A Data Flow Model with Frequency Arithmetic

Abstract

Data flow formalisms are commonly used to model systems in order to solve problems of buffer sizing and task scheduling. A prerequisite for static analysis of a modeled system is the existence of a periodic schedule in which the sizes of communication channels can be bounded for an unbounded execution (consistency), and that communication dependencies do not introduce a deadlock in such an execution (liveness). In the context of Cyber-Physical Systems, components are often interfaced with the physical world and have frequency constraints. The existing data flow formalisms lack expressiveness to fully cover the expected behavior of these components. We propose an extension to Synchronous Data Flow (SDF) formalism, called Polygraph, that includes frequency constraints and adjustable communication rates. We show that with these extensions, the conditions for a model to be consistent and live are no longer sufficient, and we extend the corresponding theorems with necessary and sufficient conditions to preserve these properties. We also introduce a framework to check the liveness of a Polygraph model, implemented in the tool DIVERSITY, along with preliminary experiments to validate this approach.

A survey of main dataflow MoCCs for CPS design and verification

“…2) PolyGraph: PolyGraph ( [28]) enhances the semantic of rational rates of FRDF. A rate of p q means p tokens are produced/consumed every q firings.…”

Scheduling of Synchronous Dataflow Graphs with Partially Periodic Real-Time Constraints

“…Indeed all periods are linearly related, as expressed in Section 3.1. According to the Polygraph model [14], P corresponds to actors having a frequency. Delays on buffers are allowed, with some restrictions for cycles in .…”

“…As MAPS is not freely accessible, we did not compare to it. Deadlock [12] and consistency [14] analysis of SDF graphs with partially periodic constraints have also been studied. Other tools and papers are closely related to our scheduling problem and are listed in the three next paragraphs, according to there category.…”

“…In this paper, we consider applications modeled with an SDF graph, where some actors have periodic release times with implicit deadline. Our model is a restriction of the Polygraph model [14] to SDF graphs, but extended with deadlines. We say that such graph has partially periodic constraints.…”

Dynamic Reconfigurations in Frequency Constrained Data Flow

“…Dynamic data flow models are adapted to capture reconfigurations in a CPS, but they lack expressiveness regarding the real-time synchronization of the components interfaced with the physical world. Recent research introduced Polygraph, a new static data flow formalism that covers such synchronous behavior [5], while allowing asynchronous behavior for computation kernels. Our goal is to extend Polygraph to support the expression of dynamic reconfigurations, describing more precisely the behavior of distributed CPS, thus allowing a refinement of the static performance analysis of the resulting models.…”