On the analysis of random replacement caches using static probabilistic timing methods for multi-path programs

Probabilistic hard real-time systems, based on hardware architectures that use a random replacement cache, provide a potential means of reducing the hardware over-provision required to accommodate pathological scenarios and the associated extremely rare, but excessively long, worst-case execution times that can occur in deterministic systems. Timing analysis for probabilistic hard real-time systems requires the provision of probabilistic worst-case execution time (pWCET) estimates. The pWCET distribution can be described as an exceedance function which gives an upper bound on the probability that the execution time of a task will exceed any given execution time budget on any particular run. This paper introduces a more effective static probabilistic timing analysis (SPTA) for multi-path programs. The analysis estimates the temporal contribution of an evict-on-miss, random replacement cache to the pWCET distribution of multi-path programs. The analysis uses a conservative join function that provides a proper over-approximation of the possible cache contents and the pWCET distribution on path convergence, irrespective of the actual path followed during execution. Simple program transformations are introduced that reduce the impact of path indeterminism while ensuring sound pWCET estimates. Evaluation shows that the proposed method is efficient at capturing locality in the cache, and substantially outperforms the only prior approach to SPTA for multi-path programs based on path merging. The evaluation results show incomparability with analysis for an equivalent deterministic system using an LRU cache. For some benchmarks the performance of LRU is better, while for others, the new analysis techniques show that random replacement has provably better performance

Resilient random modulo cache memories for probabilistically-analyzable real-time systems

Fault tolerance has often been assessed separately in safety-related real-time systems, which may lead to inefficient solutions. Recently, Measurement-Based Probabilistic Timing Analysis (MBPTA) has been proposed to estimate Worst-Case Execution Time (WCET) on high performance hardware. The intrinsic probabilistic nature of MBPTA-commpliant hardware matches perfectly with the random nature of hardware faults. Joint WCET analysis and reliability assessment has been done so far for some MBPTA-compliant designs, but not for the most promising cache design: random modulo. In this paper we perform, for the first time, an assessment of the aging-robustness of random modulo and propose new implementations preserving the key properties of random modulo, a.k.a. low critical path impact, low miss rates and MBPTA compliance, while enhancing reliability in front of aging by achieving a better – yet random – activity distribution across cache sets.Peer ReviewedPostprint (author's final draft

Toward Contention Analysis for Parallel Executing Real-Time Tasks

In measurement-based probabilistic timing analysis, the execution conditions imposed to tasks as measurement scenarios, have a strong impact to the worst-case execution time estimates. The scenarios and their effects on the task execution behavior have to be deeply investigated. The aim has to be to identify and to guarantee the scenarios that lead to the maximum measurements, i.e. the worst-case scenarios, and use them to assure the worst-case execution time estimates. We propose a contention analysis in order to identify the worst contentions that a task can suffer from concurrent executions. The work focuses on the interferences on shared resources (cache memories and memory buses) from parallel executions in multi-core real-time systems. Our approach consists of searching for possible task contenders for parallel executions, modeling their contentiousness, and classifying the measurement scenarios accordingly. We identify the most contentious ones and their worst-case effects on task execution times. The measurement-based probabilistic timing analysis is then used to verify the analysis proposed, qualify the scenarios with contentiousness, and compare them. A parallel execution simulator for multi-core real-time system is developed and used for validating our framework. The framework applies heuristics and assumptions that simplify the system behavior. It represents a first step for developing a complete approach which would be able to guarantee the worst-case behavior

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

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

Random Modulo: A new processor cache design for real-time critical systems

Cache memories have a huge impact on software's worst-case execution time (WCET). While enabling the seamless use of caches is key to provide the increasing levels of (guaranteed) performance required by automotive software, caches complicate timing analysis. In the context of Measurement-Based Probabilistic Timing Analysis (MBPTA) - a promising technique to ease timing analyis of complex hardware - we propose Random Modulo (RM), a new cache design that provides the probabilistic behavior required by MBPTA and with the following advantages over existing MBPTA-compliant cache designs: (i) an outstanding reduction in WCET estimates, (ii) lower latency and area overhead, and (iii) competitive average performance w.r.t conventional caches.Peer ReviewedPostprint (author's final draft