An exact schedulability test for fixed-priority preemptive mixed-criticality real-time systems

The current literature of fixed-priority scheduling algorithms relies on sufficient tests to determine if a set of mixed-criticality sporadic tasks is schedulable on a single processor. The drawback of these safe tests is their pessimism, a matter that could be solved if an exact schedulability analysis is used. However, because of the non-deterministic behavior of tasks in the mentioned setups, exact quantification of worst-case response times, needed for the test, is a difficult problem; more precisely, such a quantification needs evaluation of enormous sequences of job executions. The core problem is thus to merge such sequences to make the analysis practical. This paper, for the first time, gives an algorithm for exact worst-case response time characterization of mixed-criticality sporadic real-time tasks executing according to a given fixed-priority scheduler. We use a set of techniques which carefully consider the task properties and their relation to the worst scenarios to prune the analysis state space. We also show an interesting result that if an exact schedulability test is used, the Audsley’s optimal priority assignment algorithm is not applicable to the mixed-criticality case. Accordingly, we need new priority assignment algorithms to work with the exact test; we give a simple task priority assignment algorithm to this aim. The performance of the proposed exact test (in terms of time complexity) is examined and the effectiveness of some heuristic priority assignment algorithms using the test (in terms of the ratio of task sets which are deemed schedulable) are compared.     

A Constant-Approximate Feasibility Test for?Multiprocessor Real-Time Scheduling

We devise an approximate feasibility test for multiprocessor real-time scheduling in the sporadic task model. We give an algorithm that, given a task system and ε>0, correctly decides either that the task system can be scheduled using the Earliest Deadline First algorithm on m speed-(2?1/m+ε) machines, or that the system is not schedulable by any algorithm on m unit speed machines. This speedup bound is known to be the best possible for EDF. The running time of the algorithm is polynomial in the size of the task system and 1/ε. We also provide a generalized tight bound that trades off speed with additional machines.     

Algorithms and optimality of scheduling soft aperiodic requests in fixed-priority preemptive systems

In this paper, we investigate the problem of scheduling soft aperiodic requests in systems where periodic tasks are scheduled on a fixed-priority, preemptive basis. First, we show that given any queueing discipline for the aperiodic requests, no scheduling algorithm can minimize the response time of every aperiodic request and guarantee that the deadlines of the periodic tasks are met when the periodic tasks are scheduled on a fixed-priority, preemptive basis. We then develop two algorithms: Algorithm is locally optimal in that it minimizes the response time of the aperiodic request at the head of the aperiodic service queue. Algorithm is globally optimal in that it completes the current backlog of work in the aperiodic service queue as early as possible.     

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.     

Exact quantification of the sub-optimality of uniprocessor fixed priority pre-emptive scheduling

This paper examines the relative effectiveness of fixed priority pre-emptive scheduling in a uniprocessor system, compared to an optimal algorithm such as Earliest Deadline First (EDF). The quantitative metric used in this comparison is the processor speedup factor, equivalent to the factor by which processor speed needs to increase to ensure that any taskset that is schedulable according to an optimal scheduling algorithm can be scheduled using fixed priority pre-emptive scheduling, assuming an optimal priority assignment policy.     

EDZL scheduling analysis

A schedulability test is derived for the global Earliest Deadline Zero Laxity (EDZL) scheduling algorithm on a platform with multiple identical processors. The test is sufficient, but not necessary, to guarantee that a system of independent sporadic tasks with arbitrary deadlines will be successfully scheduled, with no missed deadlines, by the multiprocessor EDZL algorithm. Global EDZL is known to be at least as effective as global Earliest-Deadline-First (EDF) in scheduling task sets to meet deadlines. It is shown, by testing on large numbers of pseudo-randomly generated task sets, that the combination of EDZL and the new schedulability test is able to guarantee that far more task sets meet deadlines than the combination of EDF and known EDF schedulability tests. In the second part of the paper, an improved version of the EDZL-schedulability test is presented. This new algorithm is able to efficiently exploit information on the slack values of interfering tasks, to iteratively refine the estimation of the interference a task can be subjected to. This iterative algorithm is shown to have better performance than the initial test, in terms of schedulable task sets detected.

Fault-tolerant and real-time scheduling for mixed-criticality systems

The design and analysis of real-time scheduling algorithms for safety-critical systems is a challenging problem due to the temporal dependencies among different design constraints. This paper considers scheduling sporadic tasks with three interrelated design constraints: (i) meeting the hard deadlines of application tasks, (ii) providing fault tolerance by executing backups, and (iii) respecting the criticality of each task to facilitate system’s certification. First, a new approach to model mixed-criticality systems from the perspective of fault tolerance is proposed. Second, a uniprocessor fixed-priority scheduling algorithm, called fault-tolerant mixed-criticality (FTMC) scheduling, is designed for the proposed model. The FTMC algorithm executes backups to recover from task errors caused by hardware or software faults. Third, a sufficient schedulability test is derived, when satisfied for a (mixed-criticality) task set, guarantees that all deadlines are met even if backups are executed to recover from errors. Finally, evaluations illustrate the effectiveness of the proposed test.     

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.     

多处理器固定优先级算法的可调度性分析

针对多处理器实时调度中的固定优先级(FP)调度算法,提出了一种改进的可调度性判定方法。引入Baruah的最早截止期优先(EDF)窗口分析框架,将高优先级任务带入作业的最大数量限定为m-1(m为处理器个数),进而对任务的干涉上界进行重新界定,并由此得到一个更加紧密的可调度性判定充分条件。仿真实验结果表明,该方法增加了通过判定任务集的数量,体现出更优的可调度判定性能。     

TinyOS中DSA调度策略的研究

针对TinyOS任务调度采用非剥夺的先来先服务调度策略,而产生的系统紧急任务不能及时得到响应及节点吞吐量下降情况,该文提出一种新的可抢占时限短作业调度策略——DSA。在绝对时限前执行硬实时任务,满足了系统对实时任务的响应要求,提高处理器的响应速度,对软实时任务实行短作业优先调度策略,提高系统的吞吐量。在TinyOS上测试表明,DSA策略在不影响TinyOS原有性能的情况下,改进了传感器网络承担实时性任务的运行效果。     

On the convergence of the holistic analysis for EDF distributed systems

Dynamic scheduling techniques, and EDF (Earliest Deadline First) in particular, have demonstrated their ability to increase the schedulability of real time systems compared to fixed-priority scheduling. In distributed systems, the scheduling policies of the processing nodes tend to be the same as in stand-alone systems and, although few EDF networks exist, it is foreseen that dynamic scheduling will gradually develop into real-time networks. There are some response time analysis techniques for EDF scheduled distributed systems, mostly derived from the holistic analysis developed by Spuri. A major factor influencing the response time is the release jitter of each task, which is the maximum variation suffered by the release time of the task jobs. The convergence of the holistic analysis in the context of EDF distributed systems with shared resources had not been studied until now. There is a circular dependency between the task release jitter values, response times and the preemption level ceilings of shared resources. In this paper we present an extension of Spuri’s algorithm and we demonstrate that its iterative formulas are non-decreasing, even in the presence of shared resources. This result enables us to assert that the new algorithm converges towards a solution for the response times of the tasks and messages in a distributed system.¹     

On earliest deadline first scheduling for temporal consistency maintenance

A real-time object is one whose state may become invalid with the passage of time. A temporal validity interval is associated with the object state, and the real-time object is temporally consistent if its temporal validity interval has not expired. Clearly, the problem of maintaining temporal consistency of data is motivated by the need for a real-time system to track its environment correctly. Hence, sensor transactions must be able to execute periodically and also each instance of a transaction should perform the relevant data update before its deadline. Unfortunately, the period and deadline assignment problem for periodic sensor transactions has not received the attention that it deserves. An exception is the More-Less scheme, which uses the Deadline Monotonic (DM) algorithm for scheduling periodic sensor transactions. However, there is no work addressing this problem from the perspective of dynamic priority scheduling. In this paper, we examine the problem of temporal consistency maintenance using the Earliest Deadline First (EDF) algorithm in three steps: First, the problem is transformed to another problem with a sufficient (but not necessary) condition for feasibly assigning periods and deadlines. An optimal solution for the problem can be found in linear time, and the resulting processor utilization is characterized and compared to a traditional approach. Second, an algorithm to search for the optimal periods and deadlines is proposed. The problem can be solved for sensor transactions that require any arbitrary deadlines. However, the optimal algorithm does not scale well when the problem size increases. Hence, thirdly, we propose a heuristic search-based algorithm that is more efficient than the optimal algorithm and is capable of finding a solution if one exists.

面向分布式实时系统的安全驱动调度算法研究

针对现有实时调度算法无法适应动态安全需求的问题,构建了一种安全驱动调度模型,该模型从系统安全级别、系统安全服务和任务安全策略三个方面描述了实时系统的动态安全需求,并设计了一种基于安全驱动的实时任务调度器框架。以该模型和框架为基础,提出了一种安全驱动调度算法(Security Driven Scheduling Algorithm,SDSA)。从全局角度对新到达任务进行可调度性检查,并将可调度任务分配到合适的处理机上运行。按照系统安全级别来动态调整已分配到各处理机上实时任务的安全策略,使其达到安全性和可调度性的最优平衡。采用优先级抢占式策略对各实时任务进行调度。仿真结果表明,SDSA算法与其他同类算法相比,在系统动态安全需求的适应性、关键任务的可调度性以及安全防危能力等方面具有较好的表现。     

Schedulability analysis of fixed-priority systems using timed automata

In classic scheduling theory, real-time tasks are usually assumed to be periodic, i.e. tasks are released and computed with fixed rates periodically. To relax the stringent constraints on task arrival times, we propose to use timed automata to describe task arrival patterns. In a previous work, it is shown that the general schedulability checking problem for such models is a reachability problem for a decidable class of timed automata extended with subtraction. Unfortunately, the number of clocks needed in the analysis is proportional to the maximal number of schedulable task instances associated with a model, which is in many cases huge. In this paper, we show that for fixed-priority scheduling strategy, the schedulability checking problem can be solved using standard timed automata with two   extra clocks in addition to the clocks used in the original model to describe task arrival times. The analysis can be done in a similar manner to response time analysis in classic Rate-Monotonic Analysis (RMA). The result is further extended to systems with data-dependent control, in which the release time of a task may depend on the time-point at which other tasks finish their execution. For the case when the execution times of tasks are constants, we show that the schedulability problem can be solved using n+1$n+1$ extra clocks, where n$n$ is the number of tasks. The presented analysis techniques have been implemented in the Times tool. For systems with only periodic tasks, the performance of the tool is comparable with tools implementing the classic RMA technique based on equation-solving, without suffering from the exponential explosion in the number of tasks.     

应用于实时系统的DMS算法可调度性分析

固定优先级任务的可调度性判定是实时系统调度理论研究的核心问题之一。本文提出了一种可行的DMS可调度性判定方法——确切性判定方法（precised schedulability test algorithln,简称PSTA）,利用DMS调度的充要条件,保证任何任务集均可被判定,并且判定结果是确切的。首先给出了DMS调度模型,介绍了可调度性判定的基本思想,然后进一步通过实验提出并证明了PSTA相关的定理。     

Online scheduling of moldable parallel tasks

In this paper, we study an online scheduling problem with moldable parallel tasks on m processors. Each moldable task can be processed simultaneously on any number of processors of a parallel computer, and the processing time of a moldable task depends on the number of processors allotted to it. Tasks arrive one by one. Upon arrival of each task, the scheduler has to determine both the number of processors and the starting time for the task. Moreover, these decisions cannot be changed in the future. The objective is to attain a schedule such that the longest completion time over all tasks, i.e., the makespan, is minimized. First, we provide a general framework to show that any \(\rho \)-bounded algorithm for scheduling of rigid parallel tasks (the number of processors for a task is fixed a prior) can be extended to yield an algorithm for scheduling of moldable tasks with a competitive ratio of \(4\rho \) if the ratio \(\rho \) is known beforehand. As a consequence, we achieve the first constant competitive ratio, 26.65, for the moldable parallel tasks scheduling problem. Next, we provide an improved algorithm with a competitive ratio of at most 16.74.     

Hartstone Uniprocessor Benchmark: Definitions and experiments for real-time systems

The purpose of this paper is to define a series of requirements and associated experiments called the Hartstone Uniprocessor Benchmark (HUB), to be used in testing the ability of a uniprocessor system to handle certain types of hard real-time applications. The benchmark model considers the real-time system as a set of periodic, aperiodic (sporadic), and synchronization (server) tasks. The tasks are characterized by their execution times (workloads), and deadlines. There are five series of experiments defined. They are, in order of increasing complexity, PH (Periodic Tasks, Harmonic Frequencies), PN (Periodic Tasks, Nonharmonic Frequencies), AH (Periodic Tasks with Aperiodic Processing), SH (Periodic Tasks with Synchronization), and SA (Periodic Tasks with Aperiodic Processing and Synchronization). The general stopping criteria of the experiments is defined as follows: Change one of the following four task set parameters: number of tasks, execution time(s), blocking time(s), or deadline(s) until a given task set is no longer schedulable, i.e., a deadline is missed. The derivation of the Hartstone experiments from one static scheduling algorithm (Rate Monotonic) and one dynamic scheduling algorithm (Earliest Deadline First) is presented. Because of its high-level application view of the underlying hardware and real-time system software the Hartstone experiments can be used for fast prototyping of real-time applications. Implementation of such benchmarks is useful in evaluating scheduling algorithms, scheduling protocols, and design paradigms, as well as evaluating real-time languages, the tasking system of compilers, real-time operating systems, and hardware configurations.     

On-line scheduling of parallel machines to minimize total completion times

In this paper, we consider the scheduling problem on identical parallel machines, in which jobs are arriving over time and preemption is not allowed. The goal is to minimize the total completion times. According to the idea of the Delayed-SPT Algorithm proposed by Hoogeven and Vestjens [Optimal on-line algorithms for single-machine scheduling. In: Proceedings 5th international conference on integer programming and combinatorial optimization (IPCO). Lecture notes in computer science, vol. 1084. Berlin: Springer; 1996. p. 404–14], we give an on-line algorithm for the scheduling problem on m$m$ identical parallel machines. We show that this algorithm is 2-competitive and the bound is tight.     

Task automata: Schedulability,decidability and undecidability

We present a model, task automata, for real time systems with non-uniformly recurring computation tasks. It is an extended version of timed automata with asynchronous processes that are computation tasks generated (or triggered) by timed events. Compared with classical task models for real time systems, task automata may be used to describe tasks (1) that are generated non-deterministically according to timing constraints in timed automata, (2) that may have interval execution times representing the best case and the worst case execution times, and (3) whose completion times may influence the releases of task instances. We generalize the classical notion of schedulability to task automata. A task automaton is schedulable if there exists a scheduling strategy such that all possible sequences of events generated by the automaton are schedulable in the sense that all associated tasks can be computed within their deadlines. Our first technical result is that the schedulability for a given scheduling strategy can be checked algorithmically for the class of task automata when the best case and the worst case execution times of tasks are equal. The proof is based on a decidable class of suspension automata: timed automata with bounded subtraction in which clocks may be updated by subtractions within a bounded zone. We shall also study the borderline between decidable and undecidable cases. Our second technical result shows that the schedulability checking problem will be undecidable if the following three conditions hold: (1) the execution times of tasks are intervals, (2) the precise finishing time of a task instance may influence new task releases, and (3) a task is allowed to preempt another running task.     

一种能量收集嵌入式系统自适应调度算法

能量收集嵌入式系统(energy harvesting embedded system,简称EHES)的任务调度算法需要考虑能量收集单元的能量输出、能量存储单元的能量水平和能量消耗单元的能耗.实时任务在满足能量约束的条件下,才可能满足时间约束.在这个背景下,传统固定优先级调度算法不再适用于EHES.提出一种基于分组的自适应任务调度算法,它能根据能量收集单元由于能量输出的不确定性而造成的非能量约束情况和能量约束情况,自适应地选择任务调度算法.在非能量约束的情况下,减少任务抢占次数,增强任务的可调度性;在能量约束情况下,减少电池模式切换次数,提高能量存储单元的平均能量水平,从而降低系统能量约束.在一个可进行大范围任务集合仿真的实验环境下对提出的算法进行验证,并将基于分组的自适应调度算法与现有的两个经典算法进行了对比.