Using an adversary simulator to evaluate global EDF scheduling of sporadic task sets on multiprocessors

Schedulability analysis of real-time multiprocessor systems is usually based on sufficient but not necessary tests that produce pessimistic results. One difficulty in evaluating the effectiveness of sufficient schedulability tests has been distinguishing the cause of a task set failing the test, i.e., finding out whether the task set is in fact not schedulable or it is actually schedulable but the test itself is too pessimistic. Necessary schedulability tests help to distinguish between these two situations, since if a task set fails in the test then it is guaranteed to be unschedulable. An adversary simulator is a scheduling simulator that uses the non-determinism of the task model to generate scenarios that will stress a specific scheduling algorithm, improving the odds of a deadline miss. In this paper we describe a new adversary simulator algorithm for sporadic task sets executed on multiprocessors scheduled by Global Earliest Deadline First (G-EDF). It is shown that this new adversary simulator is more effective as a necessary test than existing approaches. We also estimate the uncertainty regarding G-EDF by applying to the same task sets a well-known sufficient schedulability test from the literature and the necessary schedulability test based on the adversary simulator.     

Implementation and evaluation of global and partitioned scheduling in a real-time OS

In this work, we provide an experimental comparison between Global-EDF and Partitioned-EDF, considering the run-time overhead of a real-time operating system (RTOS). Recent works have confirmed that OS implementation aspects, such as the choice of scheduling data structures and interrupt handling mechanisms, impact real-time schedulability as much as scheduling theoretic aspects. However, these studies used real-time patches applied into a general-purpose OS. By measuring the run-time overhead of an RTOS designed from scratch, we show how close the schedulability ratio of task sets is to the theoretical hard real-time schedulability tests. Moreover, we show how a well-designed object-oriented RTOS allows code reuse of scheduling components (e.g., thread, scheduling criteria, and schedulers) and easy real-time scheduling extensions. We compare our RTOS to a real-time patch for Linux in terms of the task set schedulability ratio of several generated task sets. In some cases, Global-EDF considering the overhead of the RTOS is superior to Partitioned-EDF considering the overhead of the patched Linux, which clearly shows how different OSs impact hard real-time schedulers.     

基于改进型统一调度算法改善任务集的可调度性

实时系统要求任务在最差情况下能在其截止时间前获得结果,若超过了其截止时间,也会认为是错误的行为,所以改进任务可调度性分析、提高任务集可调度性尤其重要。统一调度能结合固定优先级调度的优点,防止不必要的抢占,降低资源额外销耗,能够提高任务集合的可调度性;但其任务的可调度性分析方法过于粗糙,影响任务最差响应时间分析的结果,降低了任务集的可调度性。针对存在的问题,基于统一调度,增加任务运行阶段数,重新建立任务模型,并提出通过分配任务抢占阈值、调整运行阶段的抢占阈值与长度,优化任务可容忍阻塞,改善任务集可调度性的算法。最后,实验表明,与统一调度算法及其他算法相比,所提出的调度算法能够有效改善任务集的可调度性。     

Unified overhead-aware schedulability analysis for slot-based task-splitting

Hard real- time multiprocessor scheduling has seen, in recent years, the flourishing of semi-partitioned scheduling algorithms. This category of scheduling schemes combines elements of partitioned and global scheduling for the purposes of achieving efficient utilization of the system’s processing resources with strong schedulability guarantees and with low dispatching overheads. The sub-class of slot-based “task-splitting” scheduling algorithms, in particular, offers very good trade-offs between schedulability guarantees (in the form of high utilization bounds) and the number of preemptions/migrations involved. However, so far there did not exist unified scheduling theory for such algorithms; each one was formulated in its own accompanying analysis. This article changes this fragmented landscape by formulating a more unified schedulability theory covering the two state-of-the-art slot-based semi-partitioned algorithms, S-EKG and NPS-F (both fixed job-priority based). This new theory is based on exact schedulability tests, thus also overcoming many sources of pessimism in existing analysis. In turn, since schedulability testing guides the task assignment under the schemes in consideration, we also formulate an improved task assignment procedure. As the other main contribution of this article, and as a response to the fact that many unrealistic assumptions, present in the original theory, tend to undermine the theoretical potential of such scheduling schemes, we identified and modelled into the new analysis all overheads incurred by the algorithms in consideration. The outcome is a new overhead-aware schedulability analysis that permits increased efficiency and reliability. The merits of this new theory are evaluated by an extensive set of experiments.     

Non-migratory feasibility and migratory schedulability analysis of multiprocessor real-time systems

The multiprocessor scheduling of collections of real-time jobs is considered. Sufficient tests are derived for feasibility analysis of a collection of sporadic jobs where job migration between processors is forbidden. The fixed-priority scheduling of real-time jobs with job migration is analyzed, and sufficient tests of schedulability are obtained for the deadline-monotonic (dm) and the earliest-deadline-first (edf) scheduling algorithms. The feasibility and schedulability tests of this paper may be applied even when the collection of jobs is incompletely specified. The applicability of these tests to the scheduling of collections of jobs that are generated by systems of recurrent real-time tasks is discussed. In particular, sufficient conditions for the dm scheduling of sporadic task systems are derived and compared to previously-known tests.     

Engineering and analysis of fixed priority schedulers

Scheduling theory holds great promise as a means to a priori validate timing correctness of real-time applications. However, there currently exists a wide gap between scheduling theory and its implementation in operating system kernels running on specific hardware platforms. The implementation of any particular scheduling algorithm introduces overhead and blocking components which must be accounted for in the timing correctness validation process. This paper presents a methodology for incorporating the costs of scheduler implementation within the context of fixed priority scheduling algorithms. Both event-driven and timer-driven scheduling implementations are analyzed. We show that for the timer-driven scheduling implementations the selection of the timer interrupt rate can dramatically affect the schedulability of a task set, and we present a method for determining the optimal timer rate. We analyzed both randomly generated and two well-defined task sets and found that their schedulability can be significantly degraded by the implementation costs. Task sets that have ideal breakdown utilization over 90% may not even be schedulable when the implementation costs are considered. This work provides a first step toward bridging the gap between real-time scheduling theory and implementation realities. This gap must be bridged for any meaningful validation of timing correctness properties of real-time applications     

基于分区的航电系统调度分析工具实现

针对仅含纯周期任务集合、符合ARINC653多分区构架航电系统两级调度模型的可调度性判定问题,提出一种基于分区的航电系统调度分析工具。通过设定时钟变量模拟航电系统各分区中任务集调度过程,依据纯周期任务集及分区航电系统时间片分派特性确定仿真区间,设计优化的调度分析算法,判定航电系统分区级时间片分派的正确性及各分区中任务集的可调度性。测试及实例分析结果表明,该工具能自动、准确、快速地判定航电系统分区以及任务级调度模型的可调度性,并能以甘特图的方式绘制系统调度过程,较现有工具更为直观、高效。     

A New Approach for Scheduling of Parallelizable Tasks in Real-Time Multiprocessor Systems

In a parallelizable task model, a task can be parallelized and the component tasks can be executed concurrently on multiple processors. We use this parallelism in tasks to meet their deadlines and also obtain better processor utilisation compared to non-parallelized tasks. Non-preemptive parallelizable task scheduling combines the advantages of higher schedulability and lower scheduling overhead offered by the preemptive and non-preemptive task scheduling models, respectively. We propose a new approach to maximize the benefits from task parallelization. It involves checking the schedulability of periodic tasks (if necessary, by parallelizing them) off-line and run-time scheduling of the schedulable periodic tasks together with dynamically arriving aperiodic tasks. To avoid the run-time anomaly that may occur when the actual computation time of a task is less than its worst case computation time, we propose efficient run-time mechanisms.We have carried out extensive simulation to study the effectiveness of the proposed approach by comparing the schedulability offered by it with that of dynamic scheduling using Earliest Deadline First (EDF), and by comparing its storage efficiency with that of the static table-driven approach. We found that the schedulability offered by parallelizable task scheduling is always higher than that of the EDF algorithm for a wide variety of task parameters and the storage overhead incurred by it is less than 3.6% of the static table-driven approach even under heavy task loads.     

Laxity dynamics and LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with a smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, little work has been made to illuminate its characteristics upon multiprocessor platforms. In this paper, we identify the dynamics of laxity from the system??s viewpoint and translate the dynamics into LLF multiprocessor schedulability analysis. More specifically, we first characterize laxity properties under LLF scheduling, focusing on laxity dynamics associated with a deadline miss. These laxity dynamics describe a lower bound, which leads to the deadline miss, on the number of tasks of certain laxity values at certain time instants. This lower bound is significant because it represents invariants for highly dynamic system parameters (laxity values). Since the laxity of a task is dependent of the amount of interference of higher-priority tasks, we can then derive a set of conditions to check whether a given task system can go into the laxity dynamics towards a deadline miss. This way, to the author??s best knowledge, we propose the first LLF multiprocessor schedulability test based on its own laxity properties. We also develop an improved schedulability test that exploits slack values. We mathematically prove that the proposed LLF tests dominate the state-of-the-art EDZL tests. We also present simulation results to evaluate schedulability performance of both the original and improved LLF tests in a quantitative manner.     

Design optimization for AUTOSAR models with preemption thresholds and mixed-criticality scheduling

Safety-critical embedded systems are often subject to multiple certification requirements from different certification authorities, giving rise to the concept of Mixed-Criticality Systems. Preemption Threshold Scheduling (PTS) is an effective technique for reducing stack memory usage by selectively disabling preemption between pairs of tasks. In this paper, we consider the AUTOSAR standard in automotive embedded software development, where each task consists of multiple runnables that are scheduled with static priority and preemption threshold. We address the problems of design synthesis from an AUTOSAR model to minimize stack usage for mixed-criticality systems with preemption threshold scheduling, and present algorithms for schedulability analysis and system stack usage minimization. Experimental results demonstrate that our approach can significantly reduce the system stack usage.     

Cache-Conscious Limited Preemptive Scheduling

In multi-tasking real-time systems, inter-task cache interference due to preemptions degrades schedulability as well as performance. To address this problem, we propose a novel scheduling scheme, called limited preemptive scheduling (LPS), that limits preemptions to execution points with small cache-related preemption costs. Limiting preemptions decreases the cache-related preemption costs of tasks but increases blocking delay of higher priority tasks. The proposed scheme makes an optimal trade-off between these two factors to maximize the schedulability of a given task set while minimizing cache-related preemption delay of tasks. Experimental results show that the LPS scheme improves the maximum schedulable utilization by up to 40\% compared with the traditional fully preemptive scheduling (FPS) scheme. The results also show that up to 20\% of processor time is saved by the LPS scheme due to reduction in the cache-related preemption costs. Finally, the results show that both the improvement of schedulability and the saving of processor time by the LPS scheme increase as the speed gap between the processor and main memory widens.     

An efficient dynamic scheduling algorithm for multiprocessorreal-time systems

Many time-critical applications require predictable performance and tasks in these applications have deadlines to be met. In this paper, we propose an efficient algorithm for nonpreemptive scheduling of dynamically arriving real-time tasks (aperiodic tasks) in multiprocessor systems. A real-time task is characterized by its deadline, resource requirements, and worst case computation time on p processors, where p is the degree of parallelization of the task. We use this parallelism in tasks to meet their deadlines and, thus, obtain better schedulability compared to nonparallelizable task scheduling algorithms. To study the effectiveness of the proposed scheduling algorithm, we have conducted extensive simulation studies and compared its performance with the myopic scheduling algorithm. The simulation studies show that the schedulability of the proposed algorithm is always higher than that of the myopic algorithm for a wide variety of task parameters     

Demand-based schedulability analysis for real-time multi-core scheduling

In real-time systems, schedulability analysis has been widely studied to provide offline guarantees on temporal correctness, producing many analysis methods. The demand-based schedulability analysis method has a great potential for high schedulability performance and broad applicability. However, such a potential is not yet fully realized for real-time multi-core scheduling mainly due to (i) the difficulty of calculating the resource demand under dynamic priority scheduling algorithms that are favorable to multi-cores, and (ii) the lack of understanding how to combine the analysis framework with deadline-miss conditions specialized for those scheduling algorithms. Addressing those two issues, to the best of our knowledge, this paper presents the first demand-based schedulability analysis for dynamic job-priority scheduling algorithms: EDZL (Earliest Deadline first until Zero-Laxity) and LLF (Least Laxity First), which are known to be effective for real-time multi-core scheduling. To this end, we first derive demand bound functions that compute the maximum possible amount of resource demand of jobs of each task while the priority of each job can change dynamically under EDZL and LLF. Then, we develop demand-based schedulability analyses for EDZL and LLF, by incorporating those new demand bound functions into the existing demand-based analysis framework. Finally, we combine the framework with additional deadline-miss conditions specialized for those two laxity-based dynamic job-priority scheduling algorithms, yielding tighter schedulability analyses. Via simulations, we demonstrate that the proposed schedulability analyses outperform the existing schedulability analyses for EDZL and LLF.     

基于双曲线边界的多处理器实时任务可调度性判定

Lopez等学者求解出基于单调速率算法和首次适应分派策略的多处理器实时任务可调度性判定边界.该边界在所有O(m)复杂度的判定边界中是最优的.基于Bini等学者针对单处理器提出的双曲线可调度性判定方法,给出了一种多处理器实时任务可调度性判定边界.新边界在相当数量的利用率分布下明显优于已有边界.新边界与已有边界具有相容性,所以虽然新边界无法在所有情况下超越已有边界,但在实际应用中可联合两种边界进行判定,在不增加计算复杂度的同时全面提高可调度任务集的数量.     

RM及其扩展可调度性判定算法性能分析

可调度性判定是实时调度算法的关键问题·单调速率算法RM(ratemonotonic)及其扩展是应用广泛的实时调度算法,大量文献讨论了实时任务在这些算法下的可调度性判定,给出了相应的判定算法·但迄今为止,对这些判定算法的性能分析都是理论上的定性分析或者只是少数几种判定算法之间的简单比较,这不利于实时系统的开发·归纳了RM及其扩展的可调度性判定算法,通过测试平台,系统地测试和分析了各算法的性能和适用场合,讨论了各种条件和实现方式对算法性能和可调度性的影响·     

一种不影响任务集合可调度性的优先级映射算法

采用静态优先级调度的实时系统中,当任务个数多于优先级个数时,只能给多个任务分配相同的优先级·现有分配算法增大了高优先级任务的最坏情况响应时间,可能造成任务集合不可调度·利用抢占阈值的调度算法,能在提高任务集合可调度性的同时,使用较少的线程·但所用优先级个数没有减少·提出了一种优先级映射算法———阈值段间映射法(threshold segment mapping,TSM),以及与之配合的事件驱动线程框架·证明了TSM是严格排序的·仿真结果表明,在保证任务集合可调度的前提下,TSM使用了比现有映射算法更少的优先级·     

Rolling-horizon scheduling for energy constrained distributed real-time embedded systems

Energy-efficient scheduling approaches are critical to battery driven real-time embedded systems. Traditional energy-aware scheduling schemes are mainly based on the individual task scheduling. Consequently, the scheduling space for each task is small, and the schedulability and energy saving are very limited, especially when the system is heavily loaded. To remedy this problem, we propose a novel rolling-horizon (RH) strategy that can be applied to any scheduling algorithm to improve schedulability. In addition, we develop a new energy-efficient adaptive scheduling algorithm (EASA) that can adaptively adjust supply voltages according to the system workload for energy efficiency. Both the RH strategy and EASA algorithm are combined to form our scheduling approach, RH-EASA. Experimental results show that in comparison with some typical traditional scheduling schemes, RH-EASA can achieve significant energy savings while meeting most task deadlines (namely, high schedulability) for distributed real-time embedded systems with dynamic workloads.     

Holistic analysis of asynchronous real-time transactions with earliest deadline scheduling

In distributed real-time systems, an application is often modeled as a set of real-time transactions, where each transaction is a chain of precedence-constrained tasks. Each task is statically allocated to a processor, and tasks allocated on the same processor are handled by a single-processor scheduling algorithm. Precedence constraints among tasks of the same transaction are modeled by properly assigning scheduling parameters as offsets, jitters and intermediate deadlines.In this paper we address the problem of schedulability analysis of distributed real-time transactions under the earliest deadline first scheduling algorithm. We propose a novel methodology that reduces the pessimism introduced by previous methods by explicitly taking into account the offsets of the tasks. Moreover, we extend the analysis to account for blocking time due to shared resources. In particular, we propose two kinds of schedulability tests, CDO-TO and MDO-TO, and show, with an extensive set of simulations, that they provides improved schedulability conditions with respect to classical algorithms. Finally, we apply the methodology to an important class of systems: heterogeneous multiprocessor systems, with a general purpose processor and one or more coprocessors (DSPs).     

Interference-aware fixed-priority schedulability analysis on multiprocessors

This paper presents new schedulability tests for preemptive global fixed-priority (FP) scheduling of sporadic tasks on identical multiprocessor platform. One of the main challenges in deriving a schedulability test for global FP scheduling is identifying the worst-case runtime behavior, i.e., the critical instant, at which the release of a job suffers the maximum interference from the jobs of its higher priority tasks. Unfortunately, the critical instant is not yet known for sporadic tasks under global FP scheduling. To overcome this limitation, pessimism is introduced during the schedulability analysis to safely approximate the worst-case. The endeavor in this paper is to reduce such pessimism by proposing three new schedulability tests for global FP scheduling. Another challenge for global FP scheduling is the problem of assigning the fixed priorities to the tasks because no efficient method to find the optimal priority ordering in such case is currently known. Each of the schedulability tests proposed in this paper can be used to determine the priority of each task based on Audsley’s approach. It is shown that the proposed tests not only theoretically dominate but also empirically perform better than the state-of-the-art schedulability test for global FP scheduling of sporadic tasks.     

Parameter adaptation for generalized multiframe tasks: schedulability analysis,case study,and applications to self-suspending tasks

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.