On the analysis of synchronous dataflow graphs: a system-theoretic perspective

Synchronous dataflow (SDF) is a graphical model of computation in which sequential process communicate through first-in-first-out (FIFO) channels, where the amount of data produced onto and consumed from each channel is known a priori. These models find their application in the analysis of stream processing systems, which operate in real-time: they must meet strict latency and/or throughput constraints. Temporal analysis of SDF models allows one to give guarantees on the performance characteristics of the system that is modelled. As such, temporal analysis may be used to verify whether the system meets the latency and throughput constraints. Existing approaches to temporal analysis are poorly scalable, and can be classified into two main schools of thought. The first approaches the analysis using exact semantics, and the other approximates these semantics. Exact semantics give rise to algorithms that require time exponential in the size of the graph. Approximations lead to polynomial time-complexity, but this comes at the expense of a loss in accuracy. Moreover, this loss in accuracy can not be assessed by current methods. A natural solution to the poor scalability of existing methods is to combine them into a method that balances computational complexity with accuracy. However, since existing methods operate on different levels of abstraction, their unification is far from trivial. This thesis presents a unification of these two existing approaches to temporal analysis, in the form of an incremental analysis of SDF graphs. In our approach, we start with a rough estimation derived from an approximation of the graph, and subsequently improve this estimation through a set of graph transformations. Underlying our approach is a fundamental characterisation of the temporal dynamics of an SDF graph, in max-plus algebra. We furthermore evaluate our method by comparing its results with existing state-of-the-art methods, on an extensive benchmark set. Results show that our approach successfully balances computational complexity with accuracy.