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

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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.

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Notes

  1. The exclusion window of a job is the time interval between its release time and the earliest possible release time of the next job from the same task. In the GMF model, this window has length \(P^T_i\) for jobs released by frame i of task T.

  2. A cycle graph is a graph consisting of one single cycle, i.e., one closed chain.

  3. The name “non-cyclic RRT” can be a bit misleading. The behavior of a non-cyclic RRT task is cyclic, in the sense that the source vertex is visited repeatedly. However, in comparison to the RRT model, the behavior is non-periodic, in the sense that revisits of the source vertex may happen in different time intervals.

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Acknowledgments

The authors would like to thank the anonymous reviewers of the Real-Time Systems journal for their constructive comments on an earlier manuscript of this article.

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  1. Department of Information Technology, Uppsala University, Box 337, 751 05, Uppsala, Sweden

    Martin Stigge & Wang Yi

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  1. Martin Stigge
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Correspondence to Martin Stigge.

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Stigge, M., Yi, W. Graph-based models for real-time workload: a survey. Real-Time Syst 51, 602–636 (2015). https://doi.org/10.1007/s11241-015-9234-z

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