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DOI: 10.4230/LIPIcs.ECRTS.2025.20

Detecting Low-Density Mixtures in High-Quantile Tails for pWCET Estimation

Authors: Blau Manau, Sergi Vilardell, Isabel Serra, Enrico Mezzetti, Jaume Abella, and Francisco J. Cazorla

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

Abstract

The variability arising from sophisticated hardware and software solutions in cutting-edge embedded products causes software to exhibit complex execution time distributions. Mixture distributions can happen, with different density (weight), as a result of inherent different features in the execution platform and multiple operational scenarios. In the context of probabilistic WCET (pWCET) analysis based on Extreme Value Theory (EVT), where identical distribution is a pre-requisite, mixtures are typically intercepted by applying stationarity tests on the full sample. Those tests, however, are instructed to detect only mixtures with sufficiently high probability (weight) and disregard low-density mixtures (which are unlikely to be preserved in the high-quantile tail of the sample) as they would prevent any form of stationarity. Nonetheless, low-density mixture distributions can persist and even exacerbate in the tail, and, when not considered, they can impair pWCET estimation in EVT-based approaches, leading to overly pessimistic or optimistic bounds. In this work, we propose TailID, an iterative point-wise approach that builds on the asymptotic convergence of the Maximum Likelihood Estimator (MLE) of the Extreme Value Index (EVI) parameter ξ to detect low-density mixture distributions on high-quantile tails and use this information to steer EVT tail selection. The benefits of the proposed method are assessed on synthetic mixture distributions and real data collected on an industrially representative embedded platform.

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Blau Manau, Sergi Vilardell, Isabel Serra, Enrico Mezzetti, Jaume Abella, and Francisco J. Cazorla. Detecting Low-Density Mixtures in High-Quantile Tails for pWCET Estimation. In 37th Euromicro Conference on Real-Time Systems (ECRTS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 335, pp. 20:1-20:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{manau_et_al:LIPIcs.ECRTS.2025.20,
  author =	{Manau, Blau and Vilardell, Sergi and Serra, Isabel and Mezzetti, Enrico and Abella, Jaume and Cazorla, Francisco J.},
  title =	{{Detecting Low-Density Mixtures in High-Quantile Tails for pWCET Estimation}},
  booktitle =	{37th Euromicro Conference on Real-Time Systems (ECRTS 2025)},
  pages =	{20:1--20:25},
  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.2025.20},
  URN =		{urn:nbn:de:0030-drops-235982},
  doi =		{10.4230/LIPIcs.ECRTS.2025.20},
  annote =	{Keywords: WCET, EVT}
}

Document

DOI: 10.4230/LIPIcs.ECRTS.2022.20

Using Markov’s Inequality with Power-Of-k Function for Probabilistic WCET Estimation

Authors: Sergi Vilardell, Isabel Serra, Enrico Mezzetti, Jaume Abella, Francisco J. Cazorla, and Joan del Castillo

Published in: LIPIcs, Volume 231, 34th Euromicro Conference on Real-Time Systems (ECRTS 2022)

Abstract

Deriving WCET estimates for software programs with probabilistic means (a.k.a. pWCET estimation) has received significant attention during last years as a way to deal with the increased complexity of the processors used in real-time systems. Many works build on Extreme Value Theory (EVT) that is fed with a sample of the collected data (execution times). In its application, EVT carries two sources of uncertainty: the first one that is intrinsic to the EVT model and relates to determining the subset of the sample that belongs to the (upper) tail, and hence, is actually used by EVT for prediction; and the second one that is induced by the sampling process and hence is inherent to all sample-based methods. In this work, we show that Markov’s inequality can be used to obtain provable trustworthy probabilistic bounds to the tail of a distribution without incurring any model-intrinsic uncertainty. Yet, it produces pessimistic estimates that we shave substantially by proposing the use of a power-of-k function instead of the default identity function used by Markov’s inequality. Lastly, we propose a method to deal with sampling uncertainty for Markov’s inequality that consistently improves EVT estimates on synthetic and real data obtained from a railway application.

Cite as

Sergi Vilardell, Isabel Serra, Enrico Mezzetti, Jaume Abella, Francisco J. Cazorla, and Joan del Castillo. Using Markov’s Inequality with Power-Of-k Function for Probabilistic WCET Estimation. In 34th Euromicro Conference on Real-Time Systems (ECRTS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 231, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{vilardell_et_al:LIPIcs.ECRTS.2022.20,
  author =	{Vilardell, Sergi and Serra, Isabel and Mezzetti, Enrico and Abella, Jaume and Cazorla, Francisco J. and del Castillo, Joan},
  title =	{{Using Markov’s Inequality with Power-Of-k Function for Probabilistic WCET Estimation}},
  booktitle =	{34th Euromicro Conference on Real-Time Systems (ECRTS 2022)},
  pages =	{20:1--20:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-239-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{231},
  editor =	{Maggio, Martina},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2022.20},
  URN =		{urn:nbn:de:0030-drops-163377},
  doi =		{10.4230/LIPIcs.ECRTS.2022.20},
  annote =	{Keywords: Markov’s inequality, probabilistic time estimates, probabilistic WCET, Extreme Value Theory}
}

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Documents authored by Vilardell, Sergi

Detecting Low-Density Mixtures in High-Quantile Tails for pWCET Estimation

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Using Markov’s Inequality with Power-Of-k Function for Probabilistic WCET Estimation

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