Scientific Programming

Volume 2016, Article ID 9136107, 13 pages

http://dx.doi.org/10.1155/2016/9136107

## A Randomization Approach for Stochastic Workflow Scheduling in Clouds

Department of Computer Science, School of Information Science and Engineering, Xiamen University, Xiamen 361005, China

Received 21 January 2016; Accepted 24 April 2016

Academic Editor: Laurence T. Yang

Copyright © 2016 Wei Zheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

In cloud systems consisting of heterogeneous distributed resources, scheduling plays a key role to obtain good performance when complex applications are run. However, there is unavoidable error in predicting individual task execution times and data transmission times. When this error is being not negligible, deterministic scheduling approaches (i.e., scheduling based on accurate time prediction) may suffer. In this paper, we assume the error in time predictions is modelled in stochastic manner, and a novel randomization approach making use of the properties of random variables is proposed to improve deterministic scheduling. The randomization approach is applied to a classic deterministic scheduling heuristic, but its applicability is not limited to this one heuristic. Evaluation results obtained from extensive simulation show that the randomized scheduling approach can significantly outperform its static counterpart and the extra overhead introduced is not only controllable but also acceptable.

#### 1. Introduction

Workflows have been widely used in various domains to depict complex computational application with multiple indivisible tasks and the data dependencies between tasks [1]. These workflows are normally derived from scientific problems in the fields of mathematics, astronomy, and so forth, for example, Montage [2]. As the massive requirements of calculation and communication became overwhelming in these disciplines, clusters and grids, as evolutionary forms of distributed computing, have been used to run workflow applications since the end of the 20th century [3, 4]. Recently, with more flexible and scalable capacity on computation and storage and less hardware/software installation expense, it has been gaining increasing popularity of using cloud computing infrastructure to run workflows [5–9].

The assignment of workflow tasks to computing resources, which is called* workflow scheduling*, is one of the key effects on the execution performance of the workflow in distributed computing environments like clouds. In general form of scheduling problems, a workflow is frequently represented by a Directed Acyclic Graph (DAG), where the nodes symbolize the tasks and the arcs with direction symbolize the data dependencies between tasks. The two terms “node” and “arc” will be interchangeably used in the rest of this paper. The most commonly focused objective of DAG scheduling is the minimization of the makespan (namely, overall execution time) of the workflow. Generally a DAG scheduling problem has been proven to be NP-Hard [10]. For getting closer favourable solution to this problem with acceptable time and space complexity, many researches have been carried out, and many heuristics have been proposed and published in the literature [11, 12].

Nevertheless, for majority of the existing DAG scheduling heuristics, the targeted DAG is modelled deterministically [13]. This means that the heuristics assumptions to the problem of inputs like task execution times and intertask communication times are deterministic and precisely defined before. Clearly, the real-world workflow execution is much more complex than the above assumption because it is not possible to obtain accurate forecast of calculation and communication. Intuitively, the modelling of task computation times and communication times as random variables might be more realistic; it is also reasonabe to assume that the expected random variables and the variance can be predicted. In contrast to their deterministic counterparts, the DAG scheduling problems modelled in stochastic fashion are called* stochastic scheduling* [14]. A big number of heuristics have been proposed for deterministic scheduling, but a small number for stochastic. There have been a plethora of studies showing deterministic DAG scheduling heuristics can hardly work well for their stochastic counterpart problems. This motivates the research on somehow adapting the existing deterministic DAG scheduling heuristics into the stochastic context and making improvement in terms of minimizing makespan, which is also the main focus of this paper.

In this paper, we consider the problem of scheduling a workflow onto a set of heterogeneous resources based on stochastic modelling of task execution times and task communication times with the objective of minimizing the makespan. For such a problem, a novel randomization scheduling approach is proposed. The proposed approach is applied to a classic deterministic scheduling heuristic and evaluated via extensive simulation experiments and the results exhibit a significant improvement of workflow execution performance with an acceptable extra overhead.

The rest of the paper is structured as follows. Related work is discussed in Section 2. The stochastic DAG scheduling problem and relevant definitions are presented in Section 3. The proposed randomization scheduling approach with an illustrative example is described in Section 4. The evaluation results are provided and discussed in Section 5. Finally, a conclusion is provided in Section 6.

#### 2. Related Work

The past few decades witnessed a large number of efforts on developing various deterministic DAG scheduling heuristics, including HEFT [11], HBMCT [16], CPOP [11], GDL (DLS) [17], WBA [18], ILS [19], GA [20], SA [21], Triplet [22], TDS [23], STDS [24], and LDBS [25]. For an extensive list and classification of these heuristics we refer to [15, 26]. These heuristics differentiate with our work at the fact that they are based on deterministic scheduling model other than our stochastic model. Apparently, even when task execution times and data transmission times are modelled by some sort of random distribution, one can still apply one of the aforementioned deterministic scheduling heuristics by using the means of the random variables as inputs. However, as will be demonstrated later in this paper, this idea does not lead to a preferable schedule in most cases. Therefore, we derive a randomization approach by taking advantage of properties of random task execution times and data transmission times (as opposed to constant values). Although our approach can work with any deterministic heuristic in stochastic scheduling problems, we choose using the commonly cited and well-known deterministic heuristic: HEFT [11].

HEFT [11] is a deterministic list scheduling heuristic which aims to minimize the makespan of DAG applications on a bounded number of heterogeneous resources. The heuristic consists of two phases. In the first phase, the heuristic computes numeric ranks for all tasks based on their execution time predictions and data dependencies and then prioritizes tasks in a list. In the second phase, by the prioritized order, each task is allocated in turn to the resource which is estimated to minimize finished time of the task. It is worth mentioning that HEFT allows a task to be inserted into the existing task queue of a resource as long as the task dependency is not violated.

It has been widely recognized that due to the inaccuracy in time prediction deterministic scheduling heuristic relying on constant input may result in bad decision [27]. Over the recent years, some works have been carried out to evaluate the performance of deterministic DAG scheduling heuristics with stochastic model, such as [26, 28]. However, the main focus of these works is not on proposing an efficient scheduling heuristic for the stochastic DAG scheduling problem. One of recently popular ideas of addressing stochastic DAG scheduling problems is adapting the existing deterministic heuristics by changing their ranking function and/or the way of comparing task attributes. Examples can be found in [29–31]. Nevertheless, these heuristics still make scheduling decision in a deterministic manner. In contrast, our heuristic is randomized.

In our previous study [15], a Monte-Carlo based approach has been applied to the stochastic DAG scheduling problem to acquire a schedule which can outperform schedules generated by other comparable means. In essence, this approach relies on a significant amount of random searches on the solution space as well as an extensive evaluation for picking up the result schedule. As a result, a result schedule with a reasonable performance requires a considerable overhead. This paper is an extension to our previous work [32]. In this paper, we only do local search around a well-crafted schedule and the cost of evaluation of the searching results is trivial. That is to say, the overhead of the heuristic proposed in this paper is much less than the Monte-Carlo based approach, while a significant improvement on makespan can still be achieved.

#### 3. Problem Description

##### 3.1. Application Model

In this paper, a workflow application is represented by a Directed Acyclic Graph (DAG) , where denotes a set of interdependent tasks, each of which is represented by , that is, , and denotes a set of directed arcs, each of which represents data dependency between two tasks, that is, . For instance, means the input of task depends on the output of task . In this case, is a child of and is a parent of ; moreover, cannot start to run before receiving all necessary data from its parents. The node without parents is called entry node, and the node without children exit node. For the sake of standardization we assume that every DAG here has only one single entry node and one single exit node. For illustration, Figure 1 presents an example of DAG with 10 nodes.