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Continuous-Emission Markov Models for Real-Time Applications: Bounding Deadline Miss Probabilities


Publication Type:

Conference/Workshop Paper


29th IEEE Real-Time and Embedded Technology and Applications Symposium




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 Constant Bandwidth 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.


author = {Anna Friebe and Filip Markovic and Alessandro Papadopoulos and Thomas Nolte},
title = {Continuous-Emission Markov Models for Real-Time Applications: Bounding Deadline Miss Probabilities},
pages = {14--26},
month = {May},
year = {2023},
booktitle = {29th IEEE Real-Time and Embedded Technology and Applications Symposium},
url = {}