Makespan-minimization workflow scheduling for complex networks with social groups in edge computing

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Abstract

Edge computing enables users to offload certain computation loads in complex applications to a nearby network consisting of multiple mobile devices such that the mobile devices’ resources can be integrated to afford these complex applications. Due to the social relationships among the owners of mobile devices, networks in edge computing are always complex and consist of multiple sub-networks intersecting at several joint devices. In such complex networks, a joint device can communicate with all devices belonging to all sub-networks that intersect at this joint device while a general device can only communicate with the devices belonging to the same sub-network. This paper studies the makespan-minimization workflow scheduling problem for the aforementioned complex networks in edge computing environments, and formulates the problem as an integer program. Due to the limited energy capacity of each device, the dependence among workflow tasks, as well as network complexity, it is challenging to achieve feasible scheduling solutions for the concerned problem. Therefore, we propose a family of task allocation strategies to cope with different types of tasks in the workflow. These strategies are further integrated with a greedy strategy to construct an improved greedy search (IGS) algorithm which is capable of generating feasible solutions satisfying all constraints. In addition, we propose an improved composite heuristic (ICH) algorithm that employs IGS to initialize a feasible solution and uses a two-layer improvement scheme to further enhance the quality of the initial solution. Simulation results show that our proposed IGS achieves an 100% probability of generating feasible solutions, as compared to a 2.3% probability achieved by using the general round-robin scheduling algorithm. Furthermore, IGS and ICH outperform the counterpart scheduling algorithms in terms of makespan reduction.

Introduction

Though the computation capabilities of mobile devices have been enhanced recently, their limited resources still cannot meet the resource requirements of complicated applications, such as machine auto-translation and image processing [1], [2], [3], [4]. This limitation becomes the obstacle to the effective use of these applications in the mobile environment. In edge computing environments [5], [6], [7], [8], a complicated application can be divided into multiple computation tasks, among which the light-workload ones are assigned to the mobile device itself while the other heavy-workload ones are offloaded to one (or more) servers. This computing paradigm can effectively address the problem of insufficient resources of mobile devices while guaranteeing the QoS of workflow applications [9]. In this work, we study the workflow scheduling problem in a mobile edge computing system that enables device-to-device offloading mechanism [10] to avoid the overload of computing nodes, i.e., computation tasks can be offloaded to nearby mobile devices or a group of device-to-device users [11].

Generally in a mobile computing system, a server can be either a SRD or a network including MHDs. As shown in Fig. 1(a), in the SRD mode, the server for task offloading is a single resource-rich device, such as cloud [12] and cloudlet [13], [14] (i.e., the server deployed in the access point nearby mobile devices). In the MHD mode [15], [16], [17], on the other hand, multiple heterogeneous mobile devices form a network in which the computing resources of mobile devices can be shared among each other. This type of network is an MDN as illustrated in Fig. 1(b). The workflow of a mobile application is generally represented by a DAG. Recently, scheduling workflows in the above-mentioned device-to-device-enabled edge computing has drawn more and more attention [17], [18], [19], [20], [21], [22]. Most existing algorithms are based on the assumption that the edge computing environment has a single all-to-all network, i.e., each device can communicate with all other devices in this network. However, considering the social relations among the users of mobile devices, networks in edge computing are more complex than an all-to-all network. Such complex networks with social groups may consist of multiple sub-networks based on different “social groups” (such as “QQ groups”1 and “WeChat groups”2) [23]. Each sub-network is a MDN and different sub-networks intersect at several joint devices. In this work, this complex network with social groups is referred to as JMDN. For example, the example JMDN shwon in Fig. 1(c) contains seven devices and can be divided into three sub-networks corresponding to three “social groups”. Devices C and E are joint devices, while the others are general devices.

Scheduling workflows in a JMDN is much more difficult than in an all-to-all network owing to the high network complexity. The connective constraints may lead to a substantial number of infeasible scheduling solutions in the solution space. In JMDNs, a joint device can offload its computation load to all devices belonging to all sub-networks that intersect at this joint device, whereas a general device can only communicate with the devices belonging to the same sub-network. Referring to the example JMDN in Fig. 1(c), joint device C can offload tasks to devices A-E, whereas general device A can only offload tasks to devices A-C. In addition, by taking into account the precedence relations among workflow tasks and the constraint of each device’s energy capacity, deriving an optimal scheduling solutions satisfying all these constraints is challenging.

To tackle the above-mentioned challenge, in this paper we study the workflow scheduling problem in JMDN and aim to optimize the makespan of scheduling tasks in a workflow under the task precedence and energy constraints3 The major contributions of this paper are summarized as follows.

  • We formulate the makespan-minimization workflow scheduling problem as ILP, which is typically NP-hard [24]. We propose an IGS algorithm to generate feasible solutions in polynomial-time. In IGS, six scheduling policies are designed considering the features of tasks.

  • We develop an ICH algorithm that starts with a feasible solution generated by IGS and employs a two-layer scheme to improve the feasible solution. This improved scheme is established based on task movements among and inside sub-networks in JMDN.

  • We perform extensive simulations on both synthetic workflow applications and real-world workflow benchmarks to validate the effectiveness of IGS and ICH algorithms.

Simulation results reveal that, when the JMDN has sufficient resources, IGS can guarantee a 100% probability of generating feasible solutions satisfying all imposed constraints. As a comparison, the general round-robin algorithm GRR does with merely a probability of 2.3%. More importantly, IGS is verified to outperform the improved round-robin algorithm IRR that is constructed by incorporating our proposed six scheduling policies into GRR to ensure the feasible solutions. The results tested on real-world workflows demonstrate that the proposed IGS and ICH can reduce makespan by up to 35.4% and 44.1% as compared to IRR, respectively.

The rest of this paper is organized as follows. Section 2 reviews related work. Section 3 presents system models and defines the studied problem. Sections 4 and 5 detail the proposed IGS and ICH algorithms, respectively. Section 6 provides an illustrative example and a complexity analysis of the proposed method. Section 7 shows simulation setups and results. Finally, the concluding remarks are summarized in Section 8.

Section snippets

Related work

In the literature, there have been a substantial number of research studies that are oriented toward workflow task scheduling problems in mobile edge computing. Most studies model task scheduling as an optimization problem and develop scheduling algorithms to obtain the optimal or sub-optimal scheduling solution [25], [26], [27], [28]. In this section, we provide a brief overview of recent research progress on the scheduling algorithms that are closely related to this work.

Numerous studies have

Preliminaries

This section introduces our application and network models as well as defines our concerned optimization problem.

Improved greedy search

Due to the many constraints in the scheduling model, there may be a large number of infeasible solutions in the solution space. To ensure a feasible solution, we classify the tasks node into different categories and develop corresponding strategies for task assignment. We further construct an IGS algorithm that incorporates the task assignment strategies to generate feasible solutions satisfying all constraints in an efficient manner.

As demonstrated in Theorem 1, all task nodes of a given DAG

Improved composite heuristic

In the previous section, we construct a family of strategies to schedule tasks and propose IGS to guarantee generating a feasible solution. In this section, we propose an improved composite heuristic ICH that uses the feasible task scheduling solution generated by IGS as the initial solution and employs a two-layer improvement scheme to further explore better solutions. The two-layer improvement scheme is constructed by moving tasks inter sub-networks and intra sub-networks. Specifically, the

Example and complexity analysis

To better illustrate the proposed scheduling algorithm, in this section we use a simple example to explain how the tasks of a given workflow application are allocated to the mobile devices in a JMDN. As mentioned previously, the proposed method consists of an IGS routine for generating a feasible solution and an ICH routine for exploring better solutions. We use the DAG example in Fig. 2 and the JMDN example in Fig. 3 to show the results produced by these two routines in a stepwise manner. We

Performance evaluation

We carry out two sets of simulations to validate the proposed algorithms. The first set of simulations are based on synthetic DAG applications while the second set of simulations ues real-world workflow benchmarks. All experiments are performed on a desktop equipped with an eight-core i7-6700 CPU operating at 3.4GHz and 8GB memory. The proposed algorithms and compared approaches are all implemented by Java programming. Below, we present the setups and results of the two sets of simulations in

Conclusions

This paper considered the workflow scheduling problem with complex networks associated with social groups in edge computing. We propose six strategies to tackle workflows with different in-degrees and out-degrees as well as integrated them with a greedy strategy to develop an IGS algorithm that is capable of generating feasible scheduling solutions as long as the JMDN have sufficient resources. We further propose an ICH algorithm that uses the solution obtained by IGS as the initial solution

Declaration of Competing Interest

We confirm that there are no known conflicts of interest associated with this article and there has been no significant financial support for this work that could have influenced its outcome.

Acknowledgment

A preliminary version of this paper appeared in [2018 IEEE International Conference on Progress in Informatics and Computing (PIC), Suzhou, China, December 14-16, 2018]. This work was supported in part by the National Natural Science Foundation of China under Grants 61872185 and 61802185, in part by the Natural Science Foundation of Jiangsu Province of China under Grants BK20180470 and BK20190447, in part by the Jiangsu Planned Projects for Postdoctoral Research Funds under Grant 2019K025, in

Jin Sun received the B.S. and M.S. degrees in computer science from Nanjing University of Science and Technology, Nanjing, China, in 2004 and 2006, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Arizona in 2011. He is currently an Associate Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include cloud and edge computing, stochastic modeling and

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    Jin Sun received the B.S. and M.S. degrees in computer science from Nanjing University of Science and Technology, Nanjing, China, in 2004 and 2006, respectively, and the Ph.D. degree in electrical and computer engineering from the University of Arizona in 2011. He is currently an Associate Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include cloud and edge computing, stochastic modeling and analysis, and cyber-physical systems. He is a member of IEEE.

    Lu Yin received the B.S. degree in software engineering from Nanjing University of Science and Technology, Nanjing, China, in 2017. She is currently working toward the M.S. degree in the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China. Her research interests include cloud computing and task scheduling.

    Minhui Zou received the B.S. degree and Ph.D. degree in computer science and technology from Chongqing University, China, in 2013 and 2018, respectively. He is currently a lecturer with the School of Computer Science and Engineering, Nanjing University of Science and Technology, China. His current research interests include hardware security, edge computing, and memory computing.

    Yi Zhang received the B.S. and Ph.D. degrees in school of computer science and engineering, Southeast University, Nanjing, China, in 2005 and 2011, respectively. From July 2009 to December 2009, he did an internship at the IBM China Research Laboratory after he was awarded the IBM Ph.D. Fellowship. In 2011, he joined the Huawei Tech. Co., as a member of technical research staff. He is currently an Assistant Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include project scheduling, workflow optimization, resource management and allocation in cloud computing and mobile computing.

    Tianqi Zhang is currently working toward the B.S. degree in network engineering at Nanjing University of Science and Technology, Nanjing, China. Her research interests include cloud computing and task scheduling.

    Junlong Zhou received the Ph.D. degree in computer science from East China Normal University, Shanghai, China, in 2017. He was a Visiting Scholar with the University of Notre Dame, Notre Dame, IN, USA, during 2014–2015. He is currently an Assistant Professor with the School of Computer Science and Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include embedded systems, Internet-of-Things, and cyber physical systems, where he has published more than 60 refereed papers, including 20+ IEEE Transactions. He has been program vice-chairs, publication chairs, publicity chairs, section chairs, and TPC members for numerous conferences. Dr. Zhou serves as an Associate Editor for the Journal of Circuits, Systems, and Computers and the IET Cyber-Physical Systems: Theory & Applications, a Subject Area Editor for the Journal of Systems Architecture: Embedded Software Design, and a Guest Editor for 5 ACM/IET/Elsevier/Wiley Journals such as ACM Transactions on Cyber-Physical Systems.

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