Affine Data-Flow Graphs for the Synthesis of Hard Real-Time Applications

Abstract

Abstract-Data-flow models ease the task of constructing feasible schedules of computations and communications of high-assurance embedded applications. One key and open issue is how to schedule data-flow graphs so as to minimize the buffering of data and reduce end-to-end latency. Most of the proposed techniques in that respect are based on either static or data-driven scheduling. This paper looks at the problem in a different way by considering priority-driven preemptive scheduling theory of periodic tasks to execute a data-flow program.Our approach to the problem can be detailed as follows.(1) We propose a model of computation in which the activation clocks of actors are related by affine functions. The affine relations describe the symbolic scheduling constraints of the data-flow graph. (2) Based on this framework, we present an algorithm that computes affine schedules in a way that minimizes buffering requirements and, in addition, guarantees the absence of overflow and underflow exceptions over communication channels. (3) Depending on the chosen scheduling policy (earliest-deadline first or rate-monotonic), we concretize the symbolic schedule by defining the period and the phase of each actor. This concretization guarantees schedulability and maximizes the processor utilization factor.

Buffer minimization in earliest-deadline first scheduling of dataflow graphs

“…The construction of the abstract affine schedule is similar to that of [8] (reviewed separately in Section 3) but also considers the deadlines adjustment as shown in Section 4. One benefit of adding precedence constraints is that the linear safe approximations used to solve the buffer minimization problem are less pessimistic than the ones obtained in [8].…”

“…When it comes to buffer sizes computation of channels between pi and p k , if a preemption occurs, then we will consider the worst-case scenarios as in [8]. …”

“…Such scheduling approach gives the maximum achievable processor utilization for large set of dataflow graphs, called matched I/O rates graphs [1]. Furthermore, EDF symbolic schedulability of IDP task systems is quite simple with a polynomial time complexity [8]. However, the IDP model may increase the latency and the buffering requirements of the graphs.…”

Design of safety-critical Java level 1 applications using affine abstract clocks

“…A periodic scheduling technique of dataflow graphs with ultimately periodic rates was presented in [14]. The proposed technique computes the timing parameters of actors assuming that deadlines are equal to periods (i.e.…”

“…The goal of this paper is to propose a dataflow design model of SCJ/L1 applications, as an extension to the affine dataflow model [14], in which handlers communicate only through lock-free channels. Dataflow models of computation are commonly used in embedded system design to describe stream processing or control applications.…”