On the Tractability of Digraph-Based Task Models

Stigge, Martin; Ekberg, Pontus; Guan, Nan; Yi, Wang

doi:10.1109/ecrts.2011.23

Cited by 31 publications

(21 citation statements)

References 10 publications

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“…Schedulability analysis has been developed for a variety of different task models, including: periodic tasks [19], sporadic tasks [22], multi-frame tasks [34], [23], generalised multiframe (GMF) tasks [5], non-cyclic GMF tasks [24], recurring real-time tasks [6], non-cyclic recurring real-time tasks [7], and the digraph task model [28], extended with constraints in [29]. Currently, the most general is the digraph task model which describes each task via a directed graph.…”

Section: A Related Workmentioning

confidence: 99%

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Schedulability tests for tasks with Variable Rate-dependent Behaviour under fixed priority scheduling

Davis

Feld

Pollex

et al. 2014

2014 IEEE 19th Real-Time and Embedded Technology and Applications Symposium (RTAS)

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Abstract-Automotive embedded real-time systems such as Engine Management utilise cyclic tasks that are activated periodically based on angular rotation rather than time. As well as having variable inter-arrival times, these tasks also have deadlines and worst-case execution times that are dependent on angular velocity i.e. engine speed or rpm. Such tasks exhibit Variable Rate-dependent Behaviour (VRB). In this paper, we introduce response time analysis for systems comprising VRB and sporadic tasks under fixed priority scheduling. Sufficient schedulability tests are introduced; from simple linear upper bounds on interference, to a more complex analysis using information about the physical limitations of the system to provide constraints for an ILP formulation of the problem.

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Section: A Related Workmentioning

confidence: 99%

“…An edge is labelled with the minimum time between activations of the jobs it connects. Constraints are added to this in [29] to specify a minimum time between nodes.…”

Section: A Related Workmentioning

confidence: 99%

Schedulability tests for tasks with Variable Rate-dependent Behaviour under fixed priority scheduling

Davis

Feld

Pollex

et al. 2014

2014 IEEE 19th Real-Time and Embedded Technology and Applications Symposium (RTAS)

View full text Add to dashboard Cite

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“…A natural representation of these complex structures is a task graph. Over years, more and more expressive graph-based task models are proposed to precisely describe complex embedded real-time systems [11], [5], [2], [3], [4], [14], [15].…”

Section: Introductionmentioning

confidence: 99%

Approximate Response Time Analysis of Real-Time Task Graphs

Guan

Stigge

et al. 2014

2014 IEEE Real-Time Systems Symposium

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The response time analysis problem is intractable for most existing real-time task models, except the simplest ones. Exact solutions for this problem in general have exponential complexity, and may run into scalability problems for large-scale task systems. In this paper, we study approximate analysis for static-priority scheduling of the Digraph Real-Time task model, which is a generalization of most existing graph-based real-time task models. We present two approximate analysis methods RBF and IBF, both of which have pseudo-polynomial complexity. We quantitatively evaluate their analysis precision using the metric speedup factor. We prove that RBF has a speedup factor of 2, and this is tight even for dual-task systems. The speedup factor of IBF is an increasing function with respect to k, the number of interfering tasks. This function converges to 2 as k approaches infinity and equals 1 when k = 1, implying that the IBF analysis is exact for dual-task systems. We also conduct simulation experiments to evaluate the precision and efficiency of RBF and IBF with randomly generated task sets. Results show that the proposed approximate analysis methods have very high efficiency with low precision loss.

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“…It has been shown that for EDF, schedulability of DRT task sets can be checked in pseudo-polynomial time [2]. Even for an extension of DRT tasks with global timing constraints, this problem has been shown to be tractable [6].…”

Section: B Schedulabilitymentioning

confidence: 99%

“…It models each task with a directed graph in which vertices represent job releases and edges represent branching structures and inter-release delays. A recent extension to this model with global timing constraints [6] shows the tractability borderline regarding schedulability with dynamic priority schedulers.…”

Section: A Prior Workmentioning

confidence: 99%

Hardness Results for Static Priority Real-Time Scheduling

Stigge

2012

2012 24th Euromicro Conference on Real-Time Systems

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Abstract-Real-time systems are often modeled as a collection of tasks, describing the structure of the processor's workload. In the literature, task-models of different expressiveness have been developed, ranging from the traditional periodic task model to highly expressive graph-based models.For dynamic priority schedulers, it has been shown that the schedulability problem can be solved efficiently, even for graphbased models. However, the situation is less clear for the case of static priority schedulers. It has been believed that the problem can be solved in pseudo-polynomial time for the generalized multiframe model (GMF). The GMF model constitutes a compromise in expressiveness by allowing cycling through a static list of behaviors, but disallowing branching. Further, the problem complexity for more expressive models has been unknown so far.In this paper, we show that previous results claiming that a precise and efficient test exists are wrong, giving a counterexample. We prove that the schedulability problem for GMF models (and thus also all more expressive models) using static priority schedulers is in fact coNP-hard in the strong sense. Our result thus establishes the fundamental hardness of analyzing static priority real-time scheduling, in contrast to its dynamic priority counterpart of pseudo-polynomial complexity.

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On the Tractability of Digraph-Based Task Models

Cited by 31 publications

References 10 publications

Schedulability tests for tasks with Variable Rate-dependent Behaviour under fixed priority scheduling

Schedulability tests for tasks with Variable Rate-dependent Behaviour under fixed priority scheduling

Approximate Response Time Analysis of Real-Time Task Graphs

Hardness Results for Static Priority Real-Time Scheduling

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