Static Scheduling of Conditional Branches in Parallel Programs

The problem of scheduling non-deterministic graphs arises in several situations in scheduling parallel programs, particularly in the cases of loops and conditional branching. When scheduling loops in a parallel program, non-determinism arises because the number of loop iterations may not be known before the execution of the program. However, since loops from a restricted class of conditional branching, there is a higher degree of non-determinism associated with scheduling conditional branching. In this case, the direction of every branch remains unknown before run time. It follows that entire subprograms of the parallel program may or may not get executed, which in turn increases the amount of non-determinism and complicates the scheduling process. Thus, the term non-determinism is frequently associated with conditional branching in the literature. In this paper, we study the problem of constructing a static schedule for task graphs that contain conditional branching on parallel computers. Generally, it is difficult to obtain optimal solutions for solving various scheduling problems, even in the deterministic case. When non-determinism is added to the scheduling problem through conditional branching, an optimal solution will be even harder to obtain. We start the paper with a brief discussion of the scheduling problem, then we introduce a model for representing parallel programs that contain branches. We present a two-step scheduling technique which employs two different approaches: a graph theoretic appraoch and a multi-phase approach. The first approach is based on exploring several graph theoretic properties of the model. This approach is used as a preprocessing step to decrease the amount of non-determinism before applying the multi-phase approach. In the second step, several execution instances of the program are generated, a schedule for every instance is obtained, and a unified schedule is constructed by merging the obtained schedules. Finally, we report the results of the experiments that we conducted to measure the performance of the techniques introduced in this paper.     

An architecture for workflow scheduling under resource allocation constraints

Research on specification and scheduling of workflows has concentrated on temporal and causality constraints, which specify existence and order dependencies among tasks. However, another set of constraints that specify resource allocation is also equally important. The resources in a workflow environment are agents such as person, machine, software, etc. that execute the task. Execution of a task has a cost and this may vary depending on the resources allocated in order to execute that task. Resource allocation constraints define restrictions on how to allocate resources, and scheduling under resource allocation constraints provide proper resource allocation to tasks. In this work, we provide an architecture to specify and to schedule workflows under resource allocation constraints as well as under the temporal and causality constraints. A specification language with the ability to express resources and resource allocation constraints and a scheduler module that contains a constraint solver in order to find correct resource assignments are core and novel parts of this architecture.     

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     

Tabu search based resource allocation in radiological examination process execution

Efficient resource scheduling and allocation in radiological examination process (REP) execution is a key requirement to improve patient throughput and radiological resource utilization and to manage unexpected events that occur when resource scheduling and allocation decisions change due to clinical needs. In this paper, a Tabu search based approach is presented to solve the resource scheduling and allocation problems in REP execution. The primary objective of the approach is to minimize a weighted sum of average examination flow time, average idle time of the resources, and delays. Unexpected events, i.e., emergent or absent examinations, are also considered. For certain parameter combinations, the optimal solution of radiological resource scheduling and allocation is found, while considering the limitations such as routing and resource constraints. Simulations in the application case are performed. Results show that the proposed approach makes efficient use of radiological resource capacity and improves the patient throughput in REP execution.     

Two processor scheduling with limited preemption

We introduce deterministic task system scheduling with limited preemption—that is, a preempted task can resume execution only on the processor where it originally executed. Two classes of limited preemptive schedules are introduced, corresponding to whether or not unforced idle time is allowed in the schedule. Our main result is to show that, on two processors, these two classes are equivalent with respect to optimal schedule lengths. We use this result to establish a hierarchy of optimal schedule lengths.     

基于可满足性模理论的多处理机通信延迟优化任务调度方法

在一组相同处理器上调度带有通信延迟的任务图以实现其最短的执行时间,这在并行计算的调度理论和实践中具有重要的意义。针对具有通信延迟的任务图调度问题,提出一种基于可满足性模理论（SMT）的改进SMT方法。首先,将处理器映射约束和任务执行顺序等约束条件进行编码,将任务图调度问题转化为SMT问题;然后,调用SMT求解器对可行解空间进行搜索,以确定问题最优解。在约束编码阶段,使用整型变量表示任务和处理器的映射关系,从而降低处理器约束编码的复杂程度;在求解器调用阶段,通过添加独立任务的约束条件减小求解器的搜索空间,进一步提升最优解的查找效率。实验结果表明,与原始SMT方法相比,改进SMT方法在20 s和1 min超时实验中的平均求解时间分别减少了65.9%与53.8%,并且在处理器数量较多时取得了更大的效率优势。改进的SMT方法可以有效求解带通信延迟的任务图调度问题,尤其适用于处理器数量较多的调度场景。     

Analysis of processor allocation in multiprogrammed,distributed-memory parallel processing systems

A main objective of scheduling independent jobs composed of multiple sequential tasks in shared-memory and distributed-memory multiprocessor computer systems is the assignment of these tasks to processors in a manner that ensures efficient operation of the system. Achieving this objective requires the analysis of a fundamental tradeoff between maximizing parallel execution, suggesting that the tasks of a job be spread across all system processors, and minimizing synchronization and communication overheads, suggesting that the job's tasks be executed on a single processor. The authors consider a class of scheduling policies that represent the essential aspects of this processor allocation tradeoff, and model the system as a distributed fork-join queueing system. They derive an approximation for the expected job response time, which includes the important effects of various parallel processing overheads (such as task synchronization and communication) induced by the processor allocation policy     

Workflow performance improvement using model-based scheduling over multiple clusters and clouds

In recent years, a variety of computational sites and resources have emerged, and users often have access to multiple resources that are distributed. These sites are heterogeneous in nature and performance of different tasks in a workflow varies from one site to another. Additionally, users typically have a limited resource allocation at each site capped by administrative policies. In such cases, judicious scheduling strategy is required in order to map tasks in the workflow to resources so that the workload is balanced among sites and the overhead is minimized in data transfer. Most existing systems either run the entire workflow in a single site or use naïve approaches to distribute the tasks across sites or leave it to the user to optimize the allocation of tasks to distributed resources. This results in a significant loss in productivity. We propose a multi-site workflow scheduling technique that uses performance models to predict the execution time on resources and dynamic probes to identify the achievable network throughput between sites. We evaluate our approach using real world applications using the Swift parallel and distributed execution framework. We use two distinct computational environments-geographically distributed multiple clusters and multiple clouds. We show that our approach improves the resource utilization and reduces execution time when compared to the default schedule.     

数据驱动的多星任务网络预测调度算法

多星任务调度是具有NP-hard特性的优化问题,随着卫星资源规模和任务需求规模的双重增长,传统调度方法求解效率不高.在轨卫星在常年运行过程中积累了丰富的调度数据.针对大规模多星任务调度场景,建立多星多波束任务调度模型,并提出数据驱动的多星任务网络预测调度算法对其求解.以分割的思想,实现多星场景下任务可调度性预测.从历史调度数据中,提取设定的3个静态特征和5个动态特征,构建并训练预测网络,预测任务被不同卫星完成的概率,并以冲突避免、负载均衡等为原则,得到初始任务和资源卫星的分配方案.进一步设计双链结构的进化算法,以双链编码形式表征上述关系,配合设计的交叉、修复等进化算子,优化初始方案中的任务序列与资源分配关系,输出最终任务调度方案.仿真结果表明,与改进蚁群算法、混合遗传算法和数据驱动并行调度算法相比,所提出算法在运行时间、方案收益和卫星负载均衡3方面均有较好的表现.     

一个调度Fork-Join任务图的新算法

任务调度是影响工作站网络效率的关键因素之一.Fork-Join任务图可以代表很多并行结构,但其他已有调度Fork-Join任务图算法忽略了在非全互连工作站网络环境中通信之间不能并行执行的问题,有些效率高的算法又没有考虑节省处理器个数的问题.因此,专门针对该任务图,综合考虑调度长度、非并行通信和节省处理器个数问题,提出了一个基于任务复制的静态调度算法TSA_FJ.通过随机产生任务的执行时间和通信时间,生成了多个Fork-Join任务图,并且采用TSA_FJ算法和其他调度算法对生成的任务图进行调度.结果表明,     

On a stochastic sequencing and scheduling problem

We present a framework for solving multistage pure 0–1 programs for a widely used sequencing and scheduling problem with uncertainty in the objective function coefficients, the constraint matrix and the right-hand side. The problem has the following form: given a set of operations to be executed along a time horizon, find a schedule to minimize a function included by the expected operations cost over the scenarios under consideration, subject to a set of constraints. Typical elements are: limited availability of the resources, multiperiod operations, subsets of operations with exclusivity and implicative constraints, precedence relationships in the execution of the operations, etc. The stochasticity is in the resources’ consumption by the operations, their availability and the operations cost along the time horizon. A multistage scenario analysis with complete recourse is used. Given the high dimensions of the problem and its combinatorial nature, it is not realistic to obtain the optimal solution for the problem. Instead, we present the so-called Fix-and-Relax Coordination algorithmic framework to exploit the characteristics of the non-anticipativity constraints for each scenario group in the stochastic model. This exploitation basically consists of selectively exploring the nodes of the branching trees in which the branch-and-bound tree is decomposed while the non-anticipativity constraints are relaxed. The algorithm is specifically designed for coordinating and reinforcing the node pruning, and the branching node and variable selection at each branching tree, such that the non-anticipativity constraints are satisfied. Some computational experience is reported.     

Real-time load balancing scheduling algorithm for periodic simulation models

A scheduling algorithm is crucial for real-time simulations because it guarantees that each model meets its deadline. Traditional online real-time scheduling algorithms such as Earliest Deadline First (EDF) introduce a high overhead when scheduling a large number of models. In this paper, a new algorithm called time-stepped load balancing (TLS) is proposed to address the real-time execution of a model set in a time-stepped simulation. A load balancing schedule table is generated before a simulation and rebalanced at runtime to dynamically schedule the changed model set. This table is organized by the execution periods of the models and balanced according to the load of each time step. Moreover, the slack time is distributed evenly among the steps to improve the real-time reliability. An extension to the algorithm for a multi-core environment is further studied to address those models with long execution times. Experimental results show that our scheduling algorithm outperforms the classical EDF approach. The highest performance improvement of TLS over EDF reaches 3–4% in terms of saving processor resources, and the jitter is about 4 times less when 90 entities are employed in a typical tank combat simulation scenario.     

Solving multiple processor and multiple resource constrained scheduling problems using a genetic algorithm approach

We consider the multiprocessor scheduling of unit time tasks with precedence constraints and finite set of limited resources. Each task demands some amount of resources for its execution and the total demand for each kind of resources must not exceed a certain limit at any instant of time. Our objective is to find out the minimum time schedule which satisfies the partial orders and the resource usage constraints. We have applied Genetic Algorithm for the present problem. We have shown that the Genetic Algorithm is quite superior to the First Fit Decreasing method.     

权重队列实时调度系统的反馈控制

针对工作在不可预测环境下具有不确定性任务特征的实时调度系统的服务区分问题,利用队列理论对权重队列实时调度系统进行多变量控制建模,并结合模型预测控制方法将控制问题转化为受限多变量优化问题,进而基于标准的最小二乘求解器设计预测控制调度框架以及算法。通过调整任务类的权重因子来改变任务类的计算资源分配,以实现为调度任务类提供相对延迟时间比保证。仿真试验结果表明,所设计方法在任务到达速率和执行时间变化且不能预知的情况下,仍然能为系统提供良好的相对延迟时间比控制。     

Cluster-based multicore real-time mixed-criticality scheduling

Cluster-based scheduling is recently gaining importance to be applied to mixed-criticality real-time systems on multicore processors platform. In this approach, the cores are grouped into clusters, and tasks that are partitioned among different clusters are scheduled by global scheduler in each cluster. This research work introduces a new cluster-based task allocation scheme for the mixed-criticality real-time task sets on multicore processors. For task allocation, smaller clusters sizes (sub-clusters) are used for mixed-criticality tasks in low criticality mode, while relatively larger cluster sizes are used for high criticality tasks in high criticality mode. In this research paper, the mixed-criticality task set is allocated to clusters using worst-fit heuristic. The tasks from each cluster are also allocated to its sub-clusters, using the same worst-fit heuristic. A fixed-priority response time analysis approach based on Audsley’s approach is used for the schedulability analysis of tasks in each cluster and sub-cluster. If the high criticality job is not completed after its worst case execution time in low mode, then the system is switched to high criticality mode. After mode switch, all the low criticalities tasks are discarded and only high criticality tasks are further executed in high criticality mode. Simulation results indicate that the percentage of schedulable task sets significantly increases under cluster scheduling as compared to partitioned and global mixed-criticality scheduling schemes.     

基于多目标全局约束的任务分配和调度算法

针对嵌入式系统中大多数任务执行算法不考虑目标成本问题,提出了一种基于多目标全局约束的任务分配和调度算法。算法使用约束逻辑编程来对任务执行资源如处理单元、通信设备以及代码和数据存储量的使用进行多目标全局约束。算法假设ROM和RAM分别用于代码存储和数据存储,算法还考虑数据在数据存储器中的位置。实验结果表明,尽管在多个约束条件下,提出的任务分配和调度算法无论在代码存储和数据存储量使用方面,还是在对任务有效求解方面都能取得比普遍采用的贪婪调度算法更好的结果。     

Stochastic allocation and scheduling for conditional task graphs in multi-processor systems-on-chip

Embedded systems designers are turning to multicore architectures to satisfy the ever-growing computational needs of applications within a reasonable power envelope. One of the most daunting challenges for MultiProcessor System-on-Chip (MPSoC) platforms is the development of tools for efficient mapping multi-task applications onto hardware platforms. Software mapping can be formulated as an optimal allocation and scheduling problem, where the application is modeled as a task graph, the target hardware is modeled as a set of heterogeneous resources, and the objective function represents a design goal α (e.g. minimum execution time, minimum usage of communication resources, etc.). Conditional task graphs, where inter-task edges represent data as well as control dependencies, are a well-known computational model to describe complex real-life applications where alternative execution paths, guarded by conditionals, can be specified. Each condition has a probability associated with each possible outcome.     

Iterative-Improvement-Based Heuristics for Adaptive Scheduling of Tasks Sharing Files on Heterogeneous Master-Slave Environments

The scheduling of independent but file-sharing tasks on heterogeneous master-slave platforms has recently found important applications in Grid environments. The scheduling heuristics recently proposed for this problem are all constructive in nature and based on a common greedy criterion which depends on the momentary completion time values of the tasks. We show that this greedy decision criterion has shortcomings in exploiting the file-sharing interaction among tasks since completion time values are inadequate to extract the global view of this interaction. We propose a three-phase scheduling approach which involves initial task assignment, refinement, and execution ordering phases. For the refinement phase, we model the target application as a hypergraph and, with an elegant hypergraph-partitioning-like formulation, we propose using iterative-improvement-based heuristics for refining the task assignments according to two novel objective functions. Unlike the turnaround time, which is the actual schedule cost, the smoothness of proposed objective functions enables the use of iterative-improvement-based heuristics successfully since their effectiveness and efficiency depend on the smoothness of the objective function. Experimental results on a wide range of synthetically generated heterogeneous master-slave frameworks show that the proposed three-phase scheduling approach performs much better than the greedy constructive approach.     

A compact task graph representation for real-time scheduling

A new task graph representation, namely the compact task graph (CTG), is developed to aid in the scheduling of a set of communicating periodic real-time tasks. This representation explicitly expresses the potential for parallelism across tasks as well as the idle times that may be encountered within application tasks. A CTG based scheduler can generate schedules that are able to meet deadlines by interleaving the execution of tasks on a single processor and/or overlapping the execution of tasks on multiple processors. The construction of a CTG is based upon the busy-idle execution profiles for the tasks generated by the compiler. The profiles are computed assuming that sufficient resources are available for parallel execution of all tasks. Thus, they expose all opportunities for overlapped and interleaved execution. The compiler analyzes the profiles to identify useful opportunities for interleaving and expresses them in the CTG without unnecessary partitioning of the tasks. The CTG is powerful because it expresses schedules that are not expressed by existing approaches for constructing task graphs. Schedules can be generated efficiently since a CTG's construction minimizes the splitting of tasks. We briefly demonstrate the usefulness of CTGs in scheduling real-time tasks and scheduling monitoring tasks without affecting the timing of application tasks.Supported in part by the National Science Foundation through a Presidential Young Investigator Award CCR-9157371 and Grant CCR-9212020.     

树型网格计算环境下的自适应任务调度算法

提出一种基于树型计算网格的自适应调度算法,实现对小粒度独立任务和用户大作业的自适应最优调度。通过对网格环境的实时检测,给出了基于节点负载状况、节点任务执行时间、任务传输时间和任务特性的自适应调度算法,即基于最优任务分配方案的启发式任务调度算法。通过实验与其他调度算法的比较,证明了所提出的任务调度算法在负载平衡和最优跨度方面具有明显的优越性。