Graph-based models for real-time workload: a survey

Abstract

This paper provides a survey on task models to characterize real-time workloads at different levels of abstraction for the design and analysis of real-time systems. It covers the classic periodic and sporadic models by Liu and Layland et al., their extensions to describe recurring and branching structures as well as general graph-and automata-based models to allow modeling of complex structures such as mode switches, local loops and also global timing constraints. The focus is on the precise semantics of the various models and on the solutions and complexity results of the respective feasibilty and schedulability analysis problems for preemptable uniprocessors.

Schedulability Analysis of Real-time Tasks with Precedence Constraints

“…2 as an example to illustrate the valid job sequences within one period. For the balance task, the job sequence of (RI, CA, CB) with the timing constraints of (0, 1, 2), (10,2,15), and (30, 1, 35) respectively is valid, because the precedent job of CA (i.e. RI) is included in this job sequence.…”

“…In the design of real-time systems, an abstract task model is usually used as an input for the schedulability analysis, and specifies the tasks' timing constraints (duration, start constraint, etc.) [2]. The precedence constraints within or between tasks, which commonly exist in real-time systems [3], [4], directly affect the schedulability and need to be concerned in the task model.…”

“…Since the well-known Liu and Layland task model [5] appeared, a large number of task models, ranging from the relatively simple periodic and sporadic ones to the more complex graph-based ones, have been proposed [2]. There is a contradicting goal of expressiveness and analysis efficiency for these task models.…”

“…Therefore, the existing task models supporting the precedence constraint are inadequate. Due to good expressiveness and analysis efficiency, the currently proposed digraph real-time (DRT) task model [12] is promising according to a thorough survey [2]. Specifically, the DRT model can specify both the sporadic and periodic tasks, and is tractable (i.e.…”

A Framework for Evaluating Schedulability Analysis Tools

“…A period task set consists of periodic, synchronous and independent tasks with implicit deadlines. To describe tasks with more diverse features, researchers have extended the Liu and Layland task model with di erent additional parameters, which lead to variations in the tractability and precision of feasibility and schedulability analysis [27].…”