Fixed-priority (FP) scheduling is widely used in safety-critical real-time systems due to its simplicity and analyzability, yet it may fail to schedule task sets whose worst-case response-time bounds exceed deadlines by small margins. Meanwhile, modern processors increasingly support short-term frequency boosting, providing additional processing capacity subject to thermal and power constraints. This paper introduces Boosted-FP, a fixed-priority scheduling framework that augments a given FP policy with controlled, limited frequency boosting. The key idea is to activate boosting based on the worst-case remaining execution demand of the currently executing job, thereby confining high-frequency execution to the tail of jobs. Per-task boost parameters are computed offline using standard fixed-priority response-time analysis under the chosen priority assignment, while boost activation decisions are made online using worst-case remaining-work information. We show that Boosted-FP preserves hard real-time guarantees by relating its execution behavior to that of a task set with reduced execution times. Leveraging the sustainability of fixed-priority schedulability analysis with respect to execution-time reductions, we establish that any task set schedulable under the modified execution bounds is also schedulable under the proposed framework. We evaluate the framework under a global boost-budget constraint and show experimentally that boost usage remains bounded and often well below the offline provisioned budget. Together, these results demonstrate that controlled, work-triggered boosting can safely extend the schedulable region of fixed-priority scheduling without abandoning static priorities.

Abstract We present the first (to our knowledge) Deep-Learning based framework for real-time schedulability-analysis that guarantees to never incorrectly mis-classify an unschedulable system as being schedulable, and is hence suitable for use in safety-critical scenarios. We relate applicability of this framework to well-understood concepts in computational complexity theory: membership in the complexity class NP. We apply the framework upon the widely-studied schedulability analysis problems of determining whether a given constrained-deadline sporadic task system is schedulable on a preemptive uniprocessor under both Deadline-Monotonic and EDF scheduling. As a proof-of-concept, we implement our framework for Deadline-Monotonic scheduling, and demonstrate that it has a predictive accuracy exceeding $$70\%$$ 70 % for systems of as many as 20 tasks without making any unsafe predictions . Furthermore, the implementation has very small ( $$<1$$ < 1 ms on two widely-used embedded platforms; $$<4~\upmu$$ < 4 μ s on an embedded FPGA) and highly predictable running times.

Elastic scheduling is a framework to reduce task utilizations (often by increasing periods) in response to system overload. This paper extends elastic scheduling to uniprocessor scheduling of implicit-deadline task sets for which periods must remain harmonic. We argue that for tasks with periods constrained to continuous intervals, the problem of selecting harmonic periods from those intervals is unlikely to have a polynomial time solution. However, we outline an approach that is pseudo-polynomial in the range of acceptable periods. We then show that the problem of elastic scheduling is NP-hard with harmonic constraints. Nonetheless, if a total order is imposed on task periods (a natural restriction in many applications with execution pipelines that synchronize input data sources), the problem can be reduced offline to a lookup table, enabling polynomial-time online adaptation if available CPU bandwidth changes. We implement the proposed algorithm in two real-world applications: the Fast Integrated Mobility Spectrometer (FIMS) and ORB-SLAM3. We demonstrate that elastic scheduling allows FIMS to adjust its execution to avoid missing deadlines on a SWaP-constrained computational platform, and that it improves ORB-SLAM3's localization results by as much as lO.4x when available CPU bandwidth changes dynamically during runtime.

Algorithms that have been developed for solving computationally intractable schedulability analysis problems may be classified into two broad categories: exact algorithms that run in exponential time, and polynomial-time algorithms that provide approximate solutions. If exact algorithms are sought, it has traditionally been required that these algorithms have pseudo-polynomial running time. More recently, schedulability analysis algorithms that have polynomial running time but are allowed to make calls to an ILP solver have increasingly been considered tractable. When approximation algorithms are acceptable, an objective has been to obtain Fully Polynomial-Time Approximation Schemes, which are ‘tunable’ algorithms that provide a smooth transition between polynomial time and exponential time by letting the user of the algorithm set an appropriate value for a parameter. In this paper we take a fresh view on the connections between the various perspectives on what is considered to be tractable schedulability analysis. We seek to determine when the different forms of tractable analyses are applicable to a particular problem and what problem features rules them out, and demonstrate our findings upon concrete scheduling problems. We also suggest that ‘pseudo-polynomial time’ is perhaps a rather broad category, and propose a finer-grained classification of the class of pseudo-polynomial time algorithms.

The Butterfly Attack, introduced in an RTSS 2019 paper, was billed as a new kind of timing attack against control loops in cyber-physical systems. We conduct a close inspection of the Butterfly Attack in order to identify the root vulnerability that it exploits, and show that an appropriate application of real-time scheduling theory provides an effective countermeasure. We propose improved defenses against this and similar attacks by drawing upon techniques from real-time scheduling theory, control theory, and systems implementation, that are both provably secure and are able to make efficient use of computing resources.

The algorithmic technique of fixed-parameter analysis of computationally intractable problems seeks to obtain a deeper understanding of the underlying causes of the intractability, with a view to identifying conditions under which the problem becomes tractable. We apply fixed-parameter analysis to the fixed-priority and EDF scheduling of recurrent (periodic and sporadic) task systems upon preemptive uniprocessor platforms.

In the Vestal model of mixed-criticality systems, jobs are characterized by multiple different estimates of their actual, but unknown, worst-case execution time (WCET) parameters. Some recent research has focused upon a semi-clairvoyant model for mixed-criticality systems in which it is assumed that each job reveals upon arrival which of its WCET parameters it will respect. We study the problem of scheduling such semi-clairvoyant systems to ensure graceful degradation of service to less critical jobs in the event that the systems exhibit high-criticality behavior. We propose multiple different interpretations of graceful degradation in such systems, and derive efficient scheduling algorithms that are capable of ensuring graceful degradation under these different interpretations.

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.

We study the computational complexity of the Fixed-Priority (FP) schedulability problem for sporadic or synchronous periodic tasks with implicit deadlines on a single preemptive processor. This problem is known to be (weakly) NP-complete in the general case, but Liu and Layland's classic utilization bound trivially provides a polynomial-time solution for task sets with Rate-Monotonic (RM) priorities and utilization bounded from above by ln(2), or approximately 69%. Here we show that ln(2) is in fact the sharp boundary between computationally easy and hard schedulability testing: The FP-schedulability problem is NP-complete even if restricted to task sets with RM priorities and utilization bounded from above by any constant c > ln(2). This disproves a conjecture by Rothvoß. Further, we show that if a non-RM priority ordering can be specified, then the FP-schedulability problem is NP-complete already when utilization is bounded by any constant c> 0.

Abstract In this work we consider a measurement-based model for parallel real-time tasks represented by the work and span parameters of directed acyclic graphs, with different bounds for nominal and overload scenarios. We address the corresponding real-time scheduling problem and propose an optimal scheduling strategy with a derived tight bound on the maximum response time of a task.

In dual priority scheduling, periodic tasks are executed in a fixed-priority manner, but each job has two phases with different priorities. The second phase is entered after a fixed amount of time has passed since the release of the job, at which point the job changes its priority. Dual priority scheduling was introduced by Burns and Wellings in 1993 and was shown to successfully schedule many task sets that are not schedulable with ordinary (single) fixed-priority scheduling. Burns and Wellings conjectured that dual priority scheduling is an optimal scheduling algorithm for synchronous periodic tasks with implicit deadlines on preemptive uniprocessors. We demonstrate the falsity of this conjecture, as well as of some related conjectures that have since been stated. This is achieved by means of computer-verified counterexamples.

We study an engine control application where the behavior of engine controllers depends on the engine's rotational speed. For efficient and precise timing analysis, we use the Digraph Real-Time (DRT) task model to specify the workload of control tasks where we employ optimal control theory to faithfully calculate the respective minimum inter-release times. We show how DRT models can be refined by finer grained partitioning of the state space of the engine up to a model which enables an exact timing analysis. Compared to previously proposed methods which are either unsafe or pessimistic, our work provides both abstract and tight characterizations of the corresponding workload.

Schedulability analysis techniques that are well understood within the real-time scheduling community are applied to the analysis of recurrent real-time workloads that are modeled using the synchronous data-flow graph (SDFG) model. An enhancement to the standard SDFG model is proposed, that permits the specification of a real-time latency constraint between a specified input and a specified output of an SDFG. A technique is derived for transforming such an enhanced SDFG to a collection of traditional 3-parameter sporadic tasks, thereby allowing for the analysis of systems of SDFG tasks using the methods and algorithms that have previously been developed within the real-time scheduling community for the analysis of systems of such sporadic tasks. The applicability of this approach is illustrated by applying prior results from real-time scheduling theory to construct an exact preemptive uniprocessor schedulability test for collections of recurrent processes that are each represented using the enhanced SDFG model.

We study the computational complexity of the FP-schedulability problem for sporadic or synchronous periodic tasks on a preemptive uniprocessor. We show that this problem is (weakly) NP-hard, even when restricted to either (i) task sets with implicit deadlines and rate-monotonic priority ordering, or (ii) task sets with constrained deadlines, deadline-monotonic priority ordering and utilization bounded by any constant c, such that 0 <; c <; 1.

A real-time multiprocessor synchronization problem is studied herein that has not be extensively studied before, namely, the management of replicated resources where tasks may require multiple replicas to execute. In prior work on replicated resources, k-exclusion locks have been used, but this restricts tasks to lock only one replica at a time. To motivate the need for unrestricted replica sharing, two use cases are discussed that reveal an interesting tradeoff: in one of the use cases, blocking is the dominant lock-related factor impacting schedulability, while in the other, lock/unlock overheads are. Motivated by these use cases, three replica-allocation protocols are presented. In the first two, the lock/unlock logic is very simple, yielding low overheads, but blocking is not optimal. In the third, blocking is optimal (ignoring constant factors), but additional lock/unlock overhead is incurred to properly order lock requests. Experiments are presented that examine the overhead/blocking tradeoff motivated by these protocols in some detail.

Deciding the feasibility of a sporadic task system on a preemptive uniprocessor is a central problem in real-time scheduling theory. The computational complexity of this problem has been a long-standing open question. We show that it is coNP-complete in the strong sense, even when deadlines are constrained. This is achieved by means of a pseudo-polynomial transformation from the strongly NP-hard Simultaneous Congruences Problem to the complement of the feasibility problem.

A central problem in real-time scheduling theory is to decide whether a sporadic task system with constrained deadlines is feasible on a preemptive uniprocessor. It is known that this problem is strongly coNP-complete in the general case, but also that there exists a pseudo-polynomial time solution for instances with utilization bounded from above by any constant c, where 0 <; c <; 1. For a long time it has been unknown whether the bounded case also has a polynomial-time solution. We show that for any choice of the constant c, such that 0 <; c <; 1, the bounded feasibility problem is (weakly) coNP-complete, and thus that no polynomial-time solution exists for it, unless P = NP.

We derive demand-bound functions for mixed-criticality sporadic tasks, and use these to determine EDF-schedulability. Tasks have different demand-bound functions for each criticality mode. We show how to shift execution demand from high-to low-criticality mode by tuning the relative deadlines. This allows us to shape the demand characteristics of each task. We propose an efficient algorithm for tuning all relative deadlines of a task set in order to shape the total demand to the available supply of the computing platform. Experiments indicate that this approach is significantly more powerful than previous approaches to mixed-criticality scheduling. This new approach has the added benefit of supporting hierarchical scheduling frameworks.

Previous works on real-time task graph models have ignored the crucial resource sharing problem. Due to the non-deterministic branching behavior, resource sharing in graph-based task models is significantly more difficult than in the simple periodic or sporadic task models. In this work we address this problem with several different scheduling strategies, and quantitatively evaluate their performance. We first show that a direct application of the well-known EDF+SRP strategy to graph-based task models leads to an unbounded speedup factor. By slightly modifying EDF+SRP, we obtain a new scheduling strategy, called EDF+saSRP, which has a speedup factor of 2. Then we propose a novel resource sharing protocol, called ACP, to better manage resource sharing in the presence of branching structures. The scheduling strategy EDF+ACP, which applies ACP to EDF, can achieve a speedup factor of 1.618, the golden ratio.

In formal analysis of real-time systems, a major concern is the analysis efficiency. As the expressiveness of models grows, so grows the complexity of their analysis. A recently proposed model, the digraph real-time task model (DRT), offers high expressiveness well beyond traditional periodic task models. Still, the associated feasibility problem on preemptive uniprocessors remains tractable. It is an open question to what extent the expressiveness of the model can be further increased before the feasibility problem becomes intractable. In this paper, we study that tractability border. We show that system models with the need for global timing constraints make feasibility analysis intractable. However, our second technical result shows that it remains tractable if the number of global constraints is bounded by a constant. Thus, this paper establishes a precise borderline between tractability and intractability.

We present a novel distributed localization algorithm, called Swarm-Intelligent Localization (SIL), for computing the physical locations of nodes in wireless sensor networks. The algorithm assumes that only a small fraction of the nodes have a priori knowledge of their positions, and that noisy distance measurements are available between all neighboring nodes. The algorithm has no explicit global state and it can handle nodes that are both mobile and that can arrive in the network at any time. SIL works in two different phases, a coarse phase where nodes compute rough positions for themselves based on information about remote anchors, and a fine phase where nodes iteratively refine their positions from the coarse phase by collaborating with their neighbors. The average computational complexity per node running SIL is very low, namely constant in the network size and linear in the connectivity of the network. We evaluate the algorithm through extensive simulations. The results indicate that SIL is able to compute accurate positions for the majority of nodes in a wide range of network topologies and settings, and that it can handle difficulties such as large distance measurement errors and low network connectivity.

Models for real-time systems have to balance the inherently contradicting goals of expressiveness and analysis efficiency. Current task models with tractable feasibility tests have limited expressiveness, restricting their ability to model many systems accurately. In particular, they are all recurrent, preventing the modeling of structures like mode switches, local loops, etc. In this paper, we advance the state-of-the-art with a model that is free from these constraints. Our proposed task model is based on arbitrary directed graphs (digraphs) for job releases. We show that the feasibility problem on preemptive uniprocessors for our model remains tractable. This even holds in the case of task systems with arbitrary deadlines.

An increasing trend in embedded system design is to integrate components with different levels of criticality into a shared hardware platform for better cost and power efficiency. Such mixed-criticality systems are subject to certifications at different levels of rigorousness, for validating the correctness of different subsystems on various confidence levels. The real-time scheduling of certifiable mixed-criticality systems has been recognized to be a challenging problem, where using traditional scheduling techniques may result in unacceptable resource waste. In this paper we present an algorithm called PLRS to schedule certifiable mixed-criticality sporadic tasks systems. PLRS uses fixed-job-priority scheduling, and assigns job priorities by exploring and balancing the asymmetric effects between the workload on different criticality levels. Comparing with the state-of-the-art algorithm by Li and Baruah for such systems, which we refer to as LB, PLRS is both more effective and more efficient: (i) The schedulability test of PLRS not only theoretically dominates, but also on average significantly outperforms LB's. (ii) The run-time complexity of PLRS is polynomial (quadratic in the number of tasks), which is much more efficient than the pseudo-polynomial run-time complexity of LB.