Execution time distributions in embedded safety-critical systems using extreme value theory

Several techniques have been proposed to upper-bound the worst-case execution time behaviour of programs in the domain of critical real-time embedded systems. These computing systems have strong requirements regarding the guarantees that the longest execution time a program can take is bounded. Some of those techniques use extreme value theory (EVT) as their main prediction method. In this paper, EVT is used to estimate a high quantile for different types of execution time distributions observed for a set of representative programs for the analysis of automotive applications. A major challenge appears when the dataset seems to be heavy tailed, because this contradicts the previous assumption of embedded safety-critical systems. A methodology based on the coefficient of variation is introduced for a threshold selection algorithm to determine the point above which the distribution can be considered generalised Pareto distribution. This methodology also provides an estimation of the extreme value index and high quantile estimates. We have applied these methods to execution time observations collected from the execution of 16 representative automotive benchmarks to predict an upper-bound to the maximum execution time of this program. Several comparisons with alternative approaches are discussed.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (grant agreement 611085). This study was also partially supported by the Spanish Ministry of Science and Innovation under grants MTM2012-31118 (2013-2015) and TIN2015-65316-P. Jaume Abella is partially supported by the Ministry of Economy and Competitiveness under Ramon y Cajal postdoctoral fellowship number RYC-2013- 14717.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

pTNoC: Probabilistically time-analyzable tree-based NoC for mixed-criticality systems

The use of networks-on-chip (NoC) in real-time safety-critical multicore systems challenges deriving tight worst-case execution time (WCET) estimates. This is due to the complexities in tightly upper-bounding the contention in the access to the NoC among running tasks. Probabilistic Timing Analysis (PTA) is a powerful approach to derive WCET estimates on relatively complex processors. However, so far it has only been tested on small multicores comprising an on-chip bus as communication means, which intrinsically does not scale to high core counts. In this paper we propose pTNoC, a new tree-based NoC design compatible with PTA requirements and delivering scalability towards medium/large core counts. pTNoC provides tight WCET estimates by means of asymmetric bandwidth guarantees for mixed-criticality systems with negligible impact on average performance. Finally, our implementation results show the reduced area and power costs of the pTNoC.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (www.proxima-project.eu), grant agreement no 611085. 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 Hern´andez 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

Modelling probabilistic cache representativeness in the presence of arbitrary access patterns

Measurement-Based Probabilistic Timing Analysis (MBPTA) is a promising powerful industry-friendly method to derive worst-case execution time (WCET) estimates as needed for critical real-time embedded systems. MBPTA performs several (R) runs of the program on the target platform collecting the execution times in each run. MBPTA builds a probabilistic representativeness argument on whether those events with high impact on execution time, such as cache misses, arise on the runs made at analysis time so that their impact on execution time is captured. So far only events occurring in cache memories have been shown to challenge providing such representativeness argument. In this context, this paper introduces a representativeness validation method (RVS) to assess the probabilistic representativeness of MBPTA’s execution time observations in terms of cache behaviour. RVS resorts to cache simulation to predict worst-case miss scenarios that can appear during the deployment phase. RVS also constructs a probabilistic Worst-Case Miss Count curve based on the miss-counts captured in the R runs. If that curve upperbounds the impact of the predicted cache worst-case scenarios, R is deemed as a sufficient number of runs for which pWCET estimates can be reliably derived. Otherwise, the user is requested to perform more runs until all cache scenarios of interest are captured.Peer ReviewedPostprint (author's final draft

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

A confidence assessment of WCET estimates for software time randomized caches

Obtaining Worst-Case Execution Time (WCET) estimates is a required step in real-time embedded systems during software verification. Measurement-Based Probabilistic Timing Analysis (MBPTA) aims at obtaining WCET estimates for industrial-size software running upon hardware platforms comprising high-performance features. MBPTA relies on the randomization of timing behavior (functional behavior is left unchanged) of hard-to-predict events like the location of objects in memory — and hence their associated cache behavior — that significantly impact software's WCET estimates. Software time-randomized caches (sTRc) have been recently proposed to enable MBPTA on top of Commercial off-the-shelf (COTS) caches (e.g. modulo placement). However, some random events may challenge MBPTA reliability on top of sTRc. In this paper, for sTRc and programs with homogeneously accessed addresses, we determine whether the number of observations taken at analysis, as part of the normal MBPTA application process, captures the cache events significantly impacting execution time and WCET. If this is not the case, our techniques provide the user with the number of extra runs to perform to guarantee that cache events are captured for a reliable application of MBPTA. Our techniques are evaluated with synthetic benchmarks and an avionics application.The research leading to these results has received funding from the European Community’s Seventh Framework Programme [FP7/2007-2013] under the PROXIMA Project (www.proxima-project.eu), grant agreement no 611085. This work has also been partially supported by the Spanish Ministry of Science and Innovation under grant TIN2015-65316, the HiPEAC Network of Excellence, and COST Action IC1202: Timing Analysis On Code-Level (TACLe). Jaume Abella has been partially supported by the Ministry of Economy and Competitiveness under Ramon y Cajal postdoctoral fellowship number RYC-2013-14717.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

Modelling and predicting extreme behavior in critical real-time systems with advanced statistics

In the last decade, the market for Critical Real-Time Embedded Systems (CRTES) has increased significantly. According to Global Markets Insight [1], the embedded systems market will reach a total size of US $258 billion in 2023 at an average annual growth rate of 5.6%. Their extensive use in domains such as automotive, aerospace and avionics industry demands ever increasing performance requirements [2]. To satisfy those requirements the CRTES industry has implemented more complex processors, a higher number of memory modules, and accelerators units. Thus the demanding performance requirements have led to a merge of CRTES with High Performance systems. All of these industries work within the framework of CRTES, which puts several restrictions in their design and implementation. Real Time systems require to deliver a response to an event in a restricted time frame or deadline. Real-time systems where missing a deadline provokes a total system failure (hard real-time systems) need satisfy certain guidelines and standards to show that they comply with test for functional and timing behaviour. These standards change depending on the industry, for instance the automotive industry follows ISO 26262 [3] and the aerospace industry follows DO-178C [4]. Researches have developed techniques to analyse the timing correctness in a CRTES. Here, we will expose how they perform on the estimation of the Worst-Case Execution Time (WCET). The WCET is the maximum time that a particular software takes to execute. Estimating its value is crucial from a timing analysis point of view. However there is still not a generalised precise and safe method to produce estimates of WCET [5]. In the CRTES the estimations of the WCET cannot be lower than the true WCET, as they are deemed unsafe; but they cannot exceed it by a significant margin, as they will be deemed pessimistic and impractical

On the Representativity of Execution Time Measurements: Studying Dependence and Multi-Mode Tasks

The Measurement-Based Probabilistic Timing Analysis (MBPTA) infers probabilistic Worst-Case Execution Time (pWCET) estimates from measurements of tasks execution times; the Extreme Value Theory (EVT) is the statistical tool that MBPTA applies for inferring worst-cases from observations/measurements of the actual task behavior. MBPTA and EVT capability of estimating safe/pessimistic pWCET rely on the quality of the measurements; in particular, execution time measurements have to be representative of the actual system execution conditions and have to cover multiple possible execution conditions. In this work, we investigate statistical dependences between execution time measurements and tasks with multiple runtime operational modes. In the first case, we outline the effects of dependences on the EVT applicability as well as on the quality of the pWCET estimates. In the second case, we propose the best approaches to account for the different task execution modes and guaranteeing safe pWCET estimates that cover them all. The solutions proposed are validated with test cases

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