On uses of extreme value theory fit for industrial-quality WCET analysis

Over the last few years, considerable interest has arisen in measurement-based probabilistic timing analysis. The term MBPTA has been used to indistinctly refer to a variety of different applications of Extreme Value Theory (EVT) to the timing analysis problem. The successful application of MBPTA techniques to a score of case studies has not fully dispelled the concerns that industrial stakeholders had with the quality of the computed bounds, hence ultimately with their industrial viability. Placing focus on the MBPTA methods and techniques developed in the PROARTIS and PROXIMA projects, collectively referred to as proMBPTA, we discuss the main misconceptions and pitfalls that can prevent a sound application of EVT-based WCET analysis. Using a combination of arguments and support examples, we show that proMBPTA is a rigorous process, fully amenable to sound and sustainable industrial use.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant TIN2015-65316-P and the HiPEAC Network of Excellence. Jaume Abella has been partially supported by the MINECO under Ramon y Cajal grant RYC-2013-14717. Authors also thank George Lima for his feedback on this manuscript.Peer ReviewedPostprint (author's final draft

Software timing analysis for complex hardware with survivability and risk analysis

The increasing automation of safety-critical real-time systems, such as those in cars and planes, leads, to more complex and performance-demanding on-board software and the subsequent adoption of multicores and accelerators. This causes software's execution time dispersion to increase due to variable-latency resources such as caches, NoCs, advanced memory controllers and the like. Statistical analysis has been proposed to model the Worst-Case Execution Time (WCET) of software running such complex systems by providing reliable probabilistic WCET (pWCET) estimates. However, statistical models used so far, which are based on risk analysis, are overly pessimistic by construction. In this paper we prove that statistical survivability and risk analyses are equivalent in terms of tail analysis and, building upon survivability analysis theory, we show that Weibull tail models can be used to estimate pWCET distributions reliably and tightly. In particular, our methodology proves the correctness-by-construction of the approach, and our evaluation provides evidence about the tightness of the pWCET estimates obtained, which allow decreasing them reliably by 40% for a railway case study w.r.t. state-of-the-art exponential tails.This work is a collaboration between Argonne National Laboratory and the Barcelona Supercomputing Center within the Joint Laboratory for Extreme-Scale Computing. This research is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research, under contract number DE-AC02- 06CH11357, program manager Laura Biven, and by the Spanish Government (SEV2015-0493), by the Spanish Ministry of Science and Innovation (contract TIN2015-65316-P), by Generalitat de Catalunya (contract 2014-SGR-1051).Peer ReviewedPostprint (author's final draft

Measurement-Based Worst-Case Execution Time Estimation Using the Coefficient of Variation

Extreme Value Theory (EVT) has been historically used in domains such as finance and hydrology to model worst-case events (e.g., major stock market incidences). EVT takes as input a sample of the distribution of the variable to model and fits the tail of that sample to either the Generalised Extreme Value (GEV) or the Generalised Pareto Distribution (GPD). Recently, EVT has become popular in real-time systems to derive worst-case execution time (WCET) estimates of programs. However, the application of EVT is not straightforward and requires a detailed analysis of, and customisation for, the particular problem at hand. In this article, we tailor the application of EVT to timing analysis. To that end, (1) we analyse the response time of different hardware resources (e.g., cache memories) and identify those that may lead to radically different types of execution time distributions. (2) We show that one of these distributions, known as mixture distribution, causes problems in the use of EVT. In particular, mixture distributions challenge not only properly selecting GEV/GPD parameters (i.e., location, scale and shape) but also determining the size of the sample to ensure that enough tail values are passed to EVT and that only tail values are used by EVT to fit GEV/GPD. Failing to select these parameters has a negative impact on the quality of the derived WCET estimates. We tackle these problems, by (3) proposing Measurement-Based Probabilistic Timing Analysis using the Coefficient of Variation (MBPTA-CV), a new mixture-distribution aware, WCET-suited MBPTA method that builds on recent EVT developments in other fields (e.g., finance) to automatically select the distribution parameters that best fit the maxima of the observed execution times. Our results on a simulation environment and a real board show that MBPTA-CV produces high-quality WCET estimates.The research leading to these results has received funding from the European Community’s FP7 [FP7/2007- 2013] under the PROXIMA Project (www.proxima-project.eu), grant 611085. This work has also been par- tially supported by the Spanish Ministry of Science and Innovation under grant TIN2015-65316-P and the HiPEAC Network of Excellence. Jaume Abella was partially supported by the Ministry of Economy and Competitiveness under Ramon y Cajal postdoctoral fellowship RYC-2013-14717.Peer ReviewedPostprint (author's final draft

Probabilistic Worst-Case Timing Analysis: Taxonomy and Comprehensive Survey

"© ACM, 2019. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM Computing Surveys, {VOL 52, ISS 1, (February 2019)} https://dl.acm.org/doi/10.1145/3301283"[EN] The unabated increase in the complexity of the hardware and software components of modern embedded real-time systems has given momentum to a host of research in the use of probabilistic and statistical techniques for timing analysis. In the last few years, that front of investigation has yielded a body of scientific literature vast enough to warrant some comprehensive taxonomy of motivations, strategies of application, and directions of research. This survey addresses this very need, singling out the principal techniques in the state of the art of timing analysis that employ probabilistic reasoning at some level, building a taxonomy of them, discussing their relative merit and limitations, and the relations among them. In addition to offering a comprehensive foundation to savvy probabilistic timing analysis, this article also identifies the key challenges to be addressed to consolidate the scientific soundness and industrial viability of this emerging field.This work has also been partially supported by the Spanish Ministry of Science and Innovation under grant TIN2015-65316-P, the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 772773), and the HiPEAC Network of Excellence. Jaume Abella was partially supported by the Ministry of Economy and Competitiveness under a Ramon y Cajal postdoctoral fellowship (RYC-2013-14717). Enrico Mezzetti has been partially supported by the Spanish Ministry of Economy and Competitiveness under Juan de la Cierva-Incorporación postdoctoral fellowship No. IJCI-2016-27396.Cazorla, FJ.; Kosmidis, L.; Mezzetti, E.; Hernández Luz, C.; Abella, J.; Vardanega, T. (2019). Probabilistic Worst-Case Timing Analysis: Taxonomy and Comprehensive Survey. ACM Computing Surveys. 52(1):1-35. https://doi.org/10.1145/3301283S13552

Statistical-Based WCET Estimation and Validation

In this paper we present a measurement-based approach that produces both a WCET (Worst Case Execution Time) estimate, and a prediction of the probability that a future execution time will exceed our estimate. Our statistical-based approach uses extreme value theory to build a model of the tail behavior of the measured execution time value. We validate our approach using an industrial data set comprised of over 150 sampled components and nearly 200 million sample execution times. Each trace is divided into two segments, with one used to make the WCET estimate, and the second used check our prediction of the fraction of future execution time samples that exceed our WCET estimate. We show that compared to WCET estimates derived from the worst-case observed time, our WCET estimates significantly improve the ability to predict the probability that our WCET estimate is exceeded

On the limits of probabilistic timing analysis

Over the last years, we are witnessing the steady and rapid growth of Critica! Real-Time Embedded Systems (CRTES) industries, such as automotive and aerospace. Many of the increasingly-complex CRTES' functionalities that are currently implemented with mechanical means are moving towards to an electromechanical implementation controlled by critica! software. This trend results in a two-fold consequence. First, the size and complexity of critical-software increases in every new embedded product. And second, high-performance hardware features like caches are more frequently used in real-time processors. The increase in complexity of CRTES challenges the validation and verification process, a necessary step to certify that the system is safe for deployment. Timing validation and verification includes the computation of the Worst-Case Execution Time (WCET) estimates, which need to be trustworthy and tight. Traditional timing analysis are challenged by the use of complex hardware/software, resulting in low-quality WCET estimates, which tend to add significant pessimism to guarantee estimates' trustworthiness. This calls for new solutions that help tightening WCET estimates in a safe manner. In this Thesis, we investigate the novel Measurement-Based Probabilistic Timing Analysis (MBPTA), which in its original version already shows potential to deliver trustworthy and tight WCETs for tasks running on complex systems. First, we propose a methodology to assess and ensure that ali cache memory layouts, which can significantly impact WCET, have been adequately factored in the WCET estimation process. Second, we provide a solution to achieve simultaneously cache representativeness and full path coverage. This solution provides evidence proving that WCET estimates obtained are valid for ali program execution paths regardless of how code and data are laid out in the cache. Lastly, we analyse and expose the main misconceptions and pitfalls that can prevent a sound application of WCET analysis based on extreme value theory, which is used as part of MBPTA.En los últimos años, se ha podido observar un crecimiento rápido y sostenido de la industria de los sistemas embebidos críticos de tiempo real (abreviado en inglés CRTES}, como por ejemplo la industria aeronáutica o la automovilística. En un futuro cercano, muchas de las funcionalidades complejas que actualmente se están implementando a través de sistemas mecánicos en los CRTES pasarán a ser controladas por software crítico. Esta tendencia tiene dos consecuencias claras. La primera, el tamaño y la complejidad del software se incrementará en cada nuevo producto embebido que se lance al mercado. La segunda, las técnicas hardware destinadas a alto rendimiento (por ejemplo, memorias caché) serán usadas más frecuentemente en los procesadores de tiempo real. El incremento en la complejidad de los CRTES impone un reto en los procesos de validación y verificación de los procesadores, un paso imprescindible para certificar que los sistemas se pueden comercializar de forma segura. La validación y verificación del tiempo de ejecución incluye la estimación del tiempo de ejecución en el peor caso (abreviado en inglés WCET}, que debe ser precisa y certera. Desafortunadamente, los procesos tradicionales para analizar el tiempo de ejecución tienen problemas para analizar las complejas combinaciones entre el software y el hardware, produciendo estimaciones del WCET de mala calidad y conservadoras. Para superar dicha limitación, es necesario que florezcan nuevas técnicas que ayuden a proporcionar WCET más precisos de forma segura y automatizada. En esta Tesis se profundiza en la investigación referente al análisis probabilístico de tiempo de ejecución basado en medidas (abreviado en inglés MBPTA), cuyas primeras implementaciones muestran potencial para obtener un WCET preciso y certero en tareas ejecutadas en sistemas complejos. Primero, se propone una metodología para certificar que todas las distribuciones de la memoria caché, una de las estructuras más complejas de los CRTES, han sido contabilizadas adecuadamente durante el proceso de estimación del WCET. Segundo, se expone una solución para conseguir a la vez representatividad en la memoria caché y cobertura total en caminos críticos del programa. Dicha solución garantiza que la estimación WCET obtenida es válida para todos los caminos de ejecución, independientemente de como el código y los datos se guardan en la memoria caché. Finalmente, se analizan y discuten los mayores malentendidos y obstáculos que pueden prevenir la aplicabilidad del análisis de WCET basado en la teoría de valores extremos, la cual forma parte del MBPTA.Postprint (published version

Boosting Guaranteed Performance in Wormhole NoCs with Probabilistic Timing Analysis

Wormhole-based NoCs (wNoCs) are widely accepted in high-performance domains as the most appropriate solution to interconnect an increasing number of cores in the chip. However, wNoCs suitability in the context of critical real-time applications has not been demonstrated yet. In this paper, in the context of probabilistic timing analysis (PTA), we propose a PTA-compatible wNoC design that provides tight time-composable contention bounds. The proposed wNoC design builds on PTA ability to reason in probabilistic terms about hardware events impacting execution time (e.g. wNoC contention), discarding those sequences of events occurring with a negligible low probability. This allows our wNoC design to deliver improved guaranteed performance. ur results show that WCET estimates of applications running on top of probabilistic wNoCs are reduced by 40% and 75% on average for 4x4 and 6x6 wNoC setups respectively when compared against deterministic wNoCs.This work has also been partially supported by the Spanish Ministry of Science and Innovation under grant TIN2015-65316-P and the HiPEAC Network of Excellence. Mladen Slijepcevic is funded by the Obra Social Fundación la Caixa under grant Doctorado “la Caixa” - Severo Ochoa. Carles Hernández is jointly funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and FEDER funds through grant TIN2014-60404-JIN. Jaume Abella has been partially supported by the MINECO under Ramon y Cajal postdoctoral fellowship number RYC-2013-14717.Peer ReviewedPostprint (author's final draft

Using Markov’s inequality with power-of-k function for probabilistic WCET estimation

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.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant PID2019-110854RB-I00 / AEI / 10.13039/501100011033 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 772773).Peer ReviewedPostprint (published version

A Survey of Probabilistic Timing Analysis Techniques for Real-Time Systems

This survey covers probabilistic timing analysis techniques for real-time systems. It reviews and critiques the key results in the field from its origins in 2000 to the latest research published up to the end of August 2018. The survey provides a taxonomy of the different methods used, and a classification of existing research. A detailed review is provided covering the main subject areas: static probabilistic timing analysis, measurement-based probabilistic timing analysis, and hybrid methods. In addition, research on supporting mechanisms and techniques, case studies, and evaluations is also reviewed. The survey concludes by identifying open issues, key challenges and possible directions for future research

On the use of probabilistic worst-case execution time estimation for parallel applications in high performance systems

Some high performance computing (HPC) applications exhibit increasing real-time requirements, which call for effective means to predict their high execution times distribution. This is a new challenge for HPC applications but a well-known problem for real-time embedded applications where solutions already exist, although they target low-performance systems running single-threaded applications. In this paper, we show how some performance validation and measurement-based practices for real-time execution time prediction can be leveraged in the context of HPC applications on high-performance platforms, thus enabling reliable means to obtain real-time guarantees for those applications. In particular, the proposed methodology uses coordinately techniques that randomly explore potential timing behavior of the application together with Extreme Value Theory (EVT) to predict rare (and high) execution times to, eventually, derive probabilistic Worst-Case Execution Time (pWCET) curves. We demonstrate the effectiveness of this approach for an acoustic wave inversion application used for geophysical explorationThis research was funded by the Horizon 2020 Framework Programme, grant number 801137, project RECIPEPeer ReviewedPostprint (published version