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

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