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DOI: 10.4230/LIPIcs.ECRTS.2025.17

Theoretical Foundations of Utility Accrual for Real-Time Systems

Authors: Jian-Jia Chen, Junjie Shi, Mario Günzel, Georg von der Brüggen, Kuan-Hsun Chen, and Peter Bella

Published in: LIPIcs, Volume 335, 37th Euromicro Conference on Real-Time Systems (ECRTS 2025)

Abstract

Providing guaranteed quantification of properties of soft real-time systems is important in practice to ensure that a system performs correctly most of the time. We study utility accrual for real-time systems, in which the utility of a real-time job is defined as a time utility function with respect to its response time. Essentially, we answer the fundamental questions: Does the utility accrual of a periodic real-time task in the long run converge to a single value? If yes, to which value? We first show that concrete problem instances exist where evaluating the utility accrual by simulating the scheduling algorithm or conducting scheduling experiments in a long run is erroneous. Afterwards, we show how to construct a Markov chain to model the interactions between the scheduling policy, the probabilistic workload of a periodic real-time task, the service provided by the system to serve the task, and the effect on the utility accrual. For such a Markov chain, we also provide the theoretical fundamentals to determine whether the utility accrual converges in the long run and the derivation of the utility accrual if it converges.

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Jian-Jia Chen, Junjie Shi, Mario Günzel, Georg von der Brüggen, Kuan-Hsun Chen, and Peter Bella. Theoretical Foundations of Utility Accrual for Real-Time Systems. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 17:1-17:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chen_et_al:LIPIcs.ECRTS.2025.17,
  author =	{Chen, Jian-Jia and Shi, Junjie and G\"{u}nzel, Mario and von der Br\"{u}ggen, Georg and Chen, Kuan-Hsun and Bella, Peter},
  title =	{{Theoretical Foundations of Utility Accrual for Real-Time Systems}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{17:1--17:26},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-377-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{335},
  editor =	{Mancuso, Renato},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2025.17},
  URN =		{urn:nbn:de:0030-drops-235950},
  doi =		{10.4230/LIPIcs.ECRTS.2025.17},
  annote =	{Keywords: Soft Real-Time Systems, Utility Accrual, Markov Chains, Dismiss Points}
}

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Theoretical Foundations of Utility Accrual for Real-Time Systems

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