Directed Acyclic Graph Scheduling Research Articles

Multi-agent Reinforcement Learning-based Adaptive Heterogeneous DAG Scheduling

Static scheduling of computational workflow represented by a directed acyclic graph (DAG) is an important problem in many areas of computer science. The main idea and novelty of the proposed algorithm is an adaptive heuristic or graph metric that uses a different heuristic rule at each scheduling step depending on local workflow. It is also important to note that multi-agent reinforcement learning is used to determine scheduling policy based on adaptive metrics. To prove the efficiency of the approach, a comparison with the state-of-the-art DAG scheduling algorithms is provided: DONF, CPOP, HCPT, HPS, and PETS. Based on the simulation results, the proposed algorithm shows an improvement of up to 30% on specific graph topologies and an average performance gain of 5.32%, compared to the best scheduling algorithm, DONF (suitable for large-scale scheduling), on a large number of random DAGs. Another important result is that using the proposed algorithm it was possible to cover 30.01% of the proximity interval from the best scheduling algorithm to the global optimal solution. This indicates that the idea of an adaptive metric for DAG scheduling is important and requires further research and development.

Bandwidth Allocation Algorithm for Makespan Optimization in a Fog-Cloud Environment: Monitoring Application

Fog computing technology has emerged to handle a large amount of data generated by the Internet of Things (IoT) terminals and cope with latency-sensitive application requests by allocating computation and storage resources at the edge of the Internet. In many IoT applications, the data acquisition procedures must apply the Directed Acyclic Graph (DAG) to get real-time results. The principal goal of DAG scheduling is to reduce total completion time without breaking priority constraints by properly allocating tasks to processors and arranging task execution sequencing. In this paper, we propose a bandwidth-aware workflow allocation (BW-AWA) that schedules tasks by priority to the resource and optimizes the total execution time (Makespan) in the entire computing system. The task allocation process needs to consider the dependency between tasks. The proposed approach is tested with a monitoring application case study, and the results are compared to well-known approaches to demonstrate its effectiveness in optimizing the Makespan.

Research and application of the parallel computing method for the grid-based Xin'anjiang model

Abstract The grid-based Xin'anjiang model (GXM) has been widely applied to flood forecasting. However, when the model warm-up period is long and the amount of input data is large, the computational efficiency of the GXM is obviously low. Therefore, a GXM parallel algorithm based on grid flow direction division is proposed from the perspective of spatial parallelism, which realizes the parallel computing of the GXM by extracting the parallel routing sequence of the watershed grids. To solve data skew, a Directed Acyclic Graph (DAG) scheduling algorithm based on dynamic priority is proposed for task scheduling. The proposed GXM parallel algorithm is verified in the Qianhe River watershed of Shaanxi Province and the Tunxi watershed of Anhui Province. The results show that the GXM parallel algorithm based on grid flow direction division has good flood forecasting accuracy and higher computational efficiency than the traditional serial computing method. In addition, the DAG scheduling algorithm can effectively improve the parallel efficiency of the GXM.

A reinforcement learning based job scheduling algorithm for heterogeneous computing environment

Efficient job scheduling for heterogeneous computing environments has attracted widespread attention, jobs are usually modeled as directed acyclic graphs(DAG). Optimizing scheduling can improve system throughput. We propose a two-stage scheduling algorithm, which calculates task selection and processor allocation respectively. In task selection stage, we utilize a bidirectional graph convolution network to learn DAG structural features, and a fully-connected network to generate proper scheduling scheme. In the processor allocation stage, we propose a heuristic based on optimistic cost table(OCT) and task duplication, which trade-off scheduling allocation better. Experiments of various scheduling scenarios have been conducted, and the results show that the proposed algorithm has better scheduling performance than the compared heterogeneous DAG scheduling algorithms.

DAG Hierarchical Schedulability Analysis for Avionics Hypervisor in Multicore Processors

Parallel hierarchical scheduling of multicore processors in avionics hypervisor is being studied. Parallel hierarchical scheduling utilizes modular reasoning about the temporal behavior of the upper Virtual Machine (VM) by partitioning CPU time. Directed Acyclic Graphs (DAGs) are used for modeling functional dependencies. However, the existing DAG scheduling algorithm wastes resources and is inaccurate. Decreasing the completion time (CT) of DAG and offering a tight and secure boundary makes use of joint-level parallelism and inter-joint dependency, which are two key factors of DAG topology. Firstly, Concurrent Parent and Child Model (CPCM) is researched, which accurately captures the above two factors and can be applied recursively when parsing DAG. Based on CPCM, the paper puts forward a hierarchical scheduling algorithm, which focuses on decreasing the maximum CT of joints. Secondly, the new Response Time Analysis (RTA) algorithm is proposed, which offers a general limit for other execution sequences of Noncritical joints (NC-joints) and a specific limit for a fixed execution sequence. Finally, research results show that the parallel hierarchical scheduling algorithm has higher performance than other algorithms.

DAG Scheduling and Analysis on Multi-Core Systems by Modelling Parallelism and Dependency

With ever more complex functionalities being implemented in emerging real-time applications, multi-core systems are demanded for high performance, with directed acyclic graphs (DAG) being used to model functional dependencies. For a single DAG task, our previous work presented a concurrent provider and consumer (CPC) model that captures the node-level dependency and parallelism, which are the two key factors of a DAG. Based on the CPC, scheduling and analysis methods were constructed to reduce makespan and tighten the analytical bound of the task. However, the CPC-based methods cannot support multi-DAGs as the interference between DAGs (i.e., inter-task interference) is not taken into account. To address this limitation, this article proposes a novel multi-DAG scheduling approach which specifies the number of cores a DAG can utilise so that it does not incur the inter-task interference. This is achieved by modelling and understanding the workload distribution of the DAG and the system. By avoiding the inter-task interference, the constructed schedule provides full compatibility for the CPC-based methods to be applied on each DAG and reduces the pessimism of the existing analysis. Experimental results show that the proposed multi-DAG method achieves an improvement up to 80% in schedulability against the original work that it extends, and outperforms the existing multi-DAG methods by up to 60% for tightening the interference.

DAG Scheduling with Communication Delays Based on Graph Convolutional Neural Network

In vehicular edge computing (VEC), tasks and data collected by sensors on the vehicles can be offloaded to roadside units (RSUs) equipped with a set of servers through the wireless transmission. These tasks may be dependent of each other and can be modeled as a directed acyclic graph (DAG). The DAG scheduling problem is aimed at scheduling the tasks to the servers to minimize the scheduling length (makespan), i.e., the maximum finish time of all tasks. The conventional heuristic algorithms only utilize partial information of the DAG, so the performance of these algorithms is not stable. The state-of-the-art scheduling method employs the graph neural network to further reduce the makespan. However, this method ignores the fact that there are communication delays between tasks scheduled on different servers. In this paper, we tackle the DAG scheduling problem considering communication delays which makes the problem much more challenging. Our method is based on graph convolutional neural network and reinforcement learning. Experimental results show that our scheduling method reduces the DAG scheduling length by 8% to 15% compared with the representative scheduling strategies based on graph neural network models (GAT, GraphSAGE) and 15% to 25% compared with the conventional algorithms (HEFT, LC, and CPOP) and the sequence-to-sequence model.

Adaptive search strategy based chemical reaction optimization scheme for task scheduling in discrete multiphysical coupling applications

Parallel computing problems of multiphysical coupling applications based on discrete grids can be equivalently transformed into parallel computing problems based on a directed acyclic graph (DAG). Due to the problem of the discrete high-dimensional grids of the multiphysical coupling application, the directed data dependencies usually have parallelism. Moreover, this kind of scheduling problem based on DAG is NP-hard problem. Heuristic algorithms are often used to achieve optimal execution order scheduling of tasks and mapping between tasks and processors. In this paper, we propose an improved chemical reaction optimization algorithm based on adaptive search strategy (ASSCRO), which is used to solve the DAG task scheduling problem of discrete multiphysical coupling applications. ASSCRO is divided into two phases. The first phase is used to search the directed execution order of the tasks, and the second phase aims to use the heuristic strategy to map the tasks to the processors efficiently. In the four basic reactions of CRO, the algorithm can cover a larger search solution space by using an adaptive search strategy, it can obtain a better solution, and achieve less overhead and superior performance than the state-of-the-art. We conducted the experiment that applied our ASSCRO to deal with the multiphysical coupling applications. The experimental results showed that the proposed algorithm outperforms other algorithms in multiple metrics when dealing with DAG scheduling problems.

Failure-resilient DAG task scheduling in edge computing

Through placing computation, storage, and communications facilities near the data source, Edge Computing (EC) is anticipated to extend the intelligence from the central cloud to the network edge. The Quality of Experience (QoE) of user and energy efficiency of mobile device could be significantly improved through offloading their computation-intensive tasks to the network edge. With the increasing popularity of intelligent devices, tasks offloaded to the edge are becoming more complex, consisting of multiple sub-tasks with data dependency, which are typically modeled as a Directed Acyclic Graph (DAG). The scheduling of DAG tasks is more complex, which has been proved to be NP-hard. Traditional DAG scheduling algorithms developed in non-edge computing scenarios could not be directly applied due to their neglect of: (1) the competition of communication resources; and (2) the rescheduling requirement in case of edge server failure in dynamic edge network environment. In this backdrop, this paper presents a failure-resilient DAG task scheduling algorithm to minimize the response delay experienced by the tasks. After formulating the DAG task scheduling problem, a context-aware greedy task scheduling (CaGTS) algorithm is proposed. Then, to cope with the failure event of edge server, a dependency-aware task rescheduling (DaTR) algorithm is designed. To evaluate the performance of the proposed algorithms, extensive experiments have been conducted on a simulator developed using Python. Experimental results with diverse parameter settings have shown that CaGTS could reduce at least 10.47% average completion time than benchmarks, and DaTR can effectively avoid task scheduling interruption caused by server failure events.

Dynamic DAG Scheduling on Multiprocessor Systems: Reliability, Energy, and Makespan

Multiprocessor systems are increasingly deployed in real-time applications, where reliability, energy consumption, and makespan are often the main scheduling objectives. In this work, we investigate the dynamic scheduling of tasks modeled by directed acyclic graphs (DAGs), which is an NP-hard problem with all existing methods being heuristics. Our contributions have two steps: 1) assuming that the allocation of DAG nodes to processors is given, we propose optimal energy allocation (OEA) and search-based OEA (SOEA)-the first optimal methods that minimize the energy consumption while satisfying the reliability requirement-for homogeneous and heterogeneous systems, respectively and 2) we present a novel scheduling algorithm out-degree scheduling (ODS) that allocates the DAG nodes according to their out-degrees, and considering energy consumption, reliability, as well as dynamic finish time. ODS dominates the widely applied heterogeneous earliest finish time (HEFT) in makespan. Combining SOEA with ODS makes a complete solution to the problem of dynamic DAG scheduling on multiprocessor systems, and achieves generally better results compared to the existing approaches. Specifically, in most cases, we are better on all the three objectives, i.e., reliability, energy, as well as makespan, and in other cases, we are better on some of the objectives.

A Comprehensive Review of Evolutionary Algorithms for Multiprocessor DAG Scheduling

The multiprocessor task scheduling problem has received considerable attention over the last three decades. In this context, a wide range of studies focuses on the design of evolutionary algorithms. These papers deal with many topics, such as task characteristics, environmental heterogeneity, and optimization criteria. To classify the academic production in this research field, we present here a systematic literature review for the directed acyclic graph (DAG) scheduling, that is, when tasks are modeled through a directed acyclic graph. Based on the survey of 56 works, we provide a panorama about the last 30 years of research in this field. From the analyzes of the selected studies, we found a diversity of application domains and mapped their main contributions.

Chemical Reaction Multi-Objective Optimization for Cloud Task DAG Scheduling

Cloud computing systems often have two conflicting objective, maximizing service performance, and minimizing computing cost. The excellent task scheduling and resource allocation strategies can improve the cost/utility ratio efficiently. It is an NP-hard problem to optimize task scheduling of precedence-constrained parallel tasks represented by a directed acyclic graph (DAG) on the cloud system. In order to address this problem, a chemical reaction multi-objective optimization algorithm (CRMO) is proposed in this paper. The CRMO executes four chemical reaction operators (named on-wall ineffective collision, inter-molecular ineffective collision, decomposition, and synthesis) for cloud tasks DAG scheduling. The experimental results show that CRMO can produce outstanding cloud task scheduling solutions set.

Progressive Multicore RLNC Decoding With Online DAG Scheduling

A complete generation of packets coded with Random Linear Network Coding (RLNC) can be quickly decoded on a multicore system by scheduling the involved matrix block operations in parallel with an offline (pre-recorded) directed acyclic graph (DAG). The waiting for a complete generation of packets can be avoided with progressive RLNC decoding that commences the decoding (and can decode some packets) before all packets in a generation have been received. This article develops and evaluates a novel progressive RLNC decoding strategy based on the principle of DAG scheduling of parallel matrix block operations. The novel strategy involves helper matrices for conducting the Gauss Jordan elimination based on rows of blocks of matrix elements. The matrix block computations are dynamically scheduled by an online DAG which permits branching, e.g., to skip unnecessary matrix block operations. The throughput and delay of the novel progressive RLNC decoding strategy are evaluated with experiments on two heterogeneous multicore processor boards. The novel progressive RLNC decoding achieves throughput levels on par with state-of-the-art non-progressive (full-generation) RLNC decoding and achieves three times higher throughput than the fastest (highest-throughput) known progressive RLNC decoder for small generation sizes and short data packets. Also, our progressive RLNC decoding greatly reduces receiver delays for moderate to large generation sizes; the delay reductions are particularly pronounced when a low-delay RLNC version is employed (e.g., reduction to one tenth of the non-progressive decoding delay for a generation size of 256 packets).

Level-Wised Directed Acyclic Graph Scheduling on Cloud Resources

Level-Wised Directed Acyclic Graph Scheduling on Cloud Resources

Computing the expected makespan of task graphs in the presence of silent errors

Applications structured as Directed Acyclic Graphs (DAGs) of tasks occur in many domains, including popular scientific workflows. DAG scheduling has thus received an enormous amount of attention. Many of the popular DAG scheduling heuristics make scheduling decisions based on path lengths. At large scale compute platforms are subject to various types of failures with non-negligible probabilities of occurrence. Failures that have recently received increased attention are “silent errors,” which cause data corruption. Tolerating silent errors is done by checking the validity of computed results and possibly re-executing a task from scratch. The execution time of a task then becomes a random variable, and so do path lengths in a DAG. Unfortunately, computing the expected makespan of a DAG (and equivalently computing expected path lengths in a DAG) is a computationally difficult problem. Consequently, designing effective scheduling heuristics in this context is challenging. In this work, we propose an algorithm that computes a first order approximation of the expected makespan of a DAG when tasks are subject to silent errors. We find that our proposed approximation outperforms previously proposed approaches both in terms of approximation error and of speed.

Efficient task scheduling for budget constrained parallel applications on heterogeneous cloud computing systems

As the cost-driven public cloud services emerge, budget constraint is one of the primary design issues in large-scale scientific applications executed on heterogeneous cloud computing systems. Minimizing the schedule length while satisfying the budget constraint of an application is one of the most important quality of service requirements for cloud providers. A directed acyclic graph (DAG) can be used to describe an application consisted of multiple tasks with precedence constrains. Previous DAG scheduling methods tried to presuppose the minimum cost assignment for each task to minimize the schedule length of budget constrained applications on heterogeneous cloud computing systems. However, our analysis revealed that the preassignment of tasks with the minimum cost does not necessarily lead to the minimization of the schedule length. In this study, we propose an efficient algorithm of minimizing the schedule length using the budget level (MSLBL) to select processors for satisfying the budget constraint and minimizing the schedule length of an application. Such problem is decomposed into two sub-problems, namely, satisfying the budget constraint and minimizing the schedule length. The first sub-problem is solved by transferring the budget constraint of the application to that of each task, and the second sub-problem is solved by heuristically scheduling each task with low-time complexity. Experimental results on several real parallel applications validate that the proposed MSLBL algorithm can obtain shorter schedule lengths while satisfying the budget constraint of an application than existing methods in various situations.

Minimum Dependencies Energy-Efficient Scheduling in Data Centers

This work presents an on-line, energy- and communication-aware scheduling strategy for SaaS applications in data centers. The applications are composed of various services and represented as workflows. Each workflow consists of tasks related to each other by precedence constraints and represented by Directed Acyclic Graphs (DAGs). The proposed scheduling strategy combines advantages of state-of-the-art workflow scheduling strategies with energy-aware independent task scheduling approaches. The process of scheduling consists of two phases. In the first phase, virtual deadlines of individual tasks are set in the central scheduler. These deadlines are determined using a novel strategy that favors tasks which are less dependent on other tasks. During the second phase, tasks are dynamically assigned to computing servers based on the current load of network links and servers in a data center. The proposed approach, called Minimum Dependencies Energy-efficient DAG (MinD+ED) scheduling, has been implemented in the GreenCloud simulator. It outperforms other approaches in terms of energy efficiency, while keeping a satisfiable level of tardiness.

Cost-aware DAG scheduling algorithms for minimizing execution cost on cloud resources

Directed acyclic graph (DAG) scheduling is a well-known problem, because a DAG can be used to describe a wide range of complex applications, including scientific applications and parallel computing jobs. Most DAG scheduling algorithms were proposed to minimize the job makespan (i.e., execution time) on a multiprocessor computer or cluster. However, as the cost-driven public cloud services have become an attractive and popular platform for providing computing resources, cost minimization emerges as a new critical issue. Therefore, the objective of this work is to propose and solve the cost optimization problem for scheduling DAGs on an IaaS cloud platform where task scheduling must cope with resource provisioning to achieve the optimal solution. In this paper, we proposed both optimal and heuristic scheduling algorithms, and we evaluated them across a variety of DAGs using the price model from EC2. Comparing to other cost-oblivious DAG schedules that aim to minimize makespan or resource usage, the results show that our cost-aware heuristic algorithm can reduce cost by 20---50 % and achieve a cost within x1.16 of the optimal one.

A novel hybrid PSO–GA meta-heuristic for scheduling of DAG with communication on multiprocessor systems

This work presents a novel hybrid meta-heuristic that combines particle swarm optimization and genetic algorithm (PSO---GA) for the job/tasks in the form of directed acyclic graph (DAG) exhibiting inter-task communication. The proposed meta-heuristic starts with PSO and enters into GA when local best result from PSO is obtained. Thus, the proposed PSO---GA meta-heuristic is different than other such hybrid meta-heuristics as it aims at improving the solution obtained by PSO using GA. In the proposed meta-heuristic, PSO is used to provide diversification while GA is used to provide intensification. The PSO---GA is tested for task scheduling on two standard well-known linear algebra problems: LU decomposition and Gauss---Jordan elimination. It is also compared with other states-of-the-art heuristics for known solutions. Furthermore, its effectiveness is evaluated on few large sizes of random task graphs. Comparative study of the proposed PSO-GA with other heuristics depicts that the PSO---GA performs quite effectively for multiprocessor DAG scheduling problem.

Simulation-based evaluations of DAG scheduling in hard real-time multiprocessor systems

The scheduling of parallel real-time tasks on multiprocessor systems is more complicated than the one of independent sequential tasks, specially for the Directed Acyclic Graph (DAG) model. The complexity is due to the structure of DAG tasks and the precedence constraints between their subtasks. The trivial DAG scheduling approach is to directly apply common real-time scheduling algorithms on DAGs despite their lack of compatibility with the parallel model. Another scheduling approach, which is called the stretching method, aims at transforming each parallel DAG task in the set into a collection of independent sequential threads that are easier to be scheduled. In this paper, we are interested in analyzing global preemptive scheduling of DAGs using both approaches by showing that they are not comparable when associated with Deadline Monotonic (DM) and Earliest Deadline First (EDF) scheduling algorithms. Then we use extensive simulations to evaluate their schedulability performance. To this end, we use our simulation tool YARTISS to generate random DAG tasks with many parameter variations so as to guarantee reliable experimental results.