# An Efficient Satellite Resource Cooperative Scheduling Method on Spatial Information Networks
## 4 Resource Request Queue Reconstruction and Collaborative Scheduling Method
### Problem Conversion  
In order to compensate for the space-time limitation and improve the timeliness of satellite resource scheduling, we propose a dynamic reconfiguration and collaborative allocation model. The model considers the dynamic changes of inter-satellite links and the cooperative allocation of multi-satellite resources in dynamic networks and aims to solve the high timeliness of multi-satellite resource scheduling on spatial information networks. In the process of spatial information network resource scheduling, we mainly consider the time consumed by satellite resources and inter-satellite link resource scheduling operations. As shown in Formula (2), the model describes the process of minimizing the time consumption incurred by allocating resources to tasks according to the resource scheduling matrix when visible links exist between satellites or between satellites and the ground station. Where \(U_{s}^{r}(t)\) represents the time cost consumption for the resource request \(r\) of satellite \(s\) to transmit unit data. \(f_{s}^{r}(t)\) denotes the resource data amount to be transmitted for a time slot \(t\) in the spatial information network for task \(r\). \(B_{s}^{r}(t)\) shows the scheduling matrix of source request task on satellite \(s\) at time \(t\), and the value range of the element \(b_{s}^{r}(t)\) in the matrix is \(\{0,1\}\). \(L_{s,s^{\prime}}(t)\) indicates the state of establishing a communication link between satellite and satellite \(s\) at time \(t\). If it is successfully established, then \(L_{s,s^{\prime}}(t)=1\), otherwise \(L_{s,s^{\prime}}(t)=0\). \(\Phi_{s}^{r}(t)\) denotes the time consumption of the task latency, payload device transition, and the start of task execution to the end of execution during different tasks operations. We need to calculate the minimum time spent in the resource scheduling process within a period. In addition, the time calculation function should be incremental, continuously differentiable, and strictly concave. Therefore, we define the time calculation function as \(\log((U_{s}^{r}(t)f_{s}^{r}(t)+E(r))B_{s}^{r}(t)L_{s,s^{\prime}}(t)+\Phi_{s}^{r }(t))\), where \(E(r)\) denotes the time consumed by task \(r\) from the start execution time to the end execution time. The incrementality of the time calculation function is manifested in that the time required for calculation should be increased with the passage of time. The concavity is that the total number of resource request operations is constant and gradually decreases with time. We can transform the original model (2) as the following model. \[\min\sum_{t=1}^{\tau}\sum_{s=1}^{S}\sum_{r=1}^{R}\log\Bigl{(}(U_{s}^ {r}(t)f_{s}^{r}(t)+E(r))B_{s}^{r}(t)L_{s,s^{\prime}}(t)+\Phi_{s}^{r}(t)\Bigr{)}\] \[s.t.\] \[\mathrm{C1}:B_{s}^{r}(t)=1,\forall t\in\{begin{array}[]{l}begin{array} []{l}begin{array}[]{l}begin,end\end{array},\\ \mathrm{C2}:L_{s,s^{\prime}}(t)=1,\forall t\in\left\{W_{s,s^{\prime}}^{start},W_ {s,s^{\prime}}^{end}\right\},\\ \mathrm{C3}:\min_{s,s^{\prime}}^{\min}\leqslant f_{s}^{r}(t)\leqslant l_{s,s^ {\prime}}^{\max},\\ \mathrm{C4}:0<u_{s}^{r}(t)\leqslant\zeta,\\ \mathrm{C5}:b_{s}^{r}(t)\in\{0,1\},\\ \mathrm{C6}:\theta_{s}(r)-\theta_{s}(r^{\prime})=\gamma,\ \gamma>0,\\ \mathrm{C7}:s^{\prime att}\in N^{*},\\ \mathrm{C8}:L_{s}^{\mathit{ant}}\in N^{*},\\ \mathrm{C9}:\sum_{v\in s}f(u,v)=0,u\
eq s_{\mathit{source}},s_{\mathit{target}},\\ \mathrm{C10}:L_{s,s^{\prime}}(t)\in\{0,1\},\end{array} \tag{2}\]  
where \(\tau\) denotes the discrete-time period and \(t,t\in\tau\) denotes the time gap. \(S\) denotes the set of satellites available within some time gap \(t\) as \(S,s,s\in S\) denotes the satellites for which some visible time window exists. \(R\) denotes the queue of missions on satellite \(s\), and \(r,r\in R\) denotes a particular mission on satellite \(s\).