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Theoretical Foundations of Utility Accrual for Real-Time Systems

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

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Subject Classification

ACM Subject Classification
  • Computer systems organization → Embedded software
  • Computer systems organization → Real-time system specification
Keywords
  • Soft Real-Time Systems
  • Utility Accrual
  • Markov Chains
  • Dismiss Points

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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.

Cite As Get BibTex

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) https://doi.org/10.4230/LIPIcs.ECRTS.2025.17

Author Details

Jian-Jia Chen
  • TU Dortmund, Germany
Junjie Shi
  • TU Dortmund, Germany
Mario Günzel
  • TU Dortmund, Germany
Georg von der Brüggen
  • TU Dortmund, Germany
Kuan-Hsun Chen
  • University of Twente, The Netherlands
Peter Bella
  • TU Dortmund, Germany

Funding

This result is part of a project (PropRT) that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 865170).

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