We present LIME, a novel dynamic real-time task model extractor. LIME observes the temporal behavior of Linux real-time threads and automatically maps the observed activity to established real-time task models: sporadic and periodic tasks, upper and lower arrival curves, cumulative execution-time curves, and two self-suspension models (dynamic and segmented). LIME runs on unmodified Linux kernels and requires neither knowledge of real-time theory nor familiarity with Linux internals to be used effectively. An extensive evaluation shows LIME to achieve very high inference accuracy—in particular 100% accuracy for common automotive periods—with low kernel overhead, low latency impact, and low processor utilization (at best-effort priority).

Computationally demanding tasks with highly variable execution times may require parallel processing. Scheduling such tasks with low deadline miss rates but without significant overprovisioning is challenging. This issue arises in applications like nonlinear optimization for Model Predictive Control (MPC). The Constant Bandwidth Server (CBS) provides timing isolation, supporting both hard and soft real-time tasks. However, scheduling parallel, time-varying jobs across multiple CBS instances requires static job-to-server assignments, which can lead to resource underutilization due to queued jobs awaiting specific servers. This paper introduces the Job Acceptance Multi-Server (JAMS), a mechanism in which multiple CBS instances share a common job queue, enabling flexible job dispatching for parallel workloads. JAMS incorporates a job dismissal mechanism to address overloads, ensuring that only jobs with guaranteed resource availability are accepted. Each CBS instance checks if it can complete a job by its deadline, given probabilistic knowledge on its execution times, dismissing unfeasible jobs to avoid excessive tardiness across queued tasks. Implemented in Linux, JAMS is evaluated with computation times drawn from an MPC task and synthetic datasets. The extensive experimental results we provide demonstrate that JAMS effectively controls the deadline miss rate, maintaining it below a specified design threshold.

Timely observation of transient astrophysical phenomena (TAP) is of crucial importance for our understanding of the universe and the laws of physics, as recognized by the National Academies in the Astro2020 decadal survey. Ultimately, the goal is to observe TAPs as early as possible using optical telescopes. This is non-trivial due to the probabilistic nature of the search problem, where multiple potential sky locations for a TAP, each with an associated probability, must be scheduled for observation before successful localization. The problem lies at the intersection of several research disciplines, including realtime systems, cyber-physical systems, astrophysics, and operations research, motivating the need for a unified modeling framework. To this end, we introduce the first formal stochastic, response-time-aware model for search planning toward detection and localization of TAPs. We consider the problem of maximizing expected utility of early localization and show that it is reducible to the Orienteering Problem. Building on this formulation, we develop the real-time-capable Greedy-Christofides Pathfinding (GCP) algorithm. An evaluation on 37 probability maps from LIGO demonstrates that GCP consistently achieves high solution quality and computational efficiency across diverse search scenarios. GCP achieves$\leq 0.5 \%$deviation from the ILP-computed optimal solution on tractable problem instances while running within a second, on average, for larger inputs.

Real-time tasks often exhibit correlated execution-time distributions due to common factors such as shared caches, resources, and inputs. Yet state-of-the-art probabilistic analysis still overlooks the impact of correlation, a gap that has been highlighted as a major open problem in the field. This paper responds to the open problem with the first correlation-aware analysis (CAA) of periodic tasks with stochastic execution times. The proposed analysis, which derives response-time distributions to infer upper bounds on deadline-failure probabilities, applies to a novel task model that incorporates information about both intra- and inter-task dependencies. In addition, the paper shows how to statistically infer the two model parameters using confidence intervals obtained via nonparametric bootstrapping. Notably, the inference method described is distribution-agnostic, meaning that it does not assume any particular probability distribution a priori, thereby eliminating a major risk of misclassifying the ground-truth execution behavior. By design, CAA dominates state-of-the-art correlation-tolerant analysis (CTA). The significantly better accuracy of CAA is demonstrated via experiments with synthetically generated workloads, while a case study based on the WATERS’ 17 industrial challenge provides a proof-of-concept of the statistical inference method.

In theory, real-time systems are provisioned based on provably sound worst-case execution times (WCETs), but in practice often only empirically derived, unsound execution-time estimates—i.e., nominal execution times (NETs)—are available since WCETs are difficult to obtain on modern hardware. NETs pose two significant challenges: First, since NETs may be exceeded at runtime, any response-time bounds derived from NETs are transitively unsound and may be violated. Second, even a minuscule NET violation can result in large, nonlinear response-time increases due to hard-to-predict, cascading scheduling effects. To explore the risk NET exceedance poses to a system’s temporal correctness, this paper provides the first general, systematic, and explainable methodology for exceedance analysis. The proposed approach supports fixed-priority (FP), earliest-deadline first (EDF), and first-in first-out (FIFO) scheduling on a uniprocessor or within a partitioned multiprocessor platform, and the full spectrum of preemption models from fully preemptive to fully non-preemptive workloads. Additionally, it produces explainable evidence in the form of tunable example traces that engineers can adjust to take system-specific expertise into account. The proposed methodology is evaluated with synthetic task sets and workloads based on an automotive benchmark, and in a case study applied to parts of the WATERS’17 industrial challenge.

Abstract In real-time systems analysis, probabilistic models, particularly Markov chains, have proven effective for tasks with dependent executions. This paper improves upon an approach utilizing Gaussian emission distributions within a Markov task execution model that analyzes bounds on deadline miss probabilities for tasks in a reservation-based server. Our method distinctly addresses the issue of runtime complexity, prevalent in existing methods, by employing a state merging technique. This not only maintains computational efficiency but also retains the accuracy of the deadline-miss probability estimations to a significant degree. The efficacy of this approach is demonstrated through the timing behavior analysis of a Kalman filter controlling a Furuta pendulum, comparing the derived deadline miss probability bounds against various benchmarks, including real-time Linux server metrics. Our results confirm that the proposed method effectively upper-bounds the actual deadline miss probabilities, showcasing a significant improvement in computational efficiency without significantly sacrificing accuracy.

Probabilistic approaches have gained attention over the past decade, providing a modeling framework that enables less pessimistic analysis of real-time systems. Among the different proposed approaches, Markov chains have been shown effective for analyzing real-time systems, particularly in estimating the pending workload distribution and deadline miss probability. However, the state-of-the-art mainly considered discrete emission distributions without investigating the benefits of continuous ones. In this paper, we propose a method for analyzing the workload probability distribution and bounding the deadline miss probability for a task executing in a reservation-based server, where execution times are described by a Markov model with Gaussian emission distributions. The evaluation is performed for the timing behavior of a Kalman filter for Furuta pendulum control. Deadline miss probability bounds are derived with a workload accumulation scheme. The bounds are compared to 1) measured deadline miss ratios of tasks running under the Linux Constant Bandwidth Server with SCHED-DEADLINE, 2) estimates derived from a Markov Model with discrete-emission distributions (PROSIT), 3) simulation-based estimates, and 4) an estimate assuming independent execution times. The results suggest that the proposed method successfully upper bounds actual deadline miss probabilities. Compared to the discrete-emission counterpart, the computation time is independent of the range of the execution times under analysis, and resampling is not required.

The concept of a probabilistic worst-case execution time (pWCET) has gradually emerged from the work of many authors over the course of 2–3 decades. Intuitively, pWCET is a simplifying model abstraction that safely over-approximates the ground-truth probabilistic execution time (pET) of a real-time task. In particular, when analyzing the cumulative processor demand of multiple jobs, the pWCET abstraction is intended to allow for the use of techniques from probability theory that require random variables to be independent and identically distributed (IID), even though the underlying ground-truth pET random variables are usually not independent. However, while powerful, the pWCET concept is subtle and difficult to define precisely, and easily misinterpreted. To place the pWCET concept on firm, unambiguous mathematical foundations, this paper proposes the first rigorous, axiomatic definition of pWCET that is suitable for formal proof. In addition, an adequacy property is stated that formally captures the intuitive notion of an “IID upper bound on pET.” The proposed pWCET definition is shown to satisfy this adequacy condition, and thereby is the first notion of pWCET for which the IID guarantee is formally established. All definitions and proofs have been verified with the Coq proof assistant.

Estimating the worst-case deadline failure probability (WCDFP) of a real-time task is notoriously difficult, primarily because a task's execution time typically depends on prior activations (i.e., history dependence) and the execution of other tasks (e.g., via shared inputs). Previous analyses have either assumed that execution times are probabilistically independent (which is unrealistic and unsafe), or relied on complex upper-bounding abstractions such as probabilistic worst-case execution time (pWCET), which mask dependencies with pessimism. Exploring an analytically novel direction, this paper proposes the first closed-form upper bound on WCDFP that accounts for dependent execution times. The proposed correlation-tolerant analysis (CTA), based on Cantelli's inequality, targets fixed-priority scheduling and requires only two basic summary statistics of each task's ground- truth execution time distribution: upper bounds on the mean and standard deviation (for any possible job-arrival sequence). Notably, CTA does not use pWCET, nor does it require the full execution-time distribution to be known. Core parts of the analysis have been verified with the Coq proof assistant. Empirical comparison with state-of-the-art WCDFP analyses reveals that CTA can yield significantly improved bounds (e.g., a lower WCDFP than any pWCET-based method for ~70% of the workloads tested at 90% pWCET utilization and 60% average utilization). Beyond accuracy gains, the favorable results highlight the potential of the previously unexplored analytical direction underlying CTA.

Probabilistic timing and schedulability analysis of real-time systems is constrained by the problem of often intractable exact computations. The intractability problem is present whenever there is a large number of entities to be analysed, e.g., jobs, tasks, etc. In the last few years, the analytical approximations for deadline-miss probability emerged as an important solution in the above problem domain. In this paper, we explore analytical solutions for two major problems that are present in the probabilistic analysis of real-time systems. First, for a safe approximation of the entire probability distributions (e.g., of the accumulated execution workloads) we show how the Berry-Esseen theorem can be used. Second, we propose an approximation built on the Berry-Esseen theorem for efficient computation of the quantile functions of probability execution distributions. We also show the asymptotic bounds on the execution distribution of the fixed-priority preemptive tasks. In the evaluation, we investigate the complexity and accuracy of the proposed methods as the number of analysed jobs and tasks increases. The methods are compared with the circular convolution approach. We also investigate the memory footprint comparison between the proposed Berry-Esseen-based solutions and the circular convolution.. The contributions and results presented in this paper complement the state-of-the-art in accurate and efficient probabilistic analysis of real-time systems.

This paper addresses two major problems in probabilistic analysis of real-time systems: space and time complexity of convolution of discrete random variables. For years, these two problems have limited the applicability of many methods for the probabilistic analysis of real-time systems, that rely on convolution as the main operation. Convolution in probabilistic analysis leads to a substantial space explosion and therefore space reductions may be necessary to make the problem tractable. However, the reductions lead to pessimism in the obtained probabilistic distributions, affecting the accuracy of the timing analysis. In this paper, we propose an optimal algorithm for down-sampling, which minimises the probabilistic expectation (i.e., the pessimism) in polynomial time. The second problem relates to the time complexity of the convolution between discrete random variables. It has been shown that quadratic time complexity of a single linear convolution, together with the space explosion of probabilistic analysis, limits its applicability for systems with a large number of tasks, jobs, and other analysed entities. In this paper, we show that the problem can be solved with a complexity of 𝒪(n log(n)), by proposing an algorithm that utilises circular convolution and vector space reductions. Evaluation results show several important improvements with respect to other state-of-the-art techniques.

Many real-time applications have functional behaviour that requires variability in timing properties at runtime. The elastic task model provides a convenient mechanism to specify and encapsulate such variability and enables the modification of an application's periods during run-time to keep the application schedulable. Additionally, reservation-based scheduling techniques were proposed for the same purpose of taming unpredictability of timing variations, but with a different solution, i.e., by providing the spatial and temporal isolation for executing independent applications on the same hardware. In this paper, we combine the two approaches by proposing a two-level adaptive scheduling framework which is based on the elastic task model and the compositional framework based on the periodic resource model. The proposed framework minimises the number of requests for bandwidth adaption at the reservation (system) level and primarily enables schedulability by accounting for the application's elasticity by adjusting the periods. The motivation for this design choice is to rather localise the effect of the modifications within the application, without necessarily affecting all the applications at the system level compared to the changes made at the application level. The evaluation results show that the local application changes may often be enough to solve the problem of variability, significantly reducing the number of bandwidth adjustments, and therefore reducing the potential negative impact on all the applications of a system.

In the recent works that analyzed execution-time variation of real-time tasks, it was shown that such variation may conform to regular behavior. This regularity may arise from multiple sources, e.g., due to periodic changes in hardware or program state, program structure, inter-task dependence or inter-task interference. Such complexity can be better captured by a Markov Model, compared to the common approach of assuming independent and identically distributed random variables. However, despite the regularity that may be described with a Markov model, over time, the execution times may change, due to irregular changes in input, hardware state, or program state. In this paper, we propose a Bayesian approach to adapt the emission distributions of the Markov Model at runtime, in order to account for such irregular variation. A preprocessing step determines the number of states and the transition matrix of the Markov Model from a portion of the execution time sequence. In the preprocessing step, segments of the execution time trace with similar properties are identified and combined into clusters. At runtime, the proposed method switches between these clusters based on a Generalized Likelihood Ratio (GLR). Using a Bayesian approach, clusters are updated and emission distributions estimated. New clusters can be identified and clusters can be merged at runtime. The time complexity of the online step is $O(N^{2}+ NC)$ where N is the number of states in the Hidden Markov Model (HMM) that is fixed after the preprocessing step, and C is the number of clusters.

Schedulability analyses for preemptive real-time systems need to take into account cache-related preemption delays (CRPD) caused by preemptions between the tasks. The estimation of the CRPD values must be sound, i.e. it must not be lower than the worst-case CRPD that may occur at runtime, but also should minimise the pessimism of estimation. The existing methods over-approximate the computed CRPD upper bounds by accounting for multiple preemption combinations which cannot occur simultaneously during runtime. This over-approximation may further lead to the over-approximation of the worst-case response times of the tasks, and therefore a false-negative estimation of the system’s schedulability. In this paper, we propose a more precise cache-aware response time analysis for sporadic real-time systems under fully-preemptive fixed priority scheduling. The evaluation shows a significant improvement over the existing state of the art approaches.

In real-time systems that employ preemptive scheduling and cache architecture, it is essential to account as precisely as possible for cache-related preemption delays in the schedulability analysis, as an imprecise estimation may falsely deem the system unschedulable. In the current state of the art for preemptive scheduling of tasks with fixed preemption points, the existing schedulability analysis considers overly pessimistic estimation of cache-related preemption delay, which eventually leads to overly pessimistic schedulability results. In this paper, we propose a novel response time analysis for real-time tasks with fixed preemption points, accounting for a more precise estimation of cache-related preemption delays. The evaluation shows that the proposed analysis significantly dominates the existing approach by being able to always identify more schedulable tasksets.

The increasing industrial demand for handling complex functionalities has influenced the design of hardware architectures for time critical embedded systems, during the past decade. Multicore systems facilitate the inclusion of many complex functionalities, while, at the same time, inducing cache related overheads, as well as adding partitioning complexity to the overall system schedulability. One of the efficient paradigms for controlling and reducing the cache related costs in real-time systems is limited preemptive scheduling (LPS), with its particular instance fixed preemption points scheduling (LP-FPPS), which has been shown to outperform other alternatives as well as has been supported by and investigated in the automotive domain. With respect to the partitioning constraints, partitioned scheduling has been widely used to preruntime allocate tasks to specific cores, resulting in predictable cache-related preemption delays estimations. In this paper, we propose to integrate the LP-FPPS and partitioned scheduling on fixed-priority multicore real-time systems in order to increase the overall system schedulability. We define a new joint approach for task partitioning and preemption point selection, which is based on the computation of the maximum blocking tolerance upon each allocation, thus being able to quantify the schedulability of the taskset on each processor. Furthermore, we investigate the partitioning strategies based on different heuristics, i.e., first fit decreasing and worst fit decreasing, and priority and density taskset orderings. The evaluation performed on randomly generated tasksets shows that in the general case, no single partitioning strategy fully dominates the others. However, the evaluation results reveal that the certain partitioning strategies perform significantly better with respect to the overall schedulability for specific taskset characteristics. The results also reveal that the proposed partitioning strategies outperform fully preemptive and nonpreemptive partitioned scheduling in terms of successful partitioning.