## 1 Introduction  
With the popularity of mobile devices, a growing number of mobile applications are striving for computation capacity to provide various services. Nevertheless, mobile devices generally have limited computation resources and short battery lifetime, so some applications which is computationally massive cannot be successfully implemented on mobile devices [1; 2]. This conflict between the applications which is scarce of resources and mobile devices whose resources are limited hence presents a formidable challenge.  
A new technique called Mobile Cloud Computing (MCC) is likely to solve the aforementioned challenge. Cloud computing [3] offers enormous storage space and computation resources. Through transferring tasks from mobile devices to the resource-rich server, it could overcome the shortage of computation resources in mobile devices. Because mobile devices are far away from the remote cloud, large delays for mobile users has become a critical challenge for cloud computing.  
Mobile Edge Computing (MEC) is envisioned as an emerging technique to handle this challenge. It provides cloud-computing service at the mobile edge network close to mobile devices [4]. The main advantages of MEC are as follows: (i) compared with local computing [5], it can avoid the disadvantage of insufficient computation capacity of mobile devices; (ii) compared to Mobile Cloud Computing, it can overcome the large latency that occurs while tasks are transferred to the remote cloud. Thus, MEC presents a better compromise between tasks which is sensitive to delay and tasks is intensive to computation.  
Mobile devices can offload their tasks to the edge cloud for computing, or they can choose to finish it locally. The computation capability of the edge cloud is crucial for this issue. In existing works on task offloading, the computation capability of the edge cloud is assumed to be known perfectly and is supposed to be a fixed value. However, the computation capability of the edge cloud varies over time due to the dynamic of the number of computation tasks. For instance, the computation capability of the edge cloud would decline when much more tasks are processed at edge cloud.  
In this paper,we focus on the problem of computation capacity of the edge cloud, and propose an ARIMA-BP-based Selective Offloading strategy. The strategy minimizes the total energy consumption by mobile devices and simultaneously meets the tasks' delay constraints. The major contributions of this paper are summarized as follows:  
* We propose a multi-device framework for task offloading in MEC networks, and we formulate an optimization problem which minimizes the energy consumption and concurrently meets the delay constraints.
* To solve this problem, we devise an efficient strategy, called ABSO (ARIMA-BP-based Selective Offloading). In ABSO, we propose an ARIMA-BP model to estimate computation capacity of the edge cloud, and then design a Selective Offloading Algorithm for obtaining offloading strategy.  
The rest of this paper is organized as follows. In Section 2, we introduce the relevant research works review. The system model is in Section 3. In Section 4, we elaborate an ARIMA-BP model for estimating computation capacity of the edge cloud and further present a Selective Offloading Algorithm to solve offloading problem. Section 5 provide the simulation results. Finally, we come to the conclusion in Section 6.