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

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

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ACM Subject Classification
  • Computer systems organization → Real-time system architecture
  • Mathematics of computing → Probability and statistics
Keywords
  • WCET
  • EVT

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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) https://doi.org/10.4230/LIPIcs.ECRTS.2025.20

Author Details

Blau Manau
  • Barcelona Supercomputing Center (BSC), Spain
Sergi Vilardell
  • Barcelona Supercomputing Center (BSC), Spain
Isabel Serra
  • Universitat Autònoma de Barcelona (UAB), Spain
Enrico Mezzetti
  • Barcelona Supercomputing Center (BSC), Spain
Jaume Abella
  • Barcelona Supercomputing Center (BSC), Spain
Francisco J. Cazorla
  • Barcelona Supercomputing Center (BSC), Spain

Funding

The research leading to these results has received funding from the European Union’s Horizon Europe Programme under the SAFEXPLAIN Project (www.safexplain.eu), grant agreement num. 101069595 and project PLEC2023-010240 funded by MICIU/AEI/10.13039/501100011033 (CAPSUL-IA). Authors also appreciate the support given to the Research Group SSAS (Code: 2021 SGR 00637) by the Research and University Department of the Generalitat de Catalunya. This work is partially supported by the Spanish MICIU with project PID2022-137414OB-I00.

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