一种改进的RM可调度性判定算法

固定优先级任务可调度性判定是实时系统调度理论研究的核心问题之一.目前已有的各种判定方法可归结为两大类:多项式时间调度判定和确切性判定.多项式时间调度判定通常采用调度充分条件来进行,为此,许多理想条件下基于RM(rate monotonic)调度算法的CPU利用率最小上界被提了出来.确切性判定利用RM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.但是由于时间复杂度较差,确切性判定方法难以实现在线分析.提出了一种改进的RM可调度性判定方法(improved schedulability test algorithm,简称ISTA).首先介绍了任务调度空间这一概念,并提出了二叉树表示,然后进一步提出了相关的剪枝理论.在此基础上,研究了任务之间可调度性的相关性及其对判定任务集可调度性的影响,提出并证明了相关的定理.最后基于提出的定理,给出了一种改进的伪多项式时间可调度性判定算法,并与已有的判定方法进行了比较.仿真结果表明,该算法平均性能作为任务集内任务个数的函数具有显著提高.     

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。     

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.     

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.     

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.

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。     

多处理器EPDFPfair算法的可调度性判定

针对多处理器实时调度中的最早伪时限优先(EPDF)Pfair算法,分析了EPDF算法在M个处理器平台上的可调度利用率约束,根据基于利用率的充分可调度性判定,提出了一种改进的可调度性判定方法。这种方法可以得到更多的可调度任务集,从而使得满足判定的强实时系统和使用tie-breaking规则困难的动态任务系统的调度有较小的开销。实验结果表明,改进的可调度性判定方法增加了判为可调度的任务集数量,具有较好的性能。     

固定优先级调度的线性近似分析方法

通过线性逼近硬实时系统任务的工作负荷量的方法,一个更加接近精确响应时间的时间上限能有效地降低调度分析时间。同时该上限用于任务集的充分性可调度测试时具有线性时间的复杂度。这种线性上限的可调度性测试能够用于交互的系统工具设计、基于搜索的系统优化以及任务集的动态接纳新任务的设计中。并且新的调度系统模型无时间死线、抖动大小限制,适用范围更广。相关的实验也表明响应时间上限可调度性分析提高了准确调度测试的效率。     

单调速率及其扩展算法的可调度性判定

任务可调度性判定是实时系统调度理论研究的核心问题.单调速率(RM)算法是实时调度的重要算法,自其提出以来已被广泛研究.然而到目前为止,尚缺乏专题性的文章来系统而深入地探讨RM及其扩展算法的可调度性判定,以及各种现实条件和实现方式(包括任务调度的时间开销和任务同步问题等)对可调度性的影响.围绕RM算法下的可调度性判定问题,由浅入深,系统性地讨论各种不同假设和实现方式对可调度性的影响,具体为下述3大类问题：（1）理想的RM算法下的可调度性判定的CPU利用率最小上界最小及可调度的充分必要条件;（2）考虑调度时间开销情况下的可调度性判定条件;（3）优先级反转协议及其对可调度性的影响.给除了具体实例来叙述上述问题,并从算法复杂度和可检测率两方面比较各种算法的优劣。     

Improved multiprocessor global schedulability analysis

A new technique was recently introduced by Bonifaci et al. for the analysis of real-time systems scheduled on multiprocessor platforms by the global Earliest Deadline First (EDF) scheduling algorithm. In this paper, this technique is generalized so that it is applicable to the schedulability analysis of real-time systems scheduled on multiprocessor platforms by any work-conserving algorithm. The resulting analysis technique is applied to obtain a new sufficient global Deadline Monotonic (DM) schedulability test. It is shown that this new test is quantitatively superior to pre-existing DM schedulability analysis tests; in addition, the degree of its deviation from any hypothetical optimal scheduler (that may be clairvoyant) is quantitatively bounded. A new global EDF schedulability test is also proposed here that builds on the results of Bonifaci et al. This new test is shown to be less pessimistic and more widely applicable than the earlier result was, while retaining the strong theoretical properties of the earlier result.     

优先级受限系统中可调度判定方法

在通信、雷达、导航以及各种消费类电子产品等民用和军事领域,嵌入式实时调度已逐渐成为电子电气系统的控制核心。针对同优先级任务使用FIFO调度的静态优先级系统,使用反例指出给定同优先级任务初始执行顺序的前提下,Katcher可调度判定条件的必要性不成立,提出并解析证明了FP可调度的充要条件。随机实验表明,对于高利用率下任务间执行时间差异较大的情况,约有15%的可调度任务集会被Katcher条件错判为不可调度。进一步的仿真和实例分析表明,Liu、Lehoczky、Bini等提出的条件不能判定相同优先级的情况,Katcher条件的必要性不成立,论文提到的条件能够正确判定任务集的可调度性。提出方法为实时系统调度的顶层设计提供了快速离线工具。     

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.     

基于负载计算的多处理器全局EDF判定方法

在多处理器实时调度过程中,干涉上界的取值对于可调度性判定的性能具有较大影响。为此,针对实时系统的最早截止期优先调度算法,引入任务松弛的有关概念,提出一种基于负载计算的可调度性判定方法。通过减小问题区间内带入作业的工作负载取值,增加任务集通过可调度性判定的可能。实验结果表明,随着处理器数量的增加,该判定方法较传统方法有5%~10%的性能提升。     

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.     

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     

多处理器硬实时系统的抢占阈值调度研究

在实时系统中,抢占在提高系统灵活性的同时带来额外的系统开销,特别在多处理器平台上抢占导致的作业迁移会造成相当大的性能下降,减少不必要的抢占是硬实时系统研究的重要方向.抢占阈值调度是处于抢占调度和不可抢占调度之间的一种混合调度方法,在保持调度能力的基础上限制抢占.基于截止期分析建立了多处理器硬实时系统抢占阈值调度的可调度性判定条件,针对抢占阈值调度提出一种改进的优先级分配算法OPA-MLL,并建立了抢占阈值分配(preemption threshold assignment, PTA)算法.仿真结果表明,采用OPA-MLL算法和PTA算法分别给任务集分配优先级和抢占阈值时,可调度任务集比率明显提高,同时能最大程度限制抢占次数.     

FPSL, FPCL and FPZL schedulability analysis

This paper presents the Fixed Priority until Static Laxity (FPSL), Fixed Priority until Critical Laxity (FPCL) and Fixed Priority until Zero Laxity (FPZL) scheduling algorithms for multiprocessor real-time systems. FPZL is similar to global fixed priority pre-emptive scheduling; however, whenever a task reaches a state of zero laxity it is given the highest priority. FPSL and FPCL are variants of FPZL that introduce no additional scheduling points beyond those present with fixed priority scheduling. FPSL, FPCL and FPZL are minimally dynamic algorithms, in that the priority of a job can change at most once during its execution, bounding the number of pre-emptions. Polynomial time and pseudo-polynomial time sufficient schedulability tests are derived for these algorithms. The tests are then improved by computing upper bounds on the amount of execution that each task can perform at the highest priority. An empirical evaluation shows that FPSL, FPCL, and FPZL are highly effective, with a significantly larger number of tasksets deemed schedulable by the tests derived in this paper, than by state-of-the-art schedulability tests for EDZL scheduling.     

不可抢占式EDF调度算法的可调度性分析

现有的不可抢占式EDF调度算法的可调度性分析判定条件限定实时任务的截止期必须等于其周期,限制了它的使用范围。论文突破这一限制,提出了更具一般性的可调度性分析判定充要条件。通过对可调度性判定充要条件的分析,提出了基于不可抢占式EDF调度算法的周期性实时系统可调度性分析算法。     

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.     

静态实时中间件的优先级映射问题

使用截止期单调(DM)调度算法和分布式优先级冲顶资源访问控制协议(DPCP)的实时CORBA系统中,当节点的本地优先级个数不足时,必须将多个全局优先级映射成一个本地优先级.这需要：①判定映射后任务可调度性的充分必要条件;②减少时间复杂度的映射算法.为此,推导出判定条件,确定了DGPM映射算法.该算法在保证系统可调度的前提下分配任务,或者证明映射后系统不可调度.证明了DGPM算法能调度其他直序列优先级映射算法可调度的任务和GCS集合.判定条件和算法在实际项目中得到了应用.