Efficiently Approximating the Probability of Deadline Misses in Real-Time Systems

Authors Georg von der Brüggen , Nico Piatkowski , Kuan-Hsun Chen , Jian-Jia Chen , Katharina Morik

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Author Details

Georg von der Brüggen
  • Department of Computer Science, TU Dortmund University, Germany
Nico Piatkowski
  • Department of Computer Science, TU Dortmund University, Germany
Kuan-Hsun Chen
  • Department of Computer Science, TU Dortmund University, Germany
Jian-Jia Chen
  • Department of Computer Science, TU Dortmund University, Germany
Katharina Morik
  • Department of Computer Science, TU Dortmund University, Germany

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Georg von der Brüggen, Nico Piatkowski, Kuan-Hsun Chen, Jian-Jia Chen, and Katharina Morik. Efficiently Approximating the Probability of Deadline Misses in Real-Time Systems. In 30th Euromicro Conference on Real-Time Systems (ECRTS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 106, pp. 6:1-6:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


This paper explores the probability of deadline misses for a set of constrained-deadline sporadic soft real-time tasks on uniprocessor platforms. We explore two directions to evaluate the probability whether a job of the task under analysis can finish its execution at (or before) a testing time point t. One approach is based on analytical upper bounds that can be efficiently computed in polynomial time at the price of precision loss for each testing point, derived from the well-known Hoeffding's inequality and the well-known Bernstein's inequality. Another approach convolutes the probability efficiently over multinomial distributions, exploiting a series of state space reduction techniques, i.e., pruning without any loss of precision, and approximations via unifying equivalent classes with a bounded loss of precision. We demonstrate the effectiveness of our approaches in a series of evaluations. Distinct from the convolution-based methods in the literature, which suffer from the high computation demand and are applicable only to task sets with a few tasks, our approaches can scale reasonably without losing much precision in terms of the derived probability of deadline misses.

Subject Classification

ACM Subject Classification
  • Computer systems organization → Real-time systems
  • deadline miss probability
  • multinomial-based approach
  • analytical bound


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