Symbolic Analyses of Dataflow Graphs

The synchronous dataflow model of computation is widely used to design embedded stream-processing applications under strict quality-of-service requirements (e.g., buffering size, throughput, input-output latency). The required analyses can either be performed at compile time (for design space exploration) or at runtime (for resource management and reconfigurable systems). However, these analyses have an exponential time complexity, which may cause a huge runtime overhead or make design space exploration unacceptably slow. In this article, 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 with respect to different quality-of-service requirements. We provide symbolic analyses for computing the maximal throughput of acyclic synchronous dataflow graphs, the minimum required buffers for which as soon as possible (ASAP) scheduling achieves this throughput, and finally, the corresponding input-output latency of the graph. The article first investigates these problems for a single parametric edge. The results are extended to general acyclic graphs using linear approximation techniques. We assess the proposed analyses experimentally on both synthetic and real benchmarks.