Worst-case throughput analysis for parametric rate and parametric actor execution time scenario-aware dataflow graphs

Scenario-aware dataflow (SADF) is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF) graphs, each of which represents one possible application behaviour or scenario. A finite state machine (FSM) specifies the possible orders of scenario occurrences. The SADF model renders the tightest possible performance guarantees, but is limited by its finiteness. This means that from a practical point of view, it can only handle dynamic dataflow applications that are characterized by a reasonably sized set of possible behaviours or scenarios. In this paper we remove this limitation for a class of SADF graphs by means of SADF model parametrization in terms of graph port rates and actor execution times. First, we formally define the semantics of the model relevant for throughput analysis based on (max,+) linear system theory and (max,+) automata. Second, by generalizing some of the existing results, we give the algorithms for worst-case throughput analysis of parametric rate and parametric actor execution time acyclic SADF graphs with a fully connected, possibly infinite state transition system. Third, we demonstrate our approach on a few realistic applications from digital signal processing (DSP) domain mapped onto an embedded multi-processor architecture

Worst-case latency analysis of SDF-based parametrized dataflow MoCs

Modern-day streaming digital signal processing (DSP) applications are often accompanied by real-time requirements. In addition, they expose increasing levels of dynamic behavior. Dynamic dataflow models of computation (MoCs) have been introduced to model and analyze such applications. Parametrized dataflow MoCs are an important subclass of dynamic dataflow MoCs because they integrate dynamic parameters and run-time adaptation of parameters in a structured way. However, these MoCs have been primarily analyzed for functional behavior and correctness while the analysis of their temporal behavior has received little attention. In this work, we present a new analysis approach that allows analysis of worst-case latency for dynamic streaming DSP applications that can be captured using parametrized dataflow MoCs based on synchronous dataflow (SDF). We show that in the presence of parameter inter-dependencies our technique can yield tighter worst-case latency estimates than the existing techniques that operate on SDF structures that abstract the worst-case behaviour of the initial parametrized specifications. We base the approach on the (max,+) algebraic semantics of timed SDF and on its non-parametric generalization known as FSMbased scenario-aware dataflow (FSM-SADF). We evaluate the approach on a realistic case study from the multimedia domain

Worst-case performance analysis of SDF-based parameterized dataflow

Dynamic dataflow models of computation (MoCs) have been introduced to provide designers with sufficient expressive power to capture increasing levels of dynamism in present-day streaming applications. Among dynamic dataflow MoCs, parameterized dataflow MoCs hold an important place. This is due to the fact that they allow for a compact representation of fine-grained data-dependent dynamics inherent to many present-day streaming applications. However, these models have been primarily analyzed for functional behavior and correctness, while the (parametric) analysis of their temporal behavior has attracted less attention. In this work, we (in a parametric fashion) analyze worst-case performance metrics (throughput and latency) of an important class of parameterized dataflow MoCs based on synchronous dataflow (SDF). We refer to such models as SDF-based parameterized dataflow (SDF-PDF). We show that parametric analysis in many cases allows to derive tighter conservative worst-case throughput and latency guarantees than the existing (nonparametric) techniques that rely on the creation of “worst-case SDF abstractions” of original parameterized specifications. Furthermore, we discuss how by using parametric analysis we can help address the scalability issues of enumerative analysis techniques. To achieve this, we first introduce the Max-plus algebraic semantics of SDF-PDF. Thereafter, we model run-time adaptation of parameters using the theory of Max-plus automata. Finally, we show how to derive the worst-case performance metrics from the resulting Max-plus automaton structure. We evaluate our approach on a representative case study from the multimedia domain

Parameterized dataflow scenarios

A number of modeling approaches combining dataflow and finite-state machines (FSMs) have been proposed to capture applications that combine streaming data with finite control. FSM-based scenario-aware dataflow (FSM-SADF) is such an FSM/dataflow hybrid that occupies a sweet spot in the tradeoff between analyzability and expressiveness. However, the model suffers from compactness issues when the number of scenarios increases. This hampers its use in analysis of applications exposing high levels of data-dependent dynamics. In this paper, we address this problem by combining parameterized dataflow with finite control of FSM-SADF. We refer to the generalization as FSM-based parameterized SADF (FSM-π SADF). We introduce the formal semantics of the model, in terms of max-plus algebra and in particular max-plus automata. Thereafter, by leveraging the existing results of FSM-SADF, we propose a worst-case performance analysis framework for FSM-π SADF. We show that by using FSM-π SADF and its analysis framework, one can, unlike with FSM-SADF, compactly capture streaming applications exhibiting high levels of data-dependent dynamics in presence of finite control. Furthermore, we show that for practical models our analysis typically yields tighter bounds on worst-case performance indicators such as throughput and latency than the existing techniques based on conservative FSM-SADF modeling (if such modeling can be applied at all). We evaluate our approach on a realistic case-study from the multimedia domain

Worst-case throughput analysis for parametric rate and parametric actor execution time scenario-aware dataflow graphs

Scenario-aware dataflow (SADF) is a prominent tool for modeling and analysis of dynamic embedded dataflow applications. In SADF the application is represented as a finite collection of synchronous dataflow (SDF) graphs, each of which represents one possible application behaviour or scenario. A finite state machine (FSM) specifies the possible orders of scenario occurrences. The SADF model renders the tightest possible performance guarantees, but is limited by its finiteness. This means that from a practical point of view, it can only handle dynamic dataflow applications that are characterized by a reasonably sized set of possible behaviours or scenarios. In this paper we remove this limitation for a class of SADF graphs by means of SADF model parametrization in terms of graph port rates and actor execution times. First, we formally define the semantics of the model relevant for throughput analysis based on (max,+) linear system theory and (max,+) automata. Second, by generalizing some of the existing results, we give the algorithms for worst-case throughput analysis of parametric rate and parametric actor execution time acyclic SADF graphs with a fully connected, possibly infinite state transition system. Third, we demonstrate our approach on a few realistic applications from digital signal processing (DSP) domain mapped onto an embedded multi-processor architecture