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Continuous-Emission Markov Models for Real-Time Applications: Bounding Deadline Miss Probabilities
Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems.
Mälardalen University, School of Innovation, Design and Engineering, Innovation and Product Realisation. Max Planck Institute for Software Systems (MPI-SWS), Germany.ORCID iD: 0000-0002-3210-3819
Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems.ORCID iD: 0000-0002-1364-8127
Mälardalen University, School of Innovation, Design and Engineering, Embedded Systems.ORCID iD: 0000-0001-6132-7945
2023 (English)In: Proc. IEEE Real Time Embedded Technol. Appl. Symp. RTAS, Institute of Electrical and Electronics Engineers Inc. , 2023, p. 14-26Conference paper, Published paper (Refereed)
Abstract [en]

Probabilistic approaches have gained attention over the past decade, providing a modeling framework that enables less pessimistic analysis of real-time systems. Among the different proposed approaches, Markov chains have been shown effective for analyzing real-time systems, particularly in estimating the pending workload distribution and deadline miss probability. However, the state-of-the-art mainly considered discrete emission distributions without investigating the benefits of continuous ones. In this paper, we propose a method for analyzing the workload probability distribution and bounding the deadline miss probability for a task executing in a reservation-based server, where execution times are described by a Markov model with Gaussian emission distributions. The evaluation is performed for the timing behavior of a Kalman filter for Furuta pendulum control. Deadline miss probability bounds are derived with a workload accumulation scheme. The bounds are compared to 1) measured deadline miss ratios of tasks running under the Linux Constant Bandwidth Server with SCHED-DEADLINE, 2) estimates derived from a Markov Model with discrete-emission distributions (PROSIT), 3) simulation-based estimates, and 4) an estimate assuming independent execution times. The results suggest that the proposed method successfully upper bounds actual deadline miss probabilities. Compared to the discrete-emission counterpart, the computation time is independent of the range of the execution times under analysis, and resampling is not required.

Place, publisher, year, edition, pages
Institute of Electrical and Electronics Engineers Inc. , 2023. p. 14-26
Keywords [en]
Deadline Miss Probability, Hidden Markov Model, Probabilistic Schedulability Analysis, Real-time systems, Computer operating systems, Continuous time systems, Hidden Markov models, Interactive computer systems, Probability distributions, Continuous emission, Emission distribution, Hidden-Markov models, Markov modeling, Probabilistic schedulability analyse, Probabilistics, Real - Time system, Real-time application, Schedulability analysis, Real time systems
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:mdh:diva-63914DOI: 10.1109/RTAS58335.2023.00009ISI: 001017772500002Scopus ID: 2-s2.0-85164535864ISBN: 9798350321760 (print)OAI: oai:DiVA.org:mdh-63914DiVA, id: diva2:1784496
Conference
Proceedings of the IEEE Real-Time and Embedded Technology and Applications Symposium, RTAS
Available from: 2023-07-26 Created: 2023-07-26 Last updated: 2023-12-04Bibliographically approved

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Friebe, AnnaMarkovic, FilipPapadopoulos, AlessandroNolte, Thomas

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