## 3 SATLD for MGSS Considering Waiting Time
Output: A solution \(\mathcal{S}\) that includes the number of the ground station and the specific start time for each request, a total waiting time for all request \(R^{\prime}\gets sort\_By\_tArrival(R)\); \(\mathcal{S}\leftarrow\emptyset\); \(satisfiedNumber\gets 0\); waitingTime\(\leftarrow\) 0; for\(r\) in \(R^{\prime}\)do \(A^{\prime}\gets sort\_by\_tBeg(A)\); \(\mathcal{A}\gets chooseAccessWindowSet(A^{\prime})\); for\(a\) in \(\mathcal{A}\)do if(a meets the requirements of \(r\))then \(satisfiedNumber+=1\); if\(tArrival_{r}\leq ST(a)\)then \(g,y_{r}\gets gs_{a},ST(a)\);  end if else \(g,y_{r}\gets gs_{a},tArrival_{r}\);  end if \(A^{\prime}\gets update(A^{\prime},a,r,g,y_{r})\); \(\mathcal{S}\leftarrow(g,y_{r})\); break ;  end for  end for \(waitingTime\gets update(waitingTime)\)
```  
**Algorithm 2**The Algorithm Algorithm with Tabu List and Start Time Decision  
### Simulated Annealing Algorithm with Tabu List and Start Time Decision  
As shown in Algorithm 4, we propose a two-stage optimization algorithm based on simulated annealing and tabu list to solve RC-HVRPTW. The first stage is to use SA and TL to explore. This stage mainly solves the optimization problem caused by the simultaneous existence of access windows between satellites and multiple ground stations. A ground station is allocated for each downlink request through SA and TL. Additionally, then, the RC-HVRPTW can be decomposed into a single ground station scheduling problem. In the single ground station downlink scheduling, what needs to be determined is the specific start time of each downlink request. The purpose of downlink planning is to ensure that the downlink requirements are met while reducing the total wait time for each request. Therefore, downlink requests need to be scheduled as early as possible within the window time that the task can be executed. On the basis of the method in the Section 3.1, two methods for solving the exact start time are proposed. Each solution generated by SA uses FCFS-based and SJF-based to determine its specific start time. ```
Input: Downlink request set \(R\), Ground station set \(G\), Satellite set \(S\), Access window set \(A\). Output: A solution \(\mathcal{S}\) that includes the number of the ground station and the specific start time for each request, a total waiting time for all request \(R^{\prime}\gets sort\_By\_tArrival(R)\); \(\mathcal{S}\leftarrow\emptyset\); \(satisfiedNumber\gets 0\); waitingTime\(\leftarrow\) 0; for\(r\) in \(R^{\prime}\)do \(A^{\prime}\gets sort\_by\_tBeg(A)\); \(\mathcal{A}\gets chooseAccessWindowSet(A^{\prime})\); for\(a\) in \(\mathcal{A}\)do if(a meets the requirements of \(r\))then \(satisfiedNumber+=1\); if\(tArrival_{r}\leq ST(a)\)then \(g,y_{r}\gets gs_{a},ST(a)\);  end if else \(g,y_{r}\gets gs_{a},tArrival_{r}\);  end if \(A^{\prime}\gets update(A^{\prime},a,r,g,y_{r})\); \(\mathcal{S}\leftarrow(g,y_{r})\); break ;  end for  end for \(waitingTime\gets update(waitingTime)\)
```  
**Algorithm 3**The Algorithm Algorithm with Tabu List and Start Time Decision  
### Simulated Annealing Algorithm with Tabu List and Start Time Decision  
As shown in Algorithm 4, we propose a two-stage optimization algorithm based on simulated annealing and tabu list to solve RC-HVRPTW. The first stage is to use SA and TL to explore. This stage mainly solves the optimization problem caused by the simultaneous existence of access windows between satellites and multiple ground stations. A ground station is allocated for each downlink request through SA and TL. Additionally, then, the RC-HVRPTW can be decomposed into a single ground station scheduling problem. In the single ground station downlink scheduling, what needs to be determined is the specific start time of each downlink request. The purpose of downlink planning is to ensure that the downlink requirements are met while reducing the total wait time for each request. Therefore, downlink requests need to be scheduled as early as possible within the window time that the task can be executed.