Schedulability Analysis Towards Arbitrarily Activated Tasks in Mixed-Criticality Systems

The generalized multiframe task model (GMF) extends the sporadic task model and multiframe task model. Each frame in the GMF model contains an execution time, a relative deadline, and a minimum inter-arrival time. These parameters are fixed after task specification time in the GMF model. However, multimedia and adaptive control systems may be overloaded and no longer stabilized when the task parameters in such systems are not flexible. In order to address this problem, deadlines and periods of frames may change to alleviate temporal overload, e.g., in the parameter adaptation and elastic scheduling model. In this paper, we propose a new model GMF-PA (the GMF model with parameter adaptation). This model allows task parameters to be flexible in arbitrary-deadline systems. A necessary schedulability test based on mixed-integer linear programming is given to check the schedulability under EDF scheduling and optimally assign frame deadlines and periods at the same time. We also prove that the test is a sufficient and necessary schedulability test when frame deadlines and periods must be integers. An approximation algorithm is also deployed to reduce computational running time and indicates a sufficient schedulability test in general. The speed-up factor of our approximation algorithm is $$1+\epsilon $$ where $$\epsilon $$ can be arbitrarily small, with respect to the exact schedulability test of GMF-PA tasks under EDF. We also apply the GMF model to self-suspending tasks. By extending recent work on scheduling self-suspending tasks, we remove the assumption that frame deadlines are equally assigned in self-suspending tasks, and the system is extended from constrained-deadline systems to arbitrary-deadline systems. We have done extensive experiments to show that the schedulability ratio is improved using our techniques in our GMF-PA model.

In the field of real-time systems, component-based models for mixed criticality systems (MCS) on multicore platform are gaining significant attention of the researchers from the recent past. The concept of mixed-criticality is firstly applied on single core systems but after gaining attention, it evolved to multicore platform. Initially, the tasks of MCS executes in low mode however if a task having high criticality does not its scheduling requirements complete its low mode, then the system switch to high mode. In high mode, only high critical tasks executes its high mode scheduling requirements, while all low tasks are discarded from further execution. In the realm of MCS, the component-based model have high importance and has been used in large and complex real-time systems. In component-based model, the component of a system is splatted into multiple components. In this study, a new component-based scheduling approach is proposed for multicore MCS. In the multicore mixed-criticality compositional framework, special emphasis is given on deriving the supply bound function, which represents available core supply, and the demand bound function, which indicates the requirements of resources for scheduling. A mixed-criticality multicore compositional framework (MMCF) is introduced for component-based MCS having tightened deadline. For the proposed strategy, a schedulability analysis is conducted, ensuring that the system can be scheduled only if the supply bound function is equal to or less than the demand bound function. On a 4-core platform, the scheduleability for the three scheduling strategies i.e. MMCF, MC-Partition, and Global are shown at different utilization levels of resource. 100% schedulability is shown by the proposed MMCF, MC-Partition, and global techniques for target utilizations of 0.7, 0.5, and 0.4, respectively. For a given utilization U=0.6, the proposed MMCF approach shows 100 % schedulability, while the MC-partition and global approaches show 90% and 20% schedulabilities respectively. It shows that the proposed MMCF approach schedules 10% and 80% more task sets than the MC-partition and global approaches respectively. The experimental results reveal that the proposed MMCF approach offers better schedulability than the other two approaches.

End-to-end flows, which have a set of chainlike subtasks, are widely used in distributed real-time systems. For instance, multimedia and automative applications require that subtasks finish executing on a chain of processors before their end-to-end deadlines. The scheduling of such chained subtasks decides the schedulability of a distributed realtime system. Since the subtask priority assignment problem is NP-hard in general, most heuristics are presented to schedule end-to-end flows in two separate steps. The first step calculates intermediate relative deadlines for frames, and the second step makes scheduling decisions under EDF scheduling. Because the quality of the priority assignment of subtasks will directly affect the schedulability of the distributed systems, the two separate steps may cause pessimism in schedulability analysis. To reduce potential pessimism, we combine the two steps in our novel dGMF-PA (distributed generalized multiframe tasks with parameter adaption) model. We present an algorithm based on mixed-integer linear programming for optimally selecting frame relative deadlines in the dGMF-PA model. An approximation algorithm is also proposed to reduce computational running time. Our approximation algorithm has a tunable speed-up factor of 1 + ϵ where ϵ can be arbitrarily small, with respect to the exact schedulability test of dGMF-PA tasks under EDF scheduling. Extensive experiments have shown that our approximation algorithm (which is a sufficient schedulability test) can schedule at most 44 % more than HOSPA, an existing state-of-the-art algorithm.

Real-time systems usually consist of a set of periodic and sporadic tasks. Periodic tasks can be divided into two classes: synchronous and asynchronous. The first type does not define the task first release, contrary to the second. Hence, synchronous periodic tasks are assumed to be released at the worst instant: the critical instant. The schedulability test is reduced to check a single execution of the task under analysis. The integration of sporadic tasks is also straightforward: they are treated as a periodic task with maximum arrival frequency. On the other hand, asynchronous periodic tasks require a test for each release in the hyper period and the integration of sporadic tasks is not trivial: the worst release instant is unknown a priori. However, they do not assume that the tasks are released at the worst instant.This paper presents a new schedulability analysis method based on the Response Time Analysis (RTA) to determine the worst response time of both asynchronous periodic and sporadic tasks, scheduled by a fixed-priority preemptive algorithm with general deadlines. It also presents another method that enables the introduction of a user configurable degree of pessimism, reducing the hyper period dependency.

This article presents a detailed discussion of LRE-TL (Local Remaining Execution-TL-plane), an algorithm that schedules hard real-time periodic and sporadic task sets with unconstrained deadlines on identical multiprocessors. The algorithm builds upon important concepts such as the TL-plane construct used in the development of the LLREF algorithm (Largest Local Remaining Execution First). This article identifies the fundamental TL-plane scheduling principles used in the construction of LLREF . These simple principles are examined, identifying methods of simplifying the algorithm and allowing it to handle a more general task model. For example, we identify the principle that total local utilization can never increase within any TL-plane as long as a minimal number of tasks are executing. This observation leads to a straightforward approach for scheduling task arrivals within a TL-plane. In this manner LRE-TL can schedule sporadic tasks and tasks with unconstrained deadlines. Like LLREF, the LRE-TL scheduling algorithm is optimal for task sets with implicit deadlines. In addition, LRE-TL can schedule task sets with unconstrained deadlines provided they satisfy the density test for multiprocessor systems. While LLREF has a O(n 2) runtime per TL-plane, LRE-TL's runtime is O(nlog?n) per TL-plane.

In real-time systems, correctness depends not only on functionality but also on timeliness. A great number of scheduling theories have been developed for verification of the temporal correctness of jobs (software) in such systems. Among them, the Earliest Deadline first until Zero-Laxity (EDZL) scheduling algorithm has received growing attention thanks to its effectiveness in multicore real-time scheduling. However, the true potential of EDZL has not yet been fully exploited in its schedulability analysis as the state-of-the-art EDZL analysis techniques involve considerable pessimism. In this paper, we propose a new EDZL multicore schedulability test. We first introduce an interesting observation that suggests an insight toward pessimism reduction in the schedulability analysis of EDZL. We then incorporate it into a well-known existing Earliest Deadline First (EDF) schedulability test, resulting in a new EDZL schedulability test. We demonstrate that the proposed EDZL test not only has lower time complexity than existing EDZL schedulability tests, but also significantly improves the schedulability of EDZL by up to 36.6 percent compared to the best existing EDZL schedulability tests.

In real-time scheduling theory, self-suspension describes the behavior that a job can suspend itself from the ready state and thus be exempted from the scheduling for the suspension duration. This behavior makes it non-trivial to resort to established concepts such as the busy-interval analysis to self-suspending task sets which is required to analyze the worst-case response time of tasks with backlog, e.g., arbitrary-deadline task sets. In this paper, we present a novel suspension-aware busy-interval analysis for dynamic self-suspension tasks where the inter-arrival time of subsequent jobs can be bounded by an arrival curve. Based on the general analysis, we provide worst-case response time analyses and hence sufficient schedulability tests for fixed-priority preemptive uniprocessor scheduling algorithms for arrival-curve constrained and sporadic self-suspension task systems with arbitrary deadlines. Moreover, we provide evaluations based on synthetically generated task sets that show that our method indeed exploits the optimism that is introduced when enlarging the relative deadline of tasks. We demonstrate that our approach improves the state of the art by considering arrival curves that are obtained from tasks with release jitter.

Partitioned multiprocessor scheduling has been widely accepted in academia and industry to statically assign and partition real-time tasks onto identical multiprocessor systems. This paper studies fixed-priority partitioned multiprocessor scheduling for sporadic real-time systems, in which deadline-monotonic scheduling is applied on each processor. Prior to this paper, the best known results are by Fisher, Baruah, and Baker with speedup factors 4-2/M and 3-1/M for arbitrary-deadline and constrained-deadline sporadic real-time task systems, respectively, where M is the number of processors. We show that a greedy mapping strategy has a speedup factor 3-1/M when considering task systems with arbitrary deadlines. Such a factor holds for polynomial-time schedulability tests and exponential-time (exact) schedulability tests. Moreover, we also improve the speedup factor to 2.84306 when considering constrained-deadline task systems. We also provide tight examples when the fitting strategy in the mapping stage is arbitrary and M is sufficiently large. For both constrained-and arbitrary-deadline task systems, the analytical result surprisingly shows that using exact tests does not gain theoretical benefits (with respect to speedup factors) if the speedup factor analysis is oblivious of the particular fitting strategy used.

In this paper, we present a new schedulability test that can cope with complex activation patterns for mixed-criticality systems. Under this analysis we proceed to present a shaping approach that can adaptively make use of system slack to improve the quality of service to less critical tasks. Compared with the state-of-the-art scheduling analysis, our scheduling analysis is more effective in handling the case that activation events can be backlogged and task deadlines can be arbitrary; and the shaping approach furthermore reduces the dropped jobs of less critical tasks without jeopardizing the guarantee to critical tasks. Extensive simulations and real-life deployment in Raspberry Pi 3 board confirm the effectiveness of our proposed schedulability test and shaping approach.

REALISM: Reliability-aware energy management in multi-level mixed-criticality systems with service level degradation

Capacity augmentation bound is a widely used quantitative metric in theoretical studies of schedulability analysis for directed acyclic graph (DAG) parallel real-time tasks, which not only quantifies the suboptimality of the scheduling algorithms, but also serves as a simple linear-time schedulability test. Earlier studies on capacity augmentation bounds of the sporadic DAG task model were either restricted to a single DAG task or a set of tasks with implicit deadlines. In this paper, we consider parallel tasks with constrained deadlines under global earliest deadline first policy. We first show that it is impossible to obtain a constant bound for our problem setting, and derive both lower and upper bounds of the capacity augmentation bound as a function with respect to the maximum ratio of task period to deadline. Our upper bound is at most 1.47 times larger than the optimal one. We conduct experiments to compare the acceptance ratio of our capacity augmentation bound with the existing schedulability test also having linear-time complexity. The results show that our capacity augmentation bound significantly outperforms the existing linear-time schedulability test under different parameter settings.

Energy-aware fault-tolerant scheduling for imprecise mixed-criticality systems with semi-clairvoyance

There is a growing interest in adopting object technologies for the development of real-time control systems. Several commercial tools, currently available, provide object-oriented modeling and design support for real-time control systems. While these products provide many useful facilities, such as visualization tools and automatic code generation, they are all weak in addressing the central characteristic of real-time control systems design, i.e., providing support for a designer to reason about timeliness properties. We believe an approach that integrates the advancements in both object modeling and design methods and real-time scheduling theory is the key to successful use of object technology for real-time software. Surprisingly several past approaches to integrate the two either restrict the object models, or do not allow sophisticated schedulability analysis techniques. This study shows how schedulability analysis can be integrated with UML for Real-Time (UML-RT) to deal with timing properties in real time control systems. More specifically, we develop the schedulability and feasibility analysis modeling for the external messages that may suffer release jitter due to being dispatched by a tick driven scheduler in real-time control system and we also develop the scheduliablity modeling for sporadic activities, where messages arrive sporadically then execute periodically for some bounded time. This method can be used to cope with timing constraints in realistic and complex real-time control systems. Using this method, a designer can quickly evaluate the impact of various implementation decisions on schedulability. In conjunction with automatic code-generation, we believe that this will greatly streamline the design and development of real-time control systems software.

An efficient approach for the multiprocessor non-preemptive strictly periodic task scheduling problem

The Real-Time Calculus (RTC) [1] is a framework to analyze heterogeneous real-time systems that process event streams of data. The streams are characterized by pairs of curves, called arrival curves, that express upper and lower bounds on the number of events that may arrive over any specified time interval. System properties may then be computed using algebraic techniques in a compositional way. A wellknown limitation of RTC is that it cannot model systems with states and recent works [2,3,4,5] studied how to interface RTC curves with statebased models. Doing so, while trying, for example to generate a stream of events that satisfies some given pair of curves, we faced a causality problem [6]: it can be the case that, once having generated a finite prefix of an event stream, the generator deadlocks, since no extension of the prefix can satisfy the curves anymore. When trying to express the property of the curves with state-based models, one may face the same problem. This paper formally defines the problem on arrival curves, and gives algebraic ways to characterize causal pairs of curves, i.e. curves for which the problem cannot occur. Then, we provide algorithms to compute a causal pair of curves equivalent to a given curve, in several models. These algorithms provide a canonical representation for a pair of curves, which is the best pair of curves among the curves equivalent to the ones they take as input.KeywordsEvent StreamCumulative CurveCumulative CurfCausality ClosureCausality ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.