一种调度In-Tree任务图的算法

In-Tree任务图可用来表示归并、求和等分治算法的很多问题,该文针对这种任务图提出一种分层调度算法,利用队列存放被调度的任务,在同层任务调度中,优先把前驱不为空的任务调度到其一个前驱处理器上执行,只有前驱为空的任务才考虑是否分配新的处理器。实验表明,与以前的算法相比,该算法在调度长度相当的情况下,使用了更少的处理器。     

云环境下周期和非周期混合实时任务双容错调度算法

云环境中的处理机故障已成为云计算不可忽视的问题,容错成为设计和发展云计算系统的关键需求。针对一些容错调度算法在任务调度过程中调度效率低下以及任务类型单一的问题,提出一种处理机和任务主副版本分组的容错调度方法;并给出了副版本可重叠执行的判定方法,以及任务最坏响应时间的计算公式。通过实验和分析表明,和以前算法相比,将处理机分成两组分别执行任务主版本和任务副版本,减少了任务调度所需进行可调度测试的时间,增加了副版本重叠执行的机会,减少了所需的处理机个数,对提高系统处理机的利用率和容错调度的效率具有重要的意义。     

边缘计算中协作计算卸载与动态任务调度

在边缘计算场景中,通过将部分待执行任务卸载到边缘服务器执行能够达到降低移动设备的负载、提升移动应用性能和减少设备开销的目的.对于时延敏感任务,只有在截止期限内完成才具有实际意义.但是边缘服务器的资源往往有限,当同时接收来自多个设备的数据传输及处理任务时,可能造成任务长时间的排队等待,导致部分任务因超时而执行失败,因此无法兼顾多个设备的性能目标.鉴于此,在计算卸载的基础上优化边缘服务器端的任务调度顺序.一方面,将时延感知的任务调度建模为一个长期优化问题,并使用基于组合多臂赌博机的在线学习方法动态调整服务器的调度顺序.另一方面,由于不同的任务执行顺序会改变任务卸载性能提升程度,因而影响任务卸载决策的有效性.为了增加卸载策略的鲁棒性,采用了带有扰动回报的深度Q学习方法决定任务执行位置.仿真算例证明了该策略可在平衡多个用户目标的同时减少系统的整体开销.     

Static scheduling of directed acyclic data flow graphs onto multiprocessors using particle swarm optimization

An efficient method based on particle swarm optimization (PSO) is developed to solve the Multiprocessor Task Scheduling Problem (MPTSP). To efficiently execute parallelized programs on a multiprocessor environment, a scheduling problem must be solved to determine the assignment of tasks to the processors, the execution order of the tasks, and the starting time of each task, such that some optimality criteria are met. The scheduling problem is known as an NP-complete problem even when the target processors are fully connected and no communication delay is considered among the tasks in the task graph. The complexity of the scheduling problem depends on the number of tasks (N), the number of processors (M), the task processing time and the precedence constraints. The Directed Acyclic Graph (DAG) was exploited to represent the tasks and their precedence constraints. The proposed algorithm was compared with the Genetic Algorithm (GA) and the Duplication Scheduling Heuristic (DSH). We also provide a systematic investigation on the effect of varying problem settings. The results show that the proposed algorithm could not outperform the DSH while it could outperform the GA in some cases.     

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

Strict periodicity constraint is of great importance since it concerns some hard real-time systems where missing deadlines leads to catastrophic situations. However, the problem of schedulability analysis for non-preemptive strictly periodic tasks on a multiprocessor platform is even more intractable than the one with the common periodicity. In order to implement such systems, designers need effective tools based on fast and near-optimal solutions.This paper presents a schedulability analysis which results mainly in a, two versions, task assignment and start-time calculation algorithm. The first one targets the harmonic task periods case while the second one targets the non-harmonic task periods case. Each version is based on a sufficient uniprocessor schedulability test. In addition, for the non-harmonic case which is the most intractable, the uniprocessor sufficient schedulability test uses the strictly periodic task utilization factor. This factor stands for the fraction of time spent to execute a task while its strict periodicity and the ones of the already scheduled tasks are met. As a result, an efficient and easily implementable scheduling algorithm is proposed which begins by assigning tasks to processors then attributes a start-time to every task in such a way that strict periodicity and deadline constraints are met. The effectiveness of the proposed scheduling algorithm, in both versions, has been shown by a performance evaluation and comparisons with an optimal and a similar suboptimal solution.     

Real-time task scheduling by multiobjective genetic algorithm

Real-time tasks are characterized by computational activities with timing constraints and classified into two categories: a hard real-time task and a soft real-time task. In hard real-time tasks, tardiness can be catastrophic. The goal of hard real-time tasks scheduling algorithms is to meet all tasks’ deadlines, in other words, to keep the feasibility of scheduling through admission control. However, in the case of soft real-time tasks, slight violation of deadlines is not so critical.In this paper, we propose a new scheduling algorithm for soft real-time tasks using multiobjective genetic algorithm (moGA) on multiprocessors system. It is assumed that tasks have precedence relations among them and are executed on homogeneous multiprocessor environment.The objective of the proposed scheduling algorithm is to minimize the total tardiness and total number of processors used. For these objectives, this paper combines adaptive weight approach (AWA) that utilizes some useful information from the current population to readjust weights for obtaining a search pressure toward a positive ideal point. The effectiveness of the proposed algorithm is shown through simulation studies.     

改进的异构多处理器的实时任务调度算法研究*

现有的很多调度算法存在时间复杂度过高或调度成功率低的问题。提出一种新的调度算法(HRTSA),提高实时任务的调度成功率。HRTSA首先通过METC策略初始化分簇,降低算法的时间复杂度;再在放置任务时根据处理器的负载均衡进行处理器负载的有效控制;最后通过任务复制调度以提高任务调度成功率。对比实验分析表明提出的HRTSA算法时间复杂度与RTSDA相比较低,调度成功率较高。     

A gravitational task model with arbitrary anchor points for target sensitive real-time applications

Classic task models for real-time systems focus on execution windows expressing earliest start times and deadlines of tasks for feasibility. Only within these windows the execution of tasks is feasible, and it is considered of uniform utility. Some tasks, however, have target demands in addition: a task should preferably execute at a specific target point within its execution window, but can execute around this point, albeit at lower utility. Examples of such applications include control and media processing. In this paper, we present a task model based on a gravitational analogy to address these issues. Tasks are considered as massive bobs hanging on a pendulum: a single task, left to itself, will execute at the bottom, the target point. If a force, such as the weight of other tasks, is applied, it can be shifted around this point. Thus, tasks’ importance and their utility around target points can be expressed. Since the execution of a task cannot be mapped to a point in time, the model allows tasks to express an arbitrary point with its execution to represent the whole execution. This point is called the anchor point. Moreover, we show an example of a scheduling algorithm for this model which finds an approximation to the best compromise of tasks’ interests based on the equilibrium state of a pendulum. Nonetheless, this task model is not restricted to a particular scheduling algorithm. Results from a simulation study show the effectiveness of the approach.

一个调度Out-Tree任务图的新算法

Out-Tree任务图代表分治算法的一大类问题。本文专门针对该类任务图,提出了一个新的调度算法。它利用fork结构的最优调度为各任务定义优先级,准确的反映了任务对调度的影响,保证了任务的正确调度顺序,得到优的调度长度。并在不改变调度长度的情况下,将结点尽可能地分配到已用处理器上,节省了处理器。实验表明,本文算法的调度性能优于现有同类算法。     

A static scheduling algorithm for distributed hard real-time systems

A static scheduling algorithm is presented for off-line scheduling of tasks in distributed hard real-time systems. The tasks considered are instances of periodic jobs and have deadlines, resource requirements and precedence constraints. Tasks are divided into nonpreemptable blocks and all task characteristics are known a priori. The algorithm orders the tasks and iteratively schedules the tasks according to the order. Each task is scheduled globally by selecting a node to which it is assigned. Then, the task is scheduled locally by adding the task to the schedule of the selected node. Heuristics are used for both task ordering and node selection in order to guide the algorithm to a feasible schedule. Whenever local scheduling leads to an infeasible schedule, backtracking is used.Results of simulation studies of randomly generated task sets are presented. Although the scheduling problem is NP-hard, the results show that time performance is acceptable for off-line scheduling, except for extremely difficult task sets which make extensive use of the available resources.     

Benchmark-problem instances for static scheduling of task graphs with communication delays on homogeneous multiprocessor systems

Scheduling program tasks on processors is at the core of the efficient use of multiprocessor systems. Most task-scheduling problems are known to be NP-Hard and, thus, heuristics are the method of choice in all but the simplest cases. The utilization of acknowledged sets of benchmark-problem instances is essential for the correct comparison and analysis of heuristics. Yet, such sets are not available for several important classes of scheduling problems, including multiprocessor scheduling problem with communication delays (MSPCD) where one is interested in scheduling dependent tasks onto homogeneous multiprocessor systems, with processors connected in an arbitrary way, while explicitly accounting for the time required to transfer data between tasks allocated to different processors. We propose test-problem instances for the MSPCD that are representative in terms of number of processors, type of multiprocessor architecture, number of tasks to be scheduled, and task graph characteristics (task execution times, communication costs, and density of dependencies between tasks). Moreover, we define our task-graph generators in a way appropriate to ensure that the corresponding problem instances obey the theoretical principles recently proposed in the literature.     

云环境下基于强化学习的多目标任务调度算法

针对云计算环境下的多目标任务调度问题,提出一种新的基于Q学习的多目标优化任务调度算法(Multi-objective Task Scheduling Algorithm based on Q-learning,QM TS).该算法的主要思想是:首先,在任务排序阶段利用Q-learning算法中的自学习过程得到更加合理的任务序列;然后,在虚拟机分配阶段使用线性加权法综合考虑任务最早完成时间和计算节点的计算成本,达到同时优化多目标问题的目的;最后,以产生更小的makespan和总成本为目标函数对任务进行调度,得到任务完成后的实验结果.实验结果表明,QMTS算法在使用Q-learning对任务进行排序后可以得到比HEFT算法更小的makespan;并且根据优化多目标调度策略在任务执行过程中减少了makespan和总成本,是一种有效的多目标优化任务调度算法.     

A New Strategy for Improving the Effectiveness of Resource Reclaiming Algorithms in Multiprocessor Real-Time Systems

The scheduling of tasks in multiprocessor real-time systems has attracted the attention of many researchers in the recent past. Tasks in such systems have deadlines to be met, and most real-time scheduling algorithms use worst case computation times to schedule these tasks. Many resources will be left unused if the tasks are dispatched purely based on the schedule produced by these scheduling algorithms, since most of the tasks will take less time to execute than their respective worst case computation times. Resource reclaiming refers to the problem of reclaiming the resources left unused by a real-time task when it takes less time to execute than its worst case computation time. Several resource reclaiming algorithms such as Basic, Early Start, and RV algorithms have been proposed in the recent past. But these pay very little attention to the strategy by which the scheduler can better utilize the benefits of reclaimed resources. In this paper, we propose an esti- mation strategy which can be used along with a particular class of resource reclaiming algorithms (such as Early Start and RV algorithms) by which the scheduler can estimate the minimum time by which any scheduled but unexecuted task will start or finish early, based solely on the start and finish times of tasks that have started or finished execution. We then propose an approach by which dynamic scheduling strategies, which append or reschedule new tasks into the schedules, can use this estimation strategy to achieve better schedulability. Extensive simulation studies are carried out to investigate the effectiveness of this estimation strategy versus its cost.     

云平台下基于截止时间的自适应调度策略

针对在共享集群中进行任务调度时,无法兼顾任务的响应速度与任务完成时间的问题,提出一种基于截止时间的自适应调度算法。该算法以用户提交的截止时间为依据,根据任务的执行进度自适应地分配适当的计算资源。不同于传统调度方式里由用户提交固定资源参数,该算法在资源约束的情况下会对优先级高的任务进行抢占式调度以保证服务质量（QoS）,并在抢占过程结束后额外分配资源补偿被抢占的任务。在Spark平台进行的任务调度实验结果显示,与另一种资源协调者（YARN）框架下的调度算法相比,所提算法能严格地控制短任务的响应速度,并使长作业的任务完成时间缩短35%。     

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     

Scheduling DAG-based applications in multicluster environments with background workload using task duplication

Grids or multicluster computing environments are becoming increasingly popular to both scientific and commercial applications. Process scheduling remains a central issue to be effectively resolved in order to exploit the full potential that the grid or multicluster environment can offer. We use a directed acyclic graph (DAG) to model a process or an application where the nodes of the DAG represent the tasks of the process. Prior to the execution of a process in a multicluster environment, the tasks are required to be mapped onto the clusters. In this article, it is shown that the algorithm developed by He et al. [L. He, S.A. Jarvis, D.P. Spooner, D. Bacigalupo, G. Tan, and G.R. Nudd, Mapping DAG-based applications to multiclusters with background workload, Proceedings of the 2005 IEEE International Symposium on Cluster Computing and the Grid, Cardiff, 2005, pp 855–862.] for the multicluster DAG mapping problem can be significantly improved by incorporating the task duplication strategy. The proposed process scheduling algorithm has a time complexity O(| V|²(r+d+1)), where |V| represents the number of tasks; r, the number of clusters; and d, the maximum in-degree of tasks.     

基于多核处理器的关联任务并行感知调度算法

关联任务在多核处理器上并行调度所产生的通信时延,会对任务调度长度和处理器利用率造成负面影响,为了改善多核系统对关联任务的处理性能,针对关联任务在多核处理器上的调度特点,提出一种并行感知调度算法。计算各任务与终点间的最长路径值,按照该值的降序来分配任务调度次序,在分配处理器内核时兼顾关联度和任务最早可执行时间,设置最佳匹配评价函数。实验结果表明,与busHEFT和DTSV算法相比,该算法具有更短的任务调度时延、更少的通信量以及更高的处理器利用率。     

Space efficient execution of deterministic parallel programs

We model a deterministic parallel program by a directed acyclic graph of tasks, where a task can execute as soon as all tasks preceding it have been executed. Each task can allocate or release an arbitrary amount of memory (i.e., heap memory allocation can be modeled). We call a parallel schedule “space efficient” if the amount of memory required is at most equal to the number of processors times the amount of memory required for some depth-first execution of the program by a single processor. We describe a simple, locally depth-first scheduling algorithm and show that it is always space efficient. Since the scheduling algorithm is greedy, it will be within a factor of two of being optimal with respect to time. For the special case of a program having a series-parallel structure, we show how to efficiently compute the worst case memory requirements over all possible depth-first executions of a program. Finally, we show how scheduling can be decentralized, making the approach scalable to a large number of processors when there is sufficient parallelism     

Guaranteed task deadlines for fault-tolerant workloads with conditional branches

This work examines scheduling for a real-time multiprocessor (MAFT) in which both hard deadlines and fault-tolerance are necessary system components. A workload for this system consists of a set of concurrent dependent tasks, each with some execution frequency; tasks are also fully ordered by priority. Fault tolerance mechanisms include hardware-supported voting on computation results as well as on task starts, task completions, and branch conditions. The distributed agreement mechanism used on system-level decisions adds a variable threading delay to the run time of each copy of a task. These delays make current schedule verification techniques inapplicable. In the most general execution profile, each processor in the system runs a subset of the tasks, with different tasks possibly having different frequencies. In this work, however, we restrict attention to a special class of workloads, termed uni-schedule, in which each processor executes the entire task set, using the multiple processors to implement full redundancy. In addition, all tasks are assumed to have the same periodicity. Given these restrictions, we produce stable schedules consistent with the initial workload specifications. Algorithms are first given for uni-schedule workloads with no run-time branches, and then for uni-schedule workloads with branches.     

Cluster scheduling for real-time systems: utilization bounds and run-time overhead

Cluster scheduling, where processors are grouped into clusters and the tasks that are allocated to one cluster are scheduled by a global scheduler, has attracted attention in multiprocessor real-time systems research recently. In this paper, assuming that an optimal global scheduler is adopted within each cluster, we investigate the worst-case utilization bounds for cluster scheduling with different task allocation/partitioning heuristics. First, we develop a lower limit on the utilization bounds for cluster scheduling with any reasonable task allocation scheme. Then, the lower limit is shown to be the exact utilization bound for cluster scheduling with the worst-fit task allocation scheme. For other task allocation heuristics (such as first-fit, best-fit, first-fit decreasing, best-fit decreasing and worst-fit decreasing), higher utilization bounds are derived for systems with both homogeneous clusters (where each cluster has the same number of processors) and heterogeneous clusters (where clusters have different number of processors). In addition, focusing on an efficient optimal global scheduler, namely the boundary-fair (Bfair) algorithm, we propose a period-aware task allocation heuristic with the goal of reducing the scheduling overhead (e.g., the number of scheduling points, context switches and task migrations). Simulation results indicate that the percentage of task sets that can be scheduled is significantly improved under cluster scheduling even for small-size clusters, compared to that of the partitioned scheduling. Moreover, when comparing to the simple generic task allocation scheme (e.g., first-fit), the proposed period-aware task allocation heuristic markedly reduces the scheduling overhead of cluster scheduling with the Bfair scheduler.