# An Efficient Satellite Resource Cooperative Scheduling Method on Spatial Information Networks
## 3 Satellite Resource Scheduling Problem Formulation
### Problem Formulation  
The traditional satellite resource scheduling method solves the satellite resource scheduling plan at the ground base station and then transmits it to the satellite for execution.  
As shown in Figure 1, the network operation control center is the central hub of satellite work and the command post of ground control satellites. Its role is to send specific instructions after mission planning to the satellites. We can express the command set received by satellite in the form of a queue. If there is a visible time window between the satellite and the ground station, the ground station can receive the data sent by satellite. The satellite executes the instruction process sent by the ground station and the relationship between the satellite and the ground base station. The function \(g_{q}(t)\) represents the time cost of the satellite \(s_{i}\) to respond to a specific resource request task at a slot \(t\) and complete the resource scheduling. The function \(f_{s}(x)\) represents the time consumed to meet resource scheduling for all resource request operations received by satellite \(s\). The function \(f_{s}\big{(}g_{q}(t)\big{)}\) represents the time required for all satellite resource requests for job scheduling in a discrete time period \(T=\{1,2,\cdots,\tau\}\). To improve resource utilization and achieve efficient resource scheduling effects, we need to solve the minimum value of the function under the complex constraints in the spatial information network to reach the minimum time consumption. The model is established as Equation (1),  
\[\begin{split}&\min\sum_{t=1}^{\tau}\sum_{s=1}^{S}\sum_{q=1}^{Q}f_{s} \big{(}g_{q}(t)\big{)}\\ & s.t.\\ & C1:\sum_{t=\tau}^{\delta}c_{s}(t)\leqslant 1,\;\forall\sigma \in R*,\;\forall s\in\xi,\forall\delta<S,\\ & C2:\sum_{q}w_{q}(u,v)\leqslant c(u,v),\\ & C3:\tau\geqslant 1,\tau\in R*,S\geqslant 1,Q\geqslant 1,\\ & C4:l_{s,s^{\prime}}^{\min}\leqslant f_{s}^{\tau}(t)\leqslant l_{ s,s^{\prime}}^{\max},\end{split} \tag{1}\]  
As shown in Formula (1), \(S\) represents the satellites that have a visible time window with the ground base station during the period of \(t,t\;int\tau\). The task queue on the satellite \(s,s\in S\) is denoted as \(Q\), where the time required for the task \(q,q\in Q\) to be executed is denoted as \(f_{s}\big{(}g_{q}(t)\big{)}\). The execution time consumption of task \(q\) varies depending on the merit of the resource scheduling policy. The model (1) describes the minimum time cost to be consumed in discrete-time \(tau\) to execute the tasks on the satellite according to the resource scheduling scheme. Therefore, we need to calculate the minimum value of the function \(f_{s}\big{(}g_{q}(t)\big{)}\), where the constraint C1 indicates that each satellite can communicate with at most one object in a slot. The object includes satellites or observation targets, which is the constraint C2 of the inter-satellite link. The amount of data that needs to be transmitted is less than the maximum capacity of the transmission link established between the satellites. \(C3\) indicates the lower limit of the time range, the number of satellites, and the number of resource requests in the satellite queue. \(C4\) shows the link bandwidth constraint, \(l_{s,s^{\prime}}^{\min}\) represents the lower bandwidth limit, and \(l_{s,s^{\prime}}^{\max}\) denotes the upper limit of the link bandwidth.  
The paper considers the global resource scheduling optimization problem with a new idea, studies the global optimization problem of the satellite resource request queue, and proposes a dynamic reconstruction method of the multi-satellite coordination global resource request queue.