Directed Acyclic Graph Tasks Research Articles

Global EDF scheduling for parallel real-time tasks

As multicore processors become ever more prevalent, it is important for real-time programs to take advantage of intra-task parallelism in order to support computation-intensive applications with tight deadlines. In this paper, we consider the global earliest deadline first (GEDF) scheduling policy for task sets consisting of parallel tasks. Each task can be represented by a directed acyclic graph (DAG) where nodes represent computational work and edges represent dependences between nodes. In this model, we prove that GEDF provides a capacity augmentation bound of $$4-\frac{2}{m}$$ and a resource augmentation bound of $$2-\frac{1}{m}$$ . The capacity augmentation bound acts as a linear-time schedulability test since it guarantees that any task set with total utilization of at most $$m/(4-\frac{2}{m})$$ where each task’s critical-path length is at most $$1/(4-\frac{2}{m})$$ of its deadline is schedulable on $$m$$ cores under GEDF. In addition, we present a pseudo-polynomial time fixed-point schedulability test for GEDF; this test uses a carry-in work calculation based on the proof for the capacity bound. Finally, we present and evaluate a prototype platform—called PGEDF—for scheduling parallel tasks using global earliest deadline first (GEDF). PGEDF is built by combining the GNU OpenMP runtime system and the $$\text {LITMUS}^\text {RT}$$ operating system. This platform allows programmers to write parallel OpenMP tasks and specify real-time parameters such as deadlines for tasks. We perform two kinds of experiments to evaluate the performance of GEDF for parallel tasks. (1) We run numerical simulations for DAG tasks. (2) We execute randomly generated tasks using PGEDF. Both sets of experiments indicate that GEDF performs surprisingly well and outperforms an existing scheduling techniques that involves task decomposition.

Design and implementation of task scheduling strategies for massive remote sensing data processing across multiple data centers

SUMMARYData intensive applications of remote sensing data processing are more and more widespread resulting from the evolutions in computer and network technologies. Especially, bags‐of‐tasks (BoTs) applications with a mass of sharing input files and directed acyclic graph (DAG) applications with data dependencies in a widely distributed computing environment bring new challenges. In this article, a strategy of partitioning group based on hypergraph (PGH) is introduced to formulate the model of sharing files. Within the PGH algorithm, BoTs applications would be partitioned into several groups to minimize the time of data transferring. We also adopted another scheduling policy, which is called optimized task tree (OTT) strategy to handle the DAG workflow of massive remote sensing data processing with data dependencies. A scheduling queue of DAG tasks would be updated according to the priorities changing. With the help of GridSim simulation environment, we designed the Gridlets within scheduler to test the performance of PGH and OTT. Copyright © 2013 John Wiley & Sons, Ltd.

AN EFFICIENT TASK SCHEDULING IN DISTRIBUTED COMPUTING SYSTEMS BY IMPROVED GENETIC ALGORITHM

Task Scheduling problem for heterogeneous systems is concerned with arranging the various tasks to be executed on various processors of a system so that computing resources are utilized most effectively. Parallel processing refers to the concept of speeding-up the execution of a task by dividing the task into multiple fragments that can execute simultaneously, each on its own processor i.e. it is the simultaneous processing of the task on two or more processors in order to obtain faster results. It can be effectively used for tasks that involve a large number of calculations, have time constraints and can be divided into a number of smaller tasks. The scheduling problem deals with the optimal assignment of a set of tasks onto parallel multiprocessor system and orders their execution so that the total completion time is minimized. An Optimal scheduling of parallel tasks with some precedence relationship, onto a parallel machine is known to be NP-complete. This precedence relationship among tasks can be represented as Directed Acyclic Graph (DAG). In this paper, a scheduling algorithm has been proposed to schedule DAG tasks on Heterogeneous processor which uses Genetic algorithm to get optimal schedule. The scheduling problem is also considered. This study includes a search for an optimal mapping of the task and their sequence of execution and also search for an optimal configuration of the parallel system. An approach for the simultaneous optimization of all these three components of scheduling method using genetic algorithm is presented and its performance is evaluated in comparison with the Min-Min and Max-Min scheduling methods.

A reliable-adaptive scheduler for computational grids with failure recovery and rescheduling mechanisms

Computational grids (CGs) have become an attractive research area as they suggest a suitable environment for developing large scale parallel applications. CGs integrate a large amount of distributed heterogeneous resources into a single powerful platform. However, to make good use of CGs, grid resources should be scheduled efficiently. Various scheduling strategies have been introduced, including static and dynamic behaviours. The former maps tasks to resources at submission time, while the latter operates at schedule time. While static scheduling is unsuitable for the dynamic grid environment, scheduling in CGs is still more complex than the proposed dynamic ones. This paper introduces a decentralised adaptive grid scheduler (AGS) based on a novel rescheduling mechanism. AGS has several salient properties as it is: hybrid, adaptive, decentralised, and efficient. AGS is also robust as it has the ability to: 1) detect resource failures; 2) continue its functionality in spite of the failure existence; 3) recover back as soon as possible. Moreover, it integrates both static and dynamic scheduling behaviours. An initial static scheduling map is proposed for an input directed acyclic graph (DAG). However, DAG tasks may be rescheduled if the hosting resources' performance changes in a way that affects the tasks' response time. AGS tries to overcome drawbacks of traditional schedulers by utilising the mobile agent unique features to enhance the resource discovery and monitoring processes. Experimental results have shown that AGS outperforms traditional grid schedulers as it introduces a better scheduling efficiency.

Energy aware DAG scheduling on heterogeneous systems

We address the problem of scheduling directed a-cyclic task graph (DAG) on a heterogeneous distributed processor system with the twin objectives of minimizing finish time and energy consumption. Previous scheduling heuristics have assigned DAGs to processors to minimize overall run-time of the application. But applications on embedded systems, such as high performance DSP in image processing, multimedia, and wireless security, need schedules which use low energy too. We develop a new scheduling algorithm called Energy Aware DAG Scheduling (EADAGS) on heterogeneous processors that can run on discrete operating voltages. Such processors can scale down their voltages and slow down to reduce energy whenever they idle due to task dependencies. EADAGS combines dynamic voltage scaling (DVS) with Decisive Path Scheduling (DPS) to achieve the twin objectives. Using simulations we show average energy consumption reduction over DPS by 40%. Energy savings increased with increasing number of nodes or increasing Communication to Computation Ratios and decreased with increasing parallelism or increasing number of available processors. These results were based on a software simulation study over a large set of randomly generated graphs as well as graphs for real-world problems with various characteristics.

Directed Acyclic Task Graph Scheduling for Heterogeneous Computing Systems by Dynamic Critical Path Duplication Algorithm

This paper addresses the static scheduling of a directed acyclic task graph (DAG) on a heterogeneous, bounded set of distributed processors to minimize the makespan. We first derive the lower and upper bounds on the makespan of assigning a given directed acyclic task graph on heterogeneous processors by deferent scheduling strategies. Based on the analysis, we present a new heuristic, known as Heterogeneous Dynamic Critical Path Duplication (HDCPD), for scheduling DAG on a set of heterogeneous processors. HDCPD assigns the tasks on the dynamic critical path to the suitable processors which minimize the earliest finish time for them, combining insertion-based scheduling and task duplication techniques. The comparison study by simulation on Simgrid, based on randomly generated DAG, shows that HDCPD surpasses previous approaches in terms of both quality and cost of schedules, which are mainly presented with schedule length, frequency of best result, and scheduling time metrics.

A comparison of multiprocessor task scheduling algorithms with communication costs

Both parallel and distributed network environment systems play a vital role in the improvement of high performance computing. Of primary concern when analyzing these systems is multiprocessor task scheduling. Therefore, this paper addresses the challenge of multiprocessor task scheduling parallel programs, represented as directed acyclic task graph (DAG), for execution on multiprocessors with communication costs. Moreover, we investigate an alternative paradigm, where genetic algorithms (GAs) have recently received much attention, which is a class of robust stochastic search algorithms for various combinatorial optimization problems. We design the new encoding mechanism with a multi-functional chromosome that uses the priority representation—the so-called priority-based multi-chromosome (PMC). PMC can efficiently represent a task schedule and assign tasks to processors. The proposed priority-based GA has show effective performance in various parallel environments for scheduling methods.

A Performance Evaluation of Multiprocessor Scheduling with Genetic Algorithm

An efficient assignment and scheduling of tasks of a multiprocessor program is one of the key elements in the effective utilization of multiprocessor systems. This problem being hard to solve exactly, is the reason that so many heuristic methods for finding a suboptimal schedule exist (Hou et al., 1994; Tsuchiya et al., 1997). This paper addresses the problem of multiprocessor scheduling represented as a directed acyclic task graph (DAG) without communication costs to fully connected multiprocessors. We proposed an algorithm, called PGA/SPF (Priority-based Genetic Algorithm/Shortest Processor First schedule) where a priority-based genetic algorithm is improved with the introduction of some knowledge about the scheduling problem, which is represented by the use of genetic operators as crossover and mutation operators. And, a new mapping method, shortest processor first schedule, assigns the selected task to a processor that can minimize a task execution time efficiently. The proposed algorithms generate similar or even better solutions than the previous algorithms in terms of the completion times of the resulting schedules.

Scheduling directed a-cyclic task graphs on a bounded set of heterogeneous processors using task duplication

In a distributed computing environment, the schedule by which tasks are assigned to processors is critical to minimizing the overall run-time of the application. However, the problem of discovering the schedule that gives the minimum finish time is NP-Complete. This paper addresses static scheduling of a directed a-cyclic task graph (DAG) on a heterogeneous, bounded set of distributed processors to minimize the makespan. By combining several innovative techniques, including insertion-based scheduling and multiple task duplication, we present a new heuristic, known as Heterogeneous N-predecessor Decisive Path (HNDP), for scheduling directed a-cyclic weighted task graphs (DAGs) on a set of heterogeneous processors. We compare the performance of HNDP, under a range of varying input conditions, with two of the best existing heterogeneous heuristics namely HEFT and STDS. The results presented in this paper show that HNDP outperforms the two heuristics in terms of finish time and the number of processors employed over a wide range of parameters. The complexity of HNPD is O ( v 2 . p ) vs. O ( v 2 . p ) of HEFT and O ( v 2 ) of STDS where v is the number of nodes in the DAG.

Optimal algorithm for tree scheduling with unit time communication delays

A program is usually designed to act as a set of interacting tasks that can be used to construct a graph. These tasks can be assigned to processing elements in different ways. The scheduling problem is applied to defining an assignment of tasks in order to process elements that will optimise certain performance indices. One of the most important reasons for scheduling indices is to try to optimise the finishing time. The finishing time of a program is the result of two components: the computing time and communication delays. An optimal schedule is defined as the one that assigns tasks to processing elements in such a way as to finish at the earliest possible time. Completion of the optimum solution for arbitrary directed acyclic task graphs (DAGs) has been shown to be NP-complete. However, for some special classes of DAGs (such as fork, join, coarse-grain trees and some fine grain trees) many algorithms have been introduced to find optimal schedules. Note that most of these algorithms do not take into consideration the delays due to message passing among the processors. In the paper, the authors study the increase in time complexity due to communication delays. The particular problem that is addressed is the scheduling problem of the in-forest/out-forest. This paper introduces the first known linear time algorithm for finding the optimal schedule, for the special case of tree-like graphs, with unit time computation and unit time communication delays.

AUTOMATIC PARALLELIZATION TECHNIQUES BASED ON COMPACT DAG EXTRACTION AND SYMBOLIC SCHEDULING

Symbolic allocation and dynamic scheduling of tasks on a distributed memory machine for coarse-grained applications represented by parameterized task graphs (PTG) are presented in this paper. A PTG is a new computation model for symbolically representing directed acyclic task graphs (DAGs). The size of a PTG is independent of the problem size and its parameters can be instantiated at run time. Parameter independent optimization is important for exploiting non-static parallelism in scientific computing programs with varying problem sizes. Previous DAG scheduling algorithms are not able to handle such cases. We present and study a symbolic scheduling algorithm called SLC (Symbolic Linear Clustering) which derives task clusters from a PTG using affine piecewise mapping functions and then evenly assigns clusters to processors. Thus a complete automatic parallelization method is presented.

SCHEDULING PARALLEL PROGRAM TASKS WITH NON-NEGLIGIBLE INTERTASK COMMUNICATIONS ON TO NUMA MULTIPROCESSOR SYSTEMS

The purpose of this paper is to examine the impact of scheduling parallel tasks onto non-uniform memory access (NUMA) shared-memory multiprocessor systems by considering non-negligible intertask communications and communication contentions. Communication contentions arise from the communication medium having insufficient capacity to serve all transmissions, thereby causing significant contention delays. Therefore, a new scheduling algorithm, herein referred to as the Extended Critical Path (ECP) algorithm is proposed. The proposed algorithm schedules parallel tasks by considering non-negligible intertask communications and the contentions among shared communication resources. Moreover, it ensures performance within a factor of two of the optimum for general directed acyclic task graphs (DATGs). Experimental results demonstrate the superiority of the ECP algorithm over the scheduling algorithms presented in previous literature.

EXECUTING SCHEDULED TASK GRAPHS ON MESSAGE-PASSING ARCHITECTURES

A directed acyclic task graph (DAG) contains a set of tasks which access a set of data items and perform certain computations on those data items. The problem of DAG scheduling that optimizes the assignment of tasks onto the given processors has been studied extensively in the literature. We have developed a DAG scheduling system called PYRROS that maps the computation of task graphs onto message-passing machines [24]. In this paper we present a schedule executing model that incorporates several optimization strategies to reduce communication overhead and improve memory utilization. We study the correctness of task graph execution using this method and generalize this result to the iterative execution of a task graph and present experimental results on an nCUBE-2 parallel machine.

On the granularity and clustering of directed acyclic task graphs

The authors consider the impact of the granularity on scheduling task graphs. Scheduling consists of two parts, the processors assignment of tasks, also called clustering, and the ordering of tasks for execution in each processor. The authors introduce two types of clusterings: nonlinear and linear clusterings. A clustering is nonlinear if two parallel tasks are mapped in the same cluster otherwise it is linear. Linear clustering fully exploits the natural parallelism of a given directed acyclic task graph (DAG) while nonlinear clustering sequentializes independent tasks to reduce parallelism. The authors also introduce a new quantification of the granularity of a DAG and define a coarse grain DAG as the one whose granularity is greater than one. It is proved that every nonlinear clustering of a coarse grain DAG can be transformed into a linear clustering that has less or equal parallel time than the nonlinear one. This result is used to prove the optimality of some important linear clusterings used in parallel numerical computing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>