Symbolic Buffer Sizing for Throughput-Optimal Scheduling of Dataflow Graphs

The synchronous dataflow model is widely used to design real-time streaming applications which must assure a minimum quality-of-service. A benefit of that model is to allow static analyses to predict and guarantee timing (e.g., throughput) and buffering requirements of an application. Performance analyses can either be performed at compile time (for design space exploration) or at run-time (for resource management and reconfigurable systems). However, these algorithms, which often have an exponential time complexity, may cause a huge run-time overhead or make design space exploration unacceptably slow. 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. many different non-functional requirements. We first provide a symbolic expression of the maximal throughput of acyclic synchronous dataflow graphs. We then perform an analytic and exact study of the minimum buffer sizes needed to achieve this maximal throughput for a single parametric edge graph. Based on these investigations, we define symbolic analyses that approximate the minimum buffer sizes needed to achieve maximal throughput for acyclic graphs. We assess the proposed analyses experimentally on both synthetic and real benchmarks.