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The temporal correctness of safety-critical systems is typically guaranteed via a response-time analysis (RTA). However, as the systems become complex (e.g., parallel tasks running on a multicore platform), most existing RTAs either become pessimistic or do not scale with respect to e.g., the number of tasks or period values. To make a trade-off between accuracy and scalability, recently, a new reachability-based RTA called schedule-abstraction graph (SAG) has been introduced by Nasri et al. It explores the space of possible decisions that a scheduling policy can take while dispatching a set of tasks or jobs on processing resources. The analysis is at least three orders of magnitude faster than other exact RTAs and is able to identify many more schedulable task sets than the existing fixed-point iteration-based analyses. One fundamental limitation of the SAG analysis is that in its reachability graph, each edge can only account for a single scheduling decision. Therefore, the graph grows exponentially when there are large uncertainties in the release time or execution time of the jobs. In this paper, we improve the scalability of the SAG analysis by introducing partial-order reduction (POR) rules that allow combining multiple scheduling decisions on one edge and hence avoiding combinatorial exploration of all possible scheduling decisions. An empirical evaluation shows that our solution is able to reduce the runtime by five orders of magnitude and the number of explored states by 98%.

IEEE RTSS 2021

Partial-Order Reduction in Reachability-based Response-Time Analyses

dispatching

multicore processing

runtime

space exploration

scalability

uncertainty

reachability analysis

partial-order reduction

response-time analysis

real-time systems

 **RTSS 2021** has successfully concluded. Hope you have enjoyed it, and look forward to seeing you next year in person.
    Announcement for the Awards:
 * Best Paper Award goes to: Monte Carlo Response-Time Analysis, Sergey Bozhko, Georg von der Brüggen, and Björn Brandenburg
 * Best Student Paper Award goes to: Automatic Energy-Hotspot Detection and Elimination in Real-Time Deeply Embedded Systems, Mohsen Shekarisaz, Lothar Thiele, and Mehdi Kargahi.
 * Best Solution Award for Industry Session goes to: Toward Real-Time Guaranteed Scheduling for Autonomous Driving Systems. Jinghao Sun, Tianyi Wang, Kailu Duan, Bin Lu, Jiankang Ren, Zhishan Guo, and Guozhen Tan.



The IEEE Real-Time Systems Symposium (RTSS) is the premier conference in the field of real-time systems, and is a venue for researchers and practitioners to showcase innovations covering all aspects of real-time systems, including theory, design, analysis, implementation, evaluation, and experience. 

technical paper

The partitioned scheduling of periodic and sporadic task systems upon multiprocessor platforms (both identical and heterogeneous) is considered. The computational complexity of a large number of such partitioned schedulability problems is examined. New lower and upper bounds on complexity are presented for several problems. Some problems are pigeonholed into their precise complexity classes in this way. A list of problems for which exact classification remains open is compiled.

Partitioned Scheduling of Recurrent Real-Time Tasks

Though recent work has established the soft real-time (SRT)-optimality of Earliest-Deadline-First (EDF) variants on multiprocessor models with limited heterogeneity (e.g., uniform speeds or affinity masks), such models are insufficient to describe modern multiprocessors, which have grown increasingly heterogeneous. This fact highlights the need to extend theoretical results to more asymmetric models, such as the unrelated multiprocessor model. This paper presents an EDF variant tailored for this model and proves that it is at least nearly SRT-optimal. Simulation results for random task systems are also presented that suggest that the proposed EDF variant may actually be SRT-optimal.

Extending EDF for Soft Real-Time Scheduling on Unrelated Multiprocessors

Shared communication media are widely used in many applications including safety critical applications such as control systems on flights or autonomous vehicles. Noise and transient errors can cause transmission failures. We consider the problem of designing fault tolerant static schedules for transmitting messages in these media. In particular, we assume that the schedule of transmission over all messages must be computed in advance and must guarantee that all messages will be delivered as long as the number of medium errors falls below a provided upper bound, regardless of when the medium errors occur. It is crucial that the messages be delivered in a timely manner, and hence we are interested in minimizing the length of the schedule that achieves the desired level of fault tolerance. In this paper, we provide an efficient algorithm for producing a schedule for $n$ messages with total length $n+O(f^2\log^2n)$ that can tolerate $f$ medium errors. We also prove that fault-tolerant schedules with length $n+O(f\log f\log n)$ exist. Since $n$ steps are required to transmit $n$ messages, the overhead of fault tolerance is characterized by the additive terms of $O(f^2\log^2n)$ and $O(f\log f\log n)$, respectively. Both of these terms are sublinear in $n$ and represent asymptotic improvements to the previously best known schedule, which has overhead $fn/2$.

Sub-Linear Overhead in Static Schedules for Fault-Tolerant Transmission

Global scheduling of real time tasks with precedence constraints has received significant attention recently. Specifically, on multiprocessor systems, the directed acyclic graph (DAG) model well-represents parallelizable workloads with precedence constraints. Hence, many studies have recently been published analyzing DAG structures using decomposition and window-based analysis methods. We identified a set of schedulable DAG taskets that are hard-to-analyze using state-of-the-art window-based schedulability tests. Additionally, we observe that the window-based test solely depends on one structural feature of the DAG taskset, which raises concerns about its pessimism in many settings. In this paper, to address these concerns, for hard real-time sporadic implicit-deadline DAG tasksets, we perform LAG-based schedulability analysis, which offers a more holistic view of the taskset than the window-based analysis. We present a companion utilization-based schedulability test to the state-of-the-art, which considers additional structural features of DAGs. Our results show that by considering such features, our LAG-based test empirically dominates the state-of-the-art test on over 80% of the evaluated DAG tasksets. Moreover, combining our LAG-based test in conjunction with the window-based tests can achieve high schedulability in many cases.

LAG-based Analysis Techniques for Scheduling Multiprocessor Hard Real-Time Sporadic DAGs

Probabilistic timing guarantees enable a tradeoff between system safety and hardware costs in embedded real-time systems. A key metric for assessing whether timing requirements can be satisfied with sufficiently high probability is the worst- case deadline failure probability (WCDFP). This paper studies the WCDFP under earliest-deadline first (EDF) scheduling for tasks with several probabilistic execution modes (e.g., a low-needs “typical” mode and a resource-intensive “exceptional” mode). Under EDF, no known approach can bound the WCDFP for practically sized workloads since the time complexity of prior approaches is exponential in the number of jobs. This paper examines the structure of the EDF WCDFP problem and establishes a safe, efficiently computable over- approximation by restricting the analysis to a set of specific intervals and providing a criterion to stop the derivation early without risking under-approximation. The analysis first assumes independent jobs and is then extended to handle dependencies (i.e., acyclic task chains). An evaluation shows that (i) even if 99.9999% of the jobs must meet their deadlines, a significantly higher utilization is possible than in the deterministic case, (ii) the analysis is scalable to 30 tasks with more than 10 60 jobs in the hyperperiod, and (iii) assuming independence in the presence of dependent tasks can severely under-estimate the WCDFP.

Efficiently Approximating the Worst-Case Deadline Failure Probability under EDF

Real-time applications with high computational demand, e.g., autonomous driving, are emerging and their complex nature conforms to a DAG(directed acyclic graph) structure. We propose a conditionally optimal parallelization for real-time DAG tasks for global EDF, ensuring complete execution of all tasks within the deadline. To achieve this, we formalize a monotonic increasing property of both tolerance and interference to the parallelization option. Using such properties, we develop a unidirectional search algorithm that can assign parallelization options in polynomial time, which we formally prove the optimality. We observe significant improvement of schedulability through simulation experiment, and then in the following implementation experiment, we demonstrate that the algorithm is practically applicable for real-world use-cases.

Conditionally Optimal Parallelization of Real-Time DAG Tasks for Global EDF

Supporting Non-blocking Frame-Preemption in TSN Networks

Prior algorithms that have been proposed for the uniprocessor scheduling of systems of elastic real-time tasks have computational complexity quadratic (O(n^2)) in the number of tasks n, for both initialization and for admitting new tasks during run-time. In our work-already-published [1], we present a more efficient implementation in which initialization takes quasilinear (O(n log n)), and on-line admission control, linear (O(n)), time.

Linear-time admission control for elastic scheduling

In this paper, we report on the ongoing development of POET, the first foundational and automated response-time analysis tool. The certificates produced by POET are short, readable, and fully commented Coq files that can be machine-checked in (usually) minutes. Moreover, we describe the mechanisms implemented in POET to ensure the validity of the generated certificates. Finally, we report on a preliminary evaluation of the effectiveness and practicality of our approach on synthetic task sets.

Automatically Generated Response-Time Proofs as Evidence of Timeliness

Numerical simulations often play an important role when evaluating and comparing the performance of schedulability tests, as they allow to empirically demonstrate their applicability using synthesized task sets under various configurations. In order to provide a fair comparison of various schedulability tests, von der Brüggen et al. presented the first version of an evaluation framework for self-suspending task sets. In this work-in-progress, we further enhance the framework by providing more features to ease the use, e.g., Python 3 support, an improved GUI, multiprocessing, Gurobi optimization, and external task evaluation. In addition, we integrate the state-of-the-arts we are aware of into the framework. Moreover, the documentation is improved significantly to simplify the application in further research and development. To the best of our knowledge, the framework contains all suspension-aware schedulability tests for uniprocessor systems and we aim to keep it up-to-date.

Partial-Order Reduction in Reachability-based Response-Time Analyses

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