Towards component-based (max,+) algebraic throughput analysis of hierarchical synchronous data flow models

Abstract

Synchronous (or static) dataflow (SDF) is deemed the most stable and mature model to represent streaming systems. It is useful, not only to reason about functional behavior and correctness of such systems, but also about non-functional aspects, in particular timing and performance constraints. When talking about performance, throughput is a key metric. Within the SDF domain, hierarchical SDF models are of special interest as they enable compositional modeling, which is a necessity in the design of large systems. Techniques exist to analyze throughput of synchronous dataflow models. If the model is hierarchical, it first needs to be flattened before these techniques can be applied (for exact analysis at least). Furthermore, all of these techniques are adversely affected by the increase in the graph’s repetition vector entries. In this paper, for a loosely defined class of hierarchical synchronous dataflow models, we argue that these dependence issues can be mitigated by taking advantage of the hierarchical structure rather than by flattening the graph. We propose a hierarchical extension to an existing technique that is based on the (max,+) algebraic semantics of SDF