Makespan-minimized computation offloading for smart toys in edge-cloud computing

https://doi.org/10.1016/j.elerap.2019.100884Get rights and content

Highlights

  • Define and formulate a makespan-minimized offloading problem for smart toys in edge computing.

  • Propose an improved LBBD approach to solve the offloading problem.

  • Propose a novel hybrid approach integrating LBBD principle with MILP to speed up the solving process.

  • Implement the algorithms and conduct experiments to evaluate their performances.

Abstract

Computation offloading is a promising way to accelerate applications of smart toys, especially in the scenarios that integrate smart toys with edge computing techniques. Task scheduling is essential to provide an ultra-low latency in such a paradigm. However, existing scheduling approaches on computation offloading suffer from the following weaknesses: 1) Heterogeneity: They schedule tasks without joint consideration of the heterogeneity of transfer rate and processing capability; 2) Optimality: They fail to find the optimal solution efficiently. In this paper, we study a makespan-minimized problem with joint consideration of above-mentioned heterogeneity factors for a Toy-Edge-Cloud architecture and formulate it as a MILP model. To solve the problem, we propose a novel optimal approach integrating the Logic-Based Benders Decomposition (LBBD) principle with Mixed Integer Linear Programming (MILP) models, where two refinement techniques are proposed to generate cuts efficiently. Extensive experiments have been performed in which synthetic applications described by Directed Acyclic Graphs (DAGs) are mapped to a number of heterogeneous compute nodes. The results demonstrate that our approach significantly decreased the overall solution time comparing to pure MILP and LBBD and outperforms other state-of-the-art approaches.

Introduction

Smart toy, a specific IoT (Internet of Things) device that connects to a computing system with online services to extend the capacity of a traditional toy, has become popular in recent years (Schmid et al., 2011, Hong et al., 2014, Gutiérrez García et al., 2017). What’s more, the rapid development of artificial intelligence technology has provided many opportunities to the industries in developing intelligent applications for smart toys. This kind of applications are typically resource-hungry (e.g., deep learning Poon et al., 2017), computation intensive, and demand real-time processing. Nevertheless, due to cost considerations, the computing resources and battery of smart toys are in general poorly equipped, which makes it difficult to fulfill the Quality-of-Service (QoS) requirements of task processing (Hong et al., 2019, Chen et al., 2019).

Computation offloading is a promising way to accelerate applications of IoT devices, especially in the scenarios that integrate IoT with edge computing paradigm (Li et al., 2019, Li et al., 2019). Task scheduling is essential to provide an ultra-low latency in such environments. Many approaches have been proposed to deal with edge scheduling problems (Chen et al., 2018, Deng et al., 2019, Scoca et al., 2018, Huang et al., 2018, Chen et al., 2018). However, those approaches are not applicable to toy computation offloading because of the following challenges:

Heterogeneities: heterogeneities always exist in edge computing architectures. This is reflected in two aspects: transfer rate and processing capability. First, computing resources are in general deficient on toys, richer but still limited at the edge servers (Tan et al., 2017), while they are massive and powerful in the cloud. Hence, the processing time may be various in different compute nodes. Second, the transfer rate between compute nodes depends on the adopted communication technology. Toys usually access the edge servers via low energy wireless technologies (e.g., BLE or ZigBee), while edge servers communicate with each other through direct link (e.g., WiFi or LTE direct) or wide area network (e.g., 4G networks). These heterogeneities further complicate the optimization of QoS in toy computing. Existing approaches either take only processing capability or bandwidth into consideration. Therefore, the joint consideration of the two factors is an impending challenge.

Optimality: Existing approaches can be roughly categorized into the following classes: 1) Heuristic-based approaches that produce an approximate solution by applying a rule of thumb approach in a reasonable time frame (Chen et al., 2018, Ra et al., 2011); 2) Metaheuristic-based approaches that implement some form of stochastic optimization (Xiang et al., 2017); 3) Mix Integer Linear Programming (MILP) based approaches (Li et al., 2018). However, the first two classes of approaches do not guarantee that a globally optimal solution can be found, the third class may be too time-consuming due to large integrality gap. Hence, it is meaningful to explore exact algorithms to obtain the optimal solution.

To conquer the first challenge, we study the makespan-minimized problem for a Toy-Edge-Cloud architecture with joint consideration of the heterogeneity of transfer rate and processing capability and formulate it as a MILP model. For the optimality issue, we propose a novel optimal approach integrating the Logic-Based Benders Decomposition (LBBD) principle with MILP models to solve the problem efficiently, which can obtain the optimal solution faster than existing approaches. The main contributions of this paper are as follows:

  • We mathematically define and formulate the Makespan-minimized Offloading for Toy Computing problem (MOTC) as a MILP.

  • Given the complexity, we explore an LBBD approach to solve the problem. The LBBD approach decomposes the MOTC problem into a Master Problem that performs the task assignment, and a Sub-Problem to addresses the scheduling of tasks to the same node. For the generation of Benders cuts demanded by the approach, two refinement techniques are proposed to generate cuts efficiently, while the computational overhead is kept low.

  • A novel hybrid approach integrating LBBD principle with MILP is introduced. Rather than simply combining the two algorithms, we propose to run them in parallel and share their respective bounds and Benders cuts to solve the MOTC problem to optimality more efficiently. To the best of our knowledge, this is the first attempt to solve an optimization problem with an LBBD-ILP parallel approach.

  • Extensive evaluations are carried out to examine the efficiency of the proposed approach comparing to state-of-the-art approaches. The results show our approach can generate smaller makespan than other state-of-the-art approaches and can solve the problem to optimality more efficiently than pure MILP and LBBD.

The remainder of this paper is organized as follows. In Section 2, we review some related work in smart toys and edge computing and the classic workflow scheduling problem. Then, in Section 3, we introduce our system model and formulate the makespan optimization problem as a MILP model in Section 4. Next, we propose our algorithm in Section 5. In Section 6, we demonstrate the experimental results. And finally, we conclude our research and point out our future work in Section 7.

Section snippets

Smart toys and edge computing

Many smart toy products implement useful functions, such as voice recognition, human-computer interaction, to enhance their play value or educational features. Mironcika et al. (2018) described the design and deployment of a digital board game, equipped with sensors, which they use to explore the potential of using smart toys for fine motor skills assessment in children. Westeyn et al. (2012) developed a kind of smart toy, objects embedded with wireless sensors that are safe and enjoyable for

System model

In this section, we introduce the system model. For the sake of the reader’s convenience, often-used notations are summarized in Table 1.

We consider the architecture as shown in Fig. 1. It is assumed that a Toy-Edge-Cloud (TEC) network consists of three layers: 1) The layer of toys that collect data and release tasks; 2) The layer of edges that are close the toys and provide computing resources with low latency via distributed processing; 3) The layer of cloud with abundant resources based on

Problem formulation

In this section, we define and mathematically formulate the Makespan-minimized Offloading for Toy Computing (MOTC) problem as a MILP model.

Algorithm design

Given the complexity of the MOTC problem, we devise in the following a hybrid approach integrating LBBD and MILP to solve it.

Evaluation

We conduct extensive simulations to evaluate our approaches in this section. For comparison, we consider the following state-of-the-art approaches:

  • Greedy: Starting from the first task in the task graph, greedily assign one by one in the following to the nodes that result in the earliest finish time.

  • HEFT (Topcuoglu et al., 2002): A heuristic that selects the task with the highest upward rank value at each step and assigns the selected task to the processor, which minimizes its earliest finish

Conclusion and future work

In this paper, we motivated and studied the MOTC problem which addresses the computation offloading in a Toy-Edge-Cloud network. We first formulated the problem as a MILP model. To tackle the high computational complexity of solving it, we proposed a novel hybrid approach in order to prune the solution space and deliver optimal solutions. Our approach integrates the LBBD principle with MILP in a parallel way and shares bounds and Benders cuts in real time. To generate cuts efficiently, we

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The work described in this paper was supported by the National Key R&D Program of China (2018YFB1003800), the Guangdong Province Universities and Colleges Pearl River Scholar Funded Scheme 2016, the National Natural Science Foundation of China (No. 61722214), and the Program for Guangdong Introducing Innovative and Enterpreneurial Teams (No. 2017ZT07X355). Wuhui Chen is the corresponding author.

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