A Feasibility Decision Algorithm for Rate Monotonic and Deadline Monotonic Scheduling

Rate monotonic and deadline monotonic scheduling are commonly used for periodic real-time task systems. This paper discusses a feasibility decision for a given real-time task system when the system is scheduled by rate monotonic and deadline monotonic scheduling. The time complexity of existing feasibility decision algorithms depends on both the number of tasks and maximum periods or deadlines when the periods and deadlines are integers. This paper presents a new necessary and sufficient condition for a given task system to be feasible and proposes a new feasibility decision algorithm based on that condition. The time complexity of this algorithm depends solely on the number of tasks. This condition can also be applied as a sufficient condition for a task system using priority inheritance protocols to be feasible with rate monotonic and deadline monotonic scheduling.     

Utilization bound for periodic task set with composite deadline

Due to polynomial time complexity, utilization based tests are desired for online feasibility analysis of periodic task systems. However, the associated disadvantage with these tests is that they propose a bound on system utilization, which trade processor utilization for performance. On the contrary, response time based tests share pseudo-polynomial time complexity, which are very expensive in terms of analysis time and therefore, impractical for analyzing feasibility of online systems. Realizing the advantage of utilization based tests over response time tests, attempts are being made to propose utilization based exact tests that achieve 100% CPU utilization for the system by modifying task parameters such as restricting task periods to be harmonic. We show that in systems where task deadlines are large, better results are obtained by making the task deadlines harmonic. The paper proposes a novel solution to feasibility problem of periodic task system under the assumption of composite deadline by providing a utilization based exact test with an upper bound of 1 and complexity O(n).     

A group priority earliest deadline first scheduling algorithm

In most priority scheduling algorithms, the number of priority levels is assumed to be unlimited. However, if a task set requires more priority levels than the system can support, several jobs must in practice be assigned the same priority level. To solve this problem, a novel group priority earliest deadline first (GPEDF) scheduling algorithm is presented. In this algorithm, a schedulability test is given to form a job group, in which the jobs can arbitrarily change their order without reducing the schedulability. We consider jobs in the group having the same priority level and use shortest job first (SJF) to schedule the jobs in the group to improve the performance of the system. Compared with earliest deadline first (EDF), best effort (BE), and group-EDF (gEDF), simulation results show that the new algorithm exhibits the least switching, the shortest average response time, and the fewest required priority levels. It also has a higher success ratio than both EDF and gEDF.     

Energy-efficient real-time scheduling for two-type heterogeneous multiprocessors

We propose three novel mathematical optimization formulations that solve the same two-type heterogeneous multiprocessor scheduling problem for a real-time taskset with hard constraints. Our formulations are based on a global scheduling scheme and a fluid model. The first formulation is a mixed-integer nonlinear program, since the scheduling problem is intuitively considered as an assignment problem. However, by changing the scheduling problem to first determine a task workload partition and then to find the execution order of all tasks, the computation time can be significantly reduced. Specifically, the workload partitioning problem can be formulated as a continuous nonlinear program for a system with continuous operating frequency, and as a continuous linear program for a practical system with a discrete speed level set. The latter problem can therefore be solved by an interior point method to any accuracy in polynomial time. The task ordering problem can be solved by an algorithm with a complexity that is linear in the total number of tasks. The work is evaluated against existing global energy/feasibility optimal workload allocation formulations. The results illustrate that our algorithms are both feasibility optimal and energy optimal for both implicit and constrained deadline tasksets. Specifically, our algorithm can achieve up to 40% energy saving for some simulated tasksets with constrained deadlines. The benefit of our formulation compared with existing work is that our algorithms can solve a more general class of scheduling problems due to incorporating a scheduling dynamic model in the formulations and allowing for a time-varying speed profile.     

An Effective Cloud Workflow Scheduling Approach Combining PSO and Idle Time Slot-Aware Rules

Workflow scheduling is a key issue and remains a challenging problem in cloud computing.Faced with the large number of virtual machine(VM)types offered by cloud providers,cloud users need to choose the most appropriate VM type for each task.Multiple task scheduling sequences exist in a workflow application.Different task scheduling sequences have a significant impact on the scheduling performance.It is not easy to determine the most appropriate set of VM types for tasks and the best task scheduling sequence.Besides,the idle time slots on VM instances should be used fully to increase resources'utilization and save the execution cost of a workflow.This paper considers these three aspects simultaneously and proposes a cloud workflow scheduling approach which combines particle swarm optimization(PSO)and idle time slot-aware rules,to minimize the execution cost of a workflow application under a deadline constraint.A new particle encoding is devised to represent the VM type required by each task and the scheduling sequence of tasks.An idle time slot-aware decoding procedure is proposed to decode a particle into a scheduling solution.To handle tasks'invalid priorities caused by the randomness of PSO,a repair method is used to repair those priorities to produce valid task scheduling sequences.The proposed approach is compared with state-of-the-art cloud workflow scheduling algorithms.Experiments show that the proposed approach outperforms the comparative algorithms in terms of both of the execution cost and the success rate in meeting the deadline.     

Simple and integrated heuristic algorithms for scheduling tasks with time and resource constraints

We consider the problem of scheduling a set of n tasks in a system having r resources. Each task has an arbitrary, but known, processing time and a deadline, and may request use of a number of resources. A resource can be used either in shared mode or exclusive mode. In this article, we study algorithms used for determining whether or not a set of tasks is schedulable in such a system, and if so, determining a schedule for it. This scheduling problem is known to be NP-complete and hence we methodically study a set of heuristics that can be used by such an algorithm. Due to the complexity of the problem, simple heuristics do not perform satisfactorily. However, an algorithm that uses combinations of these simple heuristics works very well compared to an optimal algorithm that takes exponential time complexity. For the combination that performs the best, we also determine the scheduling costs as a function of the size of the task set scheduled.     

实时任务准入控制器的自动合成

在许多实时系统中,同一个计算平台上往往既有硬实时关键计算任务又有软实时非关键计算任务.硬实时任务必须在规定时间内完成,否则将导致系统错乱或崩溃等严重后果.而软实时任务若没有在规定时间内完成,虽会影响系统性能,但不会造成重大后果.为确保每个硬实时任务均在其规定时间内完成,在某些情况下需要拒绝一些软实时任务进入任务队列.文章提出了一种基于控制器自动合成策略的解决方案,通过所设计的准入控制器,对系统产生的每一个新任务自动决定是否准其进入任务队列.准入控制器必须使得所有被准入的任务均在规定时间内完成,并且决策序列满足以线性时态逻辑描述的服务质量要求.文章的主要贡献是提出了判定是否存在准入控制器的算法,该算法能在判定结果为真时构造出一个以有限状态时间自动机表达的准入控制器.     

Robust Adaptive Metrics for Deadline Assignment in Distributed Hard Real-Time Systems

Distributed real-time applications usually consist of several component tasks and must be completed by its end-to-end (E-T-E) deadline. As long as the E-T-E deadline of an application is met, the strategy used for dividing it up for component tasks does not affect the application itself. One would therefore like to slice each application E-T-E deadline and assign the slices to component tasks so as to maximize the schedulability of the component tasks, and hence the application. Distribution of the E-T-E deadline over component tasks is a difficult and important problem since there exists a circular dependency between deadline distribution and task assignment. We propose a new deadline-distribution scheme which has two major improvements over the best scheme known to date. It can distribute task deadlines prior to task assignment and relies on new adaptive metrics that yield significantly better performance in the presence of high resource contention. The deadline-distribution problem is formulated for distributed hard real-time systems with relaxed locality constraints, where schedulability analysis must be performed at pre-run-time, and only a subset of the tasks are constrained by pre-assignment to specific processors. Although it is applicable to any scheduling policy, the proposed deadline-distribution scheme is evaluated for a non-preemptive, time-driven scheduling policy. Using extensive simulations, we show that the proposed adaptive metrics deliver much better performance (in terms of success ratio and maximum task lateness) than their non-adaptive counterparts. In particular, the simulation results indicate that, for small systems, the adaptive metrics can improve the success ratio by as much as an order of magnitude. Moreover, the new adaptive metrics are found to exhibit very robust performance over a large variety of application and architecture scenarios.     

Lowest priority first based feasibility analysis of real-time systems

The feasibility problem of periodic tasks under fixed priority systems has always been a critical research issue in real-time systems and a number of feasibility tests have been proposed to guarantee the timing requirements of real-time systems. These tests can be broadly classified into: (a) inexact and (b) exact tests. The inexact tests are applied to the task sets that present lower utilization, while the exact tests become inevitable when system utilization is high. The exact tests can be further classified into: (a) Scheduling Points Tests (SPT) and (b) Response Time Tests (RTT). The SPT analyze task set feasibility at the arrival times while the RTT utilize fixed-point techniques to determine task feasibility. All of the available exact feasibility tests, whichever class it belongs to, share pseudo-polynomial complexity. Therefore, the aforementioned tests become impractical for online systems. Currently, both SPT and RTT employ the Highest Priority First (HPF) approach, which determines the system feasibility by testing the schedulability of individual tasks in the decreasing order of priority. In contrast, this work exploits the Lowest Priority First (LPF) alternative which is an aggressive solution based on the observation that the system infeasibility is primarily due to the lower priority tasks and not because of the higher priority tasks. For the average case analysis, our technique demonstrates promising results. Moreover, in the worst case scenario our solution is no inferior to the existing state of the art alternatives. We compare our proposed technique with the existing tests: (a) by counting the number of scheduling points used by a test that belongs to the SPT, (b) by counting the number of inner-most loops executed by an algorithm for the RTT, and (c) by measuring the actual running time of the existing alternatives.     

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.     

Non-Preemptive Real-Time Scheduling of Multimedia Tasks

Motivated by the special characteristics of multimedia tasks, we consider non-preemptive scheduling of tasks where there exists no (or very limited) information concerning the tasks before they are released. We present impossibility results and analyze algorithms for non-preemptive scheduling in single processor and multiprocessor systems. To evaluate our algorithm we assume that system obtains a value that is proportional to the processing time of the task whenever a task is completed by its deadline. Competitive analysis is used, where the goal is to keep the total value obtained by an on-line algorithm bounded by a function of the total value obtained by an off-line algorithm. In particular, one set of our results considers the competitive ratio of scheduling algorithm when the length of the tasks is not greater than C_max (and not smaller than C_min ). We show that the performance of a scheduling algorithm is improved dramatically when the release time of the tasks is O(C_max) prior to their deadline; achieving a competitive ratio that is close to one.     

非抢占式EDF算法下周期性任务的最小相对截止期计算*

现有的求解周期性任务最小相对截止期的方法均假定任务集是采取抢占式EDF调度算法,并不适用于当任务为基于非抢占式EDF调度算法的场合,如实时通信领域。在分析了非抢占式EDF调度算法的可调度性判定条件基础上,提出了基于非抢占式EDF调度算法下周期性任务最小相对截止期的计算算法。算法通过逐渐增加任务的相对截止期直到使任务集变为可调度的方式,实现某个任务相对截止期的最小化。仿真实验表明该算法具有较好的计算复杂度。     

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。     

一种考虑截止期的METCD业务组合调度方法

海洋设备检定、校准和检测（Marine Equipment Testing, Calibrate & Detection, METCD）业务规模大、紧急情况多,如何对业务进行合理的调配是海洋计量检定行业亟待解决的问题。本文提出了一种考虑截止期的任务组合METCD业务调度方法。在建立业务调度问题数学模型的基础上,采用最早截止时间优先-蚁群算法(EDF-PACO)对模型求解,在最早截止日期的约束条件下对任务组合处理的最优调度方案,达到降低任务总完成时间和减少执行空间浪费双重优化目标。为了验证方法的可行性,以国家海洋局东海标准技术中心的业务为实例,将EDF-PACO算法与传统的最早截止时间优先算法和蚁群算法进行比较,结果表明本文所提出的调度方法在满足截止期的约束条件下能高效地对海洋设备的计量检定业务进行组合调度。     

Resource reclaiming in multiprocessor real-time systems

Most real-time scheduling algorithms schedule tasks with regard to their worst case computation times. Resources reclaiming refers to the problem of utilizing the resources left unused by a task when it executes in less than its worst case computation time, or when a task is deleted from the current schedule. Dynamic resource reclaiming algorithms that are effective, avoid any run time anomalies, and have bounded overhead costs that are independent of the number of tasks in the schedule are presented. Each task is assumed to have a worst case computation time, a deadline, and a set of resource requirements. The algorithms utilize the information given in a multiprocessor task schedule and perform online local optimization. The effectiveness of the algorithms is demonstrated through simulation studies     

Deadline guaranteed packet scheduling for overloaded traffic in input-queued switches

Many applications need to solve the deadline guaranteed packet scheduling problem. However, it is a very difficult problem if three or more deadlines are present in a set of packets to be scheduled. The traditional approach to dealing with this problem is to use EDF (Earliest Deadline First) or similar methods. Recently, a non-EDF based algorithm was proposed that constantly produces a higher throughput than EDF-based algorithms by repeatedly finding an optimal scheduling for two classes. However, this new method requires the two classes be non-overloaded, which greatly restricts its applications. Since the overloaded situation is not avoidable from one iteration to the next in dealing with multiple classes, it is compelling to answer the open question: Can we find an optimal schedule for two overloaded classes efficiently? This paper first proves that this problem is NP-complete. Then, this paper proposes an optimal preprocessing algorithm that guarantees to drop a minimum number of packets from the two classes such that the remaining set is non-overloaded. This result directly improves on the new method.     

基于动态优先级策略的最优软非周期任务调度算法

周期任务与非周期任务的混合调度是实时调度研究的一个重要方向 通过定义“调度”和“逆调度” ,对实时周期任务集在使用EDF算法调度时的可挪用时间进行分析 ,求出了周期任务集在使用EDF调度时的最大可挪用时间 在此基础上 ,提出用于缩短非周期任务响应时间和周转时间的调度算法———ISA(idlestealingalgorithm) ISA算法充分使用最大可挪用时间 ,在保证周期任务满足最后期限的同时能取得非周期任务的最优响应时间和周转时间 证明了ISA算法的最优性 ,并使用仿真实验进行了性能验证     

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。     

CAN总线中EDF调度算法的研究与改进

针对平均分区的EDF算法在CAN总线中的应用出现的问题,提出了一种改进的基于指数分区的EDF算法;并通过引入量化误差的概念,推导证明当CAN网络中各节点相对截至期分布时间过大时,平均分区的EDF算法会导致CAN总线中信息传输任务可调度性的下降,而基于指数分区的EDF算法保证了信息传输任务的实时性,仿真试验验证了算法的有效性。     

Feasible processor allocation in a Hard-Real-Time environment

Consider the problem of scheduling a set of preemptible tasks in one or more processor systems. The task system consists of a set of independent tasks or a task set with precedence relations. Each task is characterized by execution time and deadline. This article presents scheduling algorithms that guarantee all time constraints. These algorithms are so easy to implement that they can be used in real-time operating systems. An overview is given for the different feasible scheduling algorithms of some task and processor systems.