Prior node selection for scheduling workflows in a heterogeneous system
Introduction
Recent distributed processing schemes, e.g., grid and cloud systems, enable submitted parallelizable jobs to be executed by idle computational resources in order to distribute the workloads imposed by those jobs. For example, resource provisioning in a cloud system and a node1 grouping strategy in a grid are needed to minimize the response time (i.e., the schedule length), maximize the throughput, or meet other requirements. In particular, the virtual machine (VM) selection policy in a resource provisioning policy has an impact on the response time. In light of the independent task scheduling used in a heterogeneous system, a node grouping method takes the performance of each node into account, i.e., each node in a group has similar processing speed or every group has a similar average processing speed.
The above examples are based on the question of how the subset of nodes should be determined from the given idle nodes to satisfy the predefined objective functions. However, no theoretical approach to this problem has yet been established. In a MapReduce architecture, although how to derive the optimal number of map tasks or nodes to minimize the response time is a challenging issue, the actual approach samples the historical execution information of the system [22]; that is, the approach investigates the correlation between the number of map tasks and actual execution time in advance. Such an approach is time consuming. Furthermore, the workflow or directed acyclic graph (DAG) scheduling problem is -complete [9]. This problem must take into account the processing speed and communication bandwidth of each node as well as the workflow characteristics such as precedence constraints among tasks. Furthermore, whether the job is data or computationally intensive must be considered to select the subset of given nodes. However, to our knowledge, no subset selection approach for workflow scheduling exists.
As cost-effective task scheduling algorithms in a workflow for heterogeneous systems, list-based scheduling algorithms are well-known [5], [16], [28], [29]. In these algorithms, the scheduling priority assigned to a task is derived from the processing speeds of all nodes and all communication bandwidths in the given set of nodes. It follows from this that the response time (hereafter, the “schedule length”) depends on not only the performance of the assigned nodes but also that of the unassigned nodes. This characteristic indicates that the schedule length has space for further improvement depending on the policy to determine the subset of the given nodes.
In practice, multiple jobs can be submitted to a scheduling system. In such a case, if an appropriate subset of the given nodes is determined for one job, the schedule length (i.e., the maximum response time for all jobs) can be prolonged by the inappropriate resource allocation for the other jobs caused by a shortage of appropriate nodes. Thus, it is necessary to fairly allocate resources among all jobs in order to reduce the maximum schedule length of the submitted jobs. Here, we consider the case in which one or more workflow jobs have been stored in the job pool in the system. They must be scheduled simultaneously to minimize the maximum schedule length among the jobs. In such a case, these multiple jobs can be integrated into a larger job, where dummy start and end tasks are added to the workflow. It can then be scheduled by conventional a scheduling algorithm, and therefore the schedule length, i.e., the maximum schedule length of those jobs is effectively reduced, while the slowdown, which is an index of fairness in terms of assignment resources, is sacrificed [31]; that is, such an integration approach can be further improved if each resource is fairly assigned.
The current challenges of node selection for workflow scheduling can be summarized as follows: (i) the scheduling priority for each task in a job is not accurate for minimizing the schedule length because it is derived from all given nodes, and (ii) whether selecting nodes before scheduling tasks can affect on the fairness in terms of slowdown or not is unknown. In the context of scheduling tasks in case of multiple workflows, minimizing the schedule length cannot always lead to a fair scheduling. However, before scheduling tasks, if we can select the nodes having similar performance each other and also each having a great effect on minimizing the schedule length, such a prior node selection can take an important role for resource provisioning.
In this paper, we propose a candidate node selection algorithm, called the lower bound based candidate node selection (LBCNS) for determining the subset of given idle nodes that achieves the minimum schedule length while fairly scheduling each job in a heterogeneous distributed system. The key concept behind LBCNS is to select a set of nodes that obtain good performance by considering both each workflow characteristic and the performance of the given idle nodes. As a result, only a set of nodes that can help minimize the schedule length are selected as assignment candidates. In particular, the running time without idleness of node is defined as . The subset of nodes with small is selected as the set of assignment candidates for scheduling tasks. Moreover, we propose dedicated node selection algorithms for state-of-the-art task scheduling algorithms that take each scheduling priority derivation policy into account to further improve the schedule length. Experimental results obtained via simulation show that a schedule length that is better than that of other node selection policies can be obtained by LBCNS for single and multiple workflow jobs. Furthermore, we show that the efficiency, which is defined as the speed-up ratio divided by the number of assigned nodes, can be reduced. Furthermore, unfairness, defined as the variance in terms of slowdown among jobs, can be reduced.
The remainder of this paper is organized as follows. Section 2 describes the assumed system and model. Related work in node grouping methods and task scheduling algorithms are reviewed in Section 3. We then present the proposed node selection algorithm LBCNS in Section 4. Extensions of LBCNS for specific task scheduling algorithms are then presented in Section 5. Experimental results are described in Section 6. Finally, we conclude this paper in Section 7.
Section snippets
Job model
We assume a job to be executed on the nodes is a DAG, or a workflow job. Let be the DAG or workflow, where is the set of tasks, is the set of edges, i.e., data communications among tasks, and is the set of assignment units, where each assignment unit contains one or more tasks. An th task is denoted as . Let be the size of , i.e., is the sum of the time units needed to process the task by the reference node. We define the data dependency and direction of data
Related work
In this section, we describe related work and results in terms of node selection approaches in a distributed system, task scheduling algorithms for a single workflow job, multiple workflow scheduling algorithms, and the derivation method for the lower bound of each node’s execution time (i.e., the lower bound of the workload for each node).
We describe the relationship between our proposal and conventional approaches given in this section. Approaches in Section has the same objective,
Lower bound-based candidate node selection
In this section, we present our proposed method, called LBCNS. We first present details of LBCNS for general task scheduling methods, and then present four node selection algorithms based on LBCNS for well-known and state-of-the-art list-based task scheduling algorithms. The notation used in this section and Section 5 is listed in Table 1.
LBCNS for list-based task scheduling
In this section, we present the node selection algorithms that takes the scheduling priority into account for several list-based scheduling algorithms such as HEFT [28], CEFT [16], HSV [29], and PEFT [5]. Since the schedule length depends on the order of the free task selection and task allocation policy, at first we describe how the order can be changed by the subset of the given nodes for each scheduling algorithms. Then we present details of LBCNS_HEFT, LBCNS_CEFT, LBCNS_HSV, and LBCNS_PEFT
Objective
In this section, we present the experimental results of our simulations. The objectives of LBCNS are to minimize the schedule length for both a single job and multiple jobs after task scheduling is applied while satisfying the fairness of the schedule length among jobs. Thus, we compared LBCNS with other methods in terms of the following points:
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The effect on the schedule length for both single and multiple workflow jobs when the subset of nodes is selected by LBCNS. In
Conclusion
In this paper, we proposed a prior node selection algorithm called LBCNS. In contrast to conventional node selection approaches that use system information, LBCNS takes each job’s characteristics such as its task graph structure and each node’s performance into account. In particular, LBCNS_DEFAULT tries to select the candidate nodes for scheduling tasks in advance by deriving the lower bound of the total workload for each node in order to determine the number of nodes needed to minimize the
Acknowledgment
This work was supported by JSPS KAKENHI Grant Number 25730077.
Hidehiro Kanemitsu received a B.S. degree in Science from Waseda University, Japan and M.S. and D.S. degrees in Global Information and Telecommunication Studies from Waseda University, Japan. His research interests include parallel and distributed computing, grid, peer-to-peer computing, and web service technology. He is currently an assistant professor at the Global Education Center, Waseda University, Japan. He is a member of the IEEE.
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Hidehiro Kanemitsu received a B.S. degree in Science from Waseda University, Japan and M.S. and D.S. degrees in Global Information and Telecommunication Studies from Waseda University, Japan. His research interests include parallel and distributed computing, grid, peer-to-peer computing, and web service technology. He is currently an assistant professor at the Global Education Center, Waseda University, Japan. He is a member of the IEEE.
Masaki Hanada received a B.E. degree in Resources Engineering from Waseda University in 1996, and M.S. and D.S. degrees in Global Information and Telecommunication Studies from Waseda University in 2003 and 2007, respectively. He is an associate professor in the Department of Information Systems, Tokyo University of Information Sciences. His research interests include QoS/traffic control and resource management in communication networks. He is a member of the IEEE.
Hidenori Nakazato received his B.E. degree in Electronics and Telecommunications from Waseda University in 1982 and his M.S. and Ph.D. degrees in Computer Science from the University of Illinois in 1989 and 1993, respectively. He was affiliated with Oki Electric from 1982 to 2000 where he developed equipment for public telephone switches, distributed environments for telecommunications systems, and communications quality control mechanisms. He is a professor at the Department of Communications and Computer Engineering, Waseda University, Japan. His research interests include information centric networking, cooperation mechanisms of distributed programs, and network QoS control. He is a member of the IEEE.