## 2 Materials and Methods  
### Preliminary Knowledge  
#### 2.1.1 Introduction of the Problem  
As shown in Figure 1, this paper considers a MEC network frame consisting of a single server serving multiple cells where the user's request and conditions are known. In this network, the MEC server cooperates with all cell base stations to provide service to M users in these cells through N independent communication resources. Each user device has a certain local computing capacity and ability to communicate with the server. The network uses the strong computing power of the MEC server to help users run their apps. In this way, the MEC network realizes local-edge collaborative working with low delay and power consumption. Users communicate with the base station through the wireless network, and base stations communicate with the server via wired communication.  
There are three kinds of tasks in this problem, including uplink tasks, such as fingerprint recognition; downlink tasks, such as video streaming; and interactive tasks, such as VR service. Currently, downlink traffic accounts for the majority of network traffic. Sometimes, it even accounts for 90% of the total. Conceivably, further consideration of the properties of downlink tasks may be helpful for optimization.  
In this problem, the result of resource allocation is mainly determined by the energy consumption of user devices and the delay of the network. The total energy consumption is the sum of the energy consumption for all computing and data transmission. The network delay is composed of two main parts: namely, the delay from user devices to the base station and the delay from the base station to the MEC server. For simplicity, this paper postulates that public communication facilities have an inexhaustible energy supply because they are powered by the grid. In addition, another prerequisite assumption is that these facilities have an extremely high transmission capacity. Based on this, only the energy consumption  
Figure 1: Optimization problem scenarios.  
of user devices and the delay of data transmission between user devices and the base station should be considered.  
According to this problem, this paper will subsequently describe the generation of the transmission, delay and energy consumption models for the downlink, uplink and interactive tasks. For downlink tasks, the user usually sends a relatively short request; then the MEC server will compute, compress and downlink transmit the corresponding content after receiving the request. It is predicted that the traffic of multimedia downlink services will account for the vast majority of network traffic in the future. For uplink tasks, users upload acquired data to the MEC server via their devices. Then, before sending the result back, the MEC server must process this content according to the data stored by itself. Generally, the result is relatively short and the downlink transmission pressure is very low. For interactive tasks, the network needs to satisfy users' demands for online real-time interaction. This kind of task requires the MEC server to complete real-time information collection upon request by user devices and then quickly send the interaction content to the user. Thus, the server and user will both conduct frequent data transmission. To summarize, users, communication facilities, different kinds of tasks and various heterogeneous communication resources together form a MEC network, as shown in Figure 1; i.e., one server serves multiple cells.