Intractability Issues in Mixed-Criticality Scheduling

Authors Kunal Agrawal , Sanjoy Baruah

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Kunal Agrawal
  • Washington University in St. Louis, St. Louis, MO, USA
Sanjoy Baruah
  • Washington University in St. Louis, St. Louis, MO, USA

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Kunal Agrawal and Sanjoy Baruah. Intractability Issues in Mixed-Criticality Scheduling. In 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 106, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


In seeking to develop mixed-criticality scheduling algorithms, one encounters challenges arising from two sources. First, mixed-criticality scheduling is an inherently an on-line problem in that scheduling decisions must be made without access to all the information that is needed to make such decisions optimally - such information is only revealed over time. Second, many fundamental mixed-criticality schedulability analysis problems are computationally intractable - NP-hard in the strong sense - but we desire to solve these problems using algorithms with polynomial or pseudo-polynomial running time. While these two aspects of intractability are traditionally studied separately in the theoretical computer science literature, they have been considered in an integrated fashion in mixed-criticality scheduling theory. In this work we seek to separate out the effects of being inherently on-line, and being computationally intractable, on the overall intractability of mixed-criticality scheduling problems. Speedup factor is widely used as quantitative metric of the effectiveness of mixed-criticality scheduling algorithms; there has recently been a bit of a debate regarding the appropriateness of doing so. We provide here some additional perspective on this matter: we seek to better understand its appropriateness as well as its limitations in this regard by examining separately how the on-line nature of some mixed-criticality problems, and their computational complexity, contribute to the speedup factors of two widely-studied mixed-criticality scheduling algorithms.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • mixed-criticality scheduling
  • speedup factor
  • competitive ratio
  • approximation ratio
  • NP-completeness results
  • sporadic tasks


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