and real benchmarks