# Application and Performance Evaluation of Resource Pool Architecture in Satellite Edge Computing
## 3 Proposed Architecture
### Satellite Node Selection
#### 3.3.4 Planning Objectives  
The response time of tasks is critical for users, especially in situations where real-time requirements are high. Waiting for the response for a long time will lose users, and there will be great losses in major cases such as natural disasters. According to the above description, for the task-oriented resource pool node selection, this paper focuses on the goal of minimizing the average response time of the task and maximizing the resource load balance of the node (that is, minimizing the \(d\)), which are modelled by (15) and (16), respectively. \(K\) is the number of tasks. \[U_{1}=\min\int_{t_{0}}^{T}{\sum\limits_{1}^{K}{T_{i}}}\Bigg{/}K \tag{15}\]  
\[U_{2}=\min(\sum\limits_{1}^{M}{d_{i}}\Bigg{/}M) \tag{16}\]  
There are many research constraints for satellites to complete tasks submitted by ground users. First, the resources required by the task shall not exceed those owned by the satellite. Expressed as follows:  
\[ \begin{array}{l}\sum\limits_{1}^{K_{i}}{R_{S_{i,k}}^{cpu}}\leq{R_{S_{i}}^{cpu }};\\ \sum\limits_{1}^{K_{i}}{R_{S_{i,k}}^{mem}}\leq{R_{S_{i}}^{mem}};\end{array}  \tag{17}\]  
where \(R_{S_{i}}^{cpu}\), \(R_{S_{i}}^{mem}\) represent computing and storage resources of the satellite \(i\), respectively. This means that the total computing and storage resources occupied by the \(K_{i}\) tasks executed on each satellite cannot exceed the resources owned by that satellite. It is assumed that \(n_{k}\) is a time slot. For the completion of a specific task, a responsive sensor of the corresponding satellite is required. Although satellites can reconfigure their software, they cannot perform tasks without corresponding hardware support. Therefore, the following constraints shall be met:  
\[R_{s_{i,k}}^{sen}(n_{k})\cap R_{S_{i}}^{sen}\
eq\varnothing \tag{18}\]  
The \(R_{s_{i,k}}^{sen}(n_{k})\) indicates that in time slot \(n_{k}\), the sensor occupied by task \(k\) on satellite \(i\) is consistent with the sensor of satellite \(i\). Service performances are constrained by the resolution, field angle, and orbital space position of the sensor. In this paper, only orbital factor is considered. The field angle of the sensor is taken as a fixed parameter, and the initial angle of the sensor is temporarily ignored. It is uniformly set to be aligned with the geocentric. Visibility is constrained by (3) and (4). When considering communication constraints, communication must first satisfy the visibility between satellite and ground and between the satellites. Communication resources then need to consider the number of satellite links and communication bandwidth. It is expressed as follows:  
\[\sum\limits_{i=1}^{N}{\sum\limits_{j=1}^{N}{(Link_{n_{k}}^{S_{ij}})}}\leq ck _{com} \tag{19}\]\[\sum_{i=1}^{N}\left(Link_{n_{k}}^{S_{ij}}\right)\leq\min\Bigl{\{}\text{B}_{S_{i} }^{band},\text{B}_{S_{j}}^{band}\Bigr{\}} \tag{20}\]  
The \(Link_{n_{k}}^{S_{ij}}\) is the connection link relationship between satellite \(i\) and satellite \(j\) during the time period \(n_{k}\). A value of one means that the two satellites establish an inter- satellite link. If it is zero, there is no communication. \(ck_{com}\) is the number of communication channels of the satellite, which limits the number of links that the satellite can establish. \(\text{B}_{S_{i}}^{band}\) is the communication bandwidth of the satellite \(i\). The total bandwidth used in the time slot of task execution cannot exceed the total bandwidth of the satellite. Synchronization constraints are largely limited to a resource conflict with observation and other attributes in the task to avoid resource waste or shortage. For example, the navigation function needs at least four satellites, and some remote sensing tasks need multiple coverage to meet the accuracy requirements of the service.