## 2 System Model and Problem Formulation
### System Model  
With the increasing number of user devices in the sea, business types and business volume surge. These businesses include various domains' ship- and shore-related data in the forms of multiple services supporting marine activities such as safe navigation, security at sea, protection, and management of the marine environment, and others. In terms of quantity and scale, these businesses in the sea generate and transmit data in real time every minute, and the data volume has exploded to exceed the PB level [26]. As users in sea applications are mostly resource-limited nodes with limited computing abilities, it is difficult to meet the increasing demand for data and business services through users'local computing and processing capacity. The traditional center computing method also cannot meet the huge demand of users on the sea. Then, we introduce edge computing techniques to solve the limited resources problems. Many works have been conducted on resource allocation in edge computing networks [27; 28; 29; 30; 31]. Generally, in the nearshore sea, multiple coastal base stations integrated with edge computing techniques can cooperate with the user's devices to realize the user's computational unloading. However, in offshore areas, due to the wide range of sea areas, it would introduce large-scale construction costs and other factors when using the multiple coastal base stations integrated with edge computing techniques. In this paper, we consider using the satellite network to provide edge computing services to user devices to ensure the applications' requirements.  
As shown in Figure 1, a multi-access edge computing assisted satellite network is given, which is composed of multiple satellites and multiple users. Each satellite is assumed to have an edge computing server. Considering the impact of energy and load, MEC servers on satellites can consider using a lightweight management platform such as Docker. By deploying MEC servers on LEO satellites, satellites are equipped with computing and content distribution capabilities [32], which can not only effectively reduce the frequent satellite-based link transmission and end-to-end service transmission delay between satellites and the ground network but also effectively save the service data transmission bandwidth between the satellite-based links. In this network, there are a set of satellites over the geographic area providing network and computation services, denoted as \(N=\{1,\ldots,N\}\). The set of user devices is given by \(M=\{1,\ldots,M\}\). The users can connect to the satellites and apply for resources from the edge servers in the satellites to support their computing demands, instead of the traditional cloud computing server. In this paper, a multi-round auction model is proposed to depict the service relationships between the users and the satellites. The satellites with edge computing servers are considered as the sellers, and the users are the buyers.  
In offshore applications, each user is assumed to have unique service requirements; thus, the tasks executed by the satellites are different. A tuple \(\{D_{m},O_{m},F_{m},V_{m},T_{m}\}\) is used to denote the tasks of user \(m\), where \(D_{m}\) denotes the data size, \(V_{m}\) denotes the number of cycles required to compute 1-bit data of the task, \(F_{m}\) denotes the clock frequency,  
Figure 1: System model.  
denotes the processing results, and \(T_{m}\) denotes the maximum tolerated delay. We use the tuple \(\{H_{n},L_{n},C_{n}\}\) to denote the resources of satellite \(n\), where \(H_{n}\) denotes the cache size, \(L_{n}\) denotes the maximum number of served users, and \(C_{n}\) denotes the computational capacity.