## 2 Methodology
### Dynamic Allocation of Satellite Resources for Emergency Scheduling
#### 2.4.2 Dynamic Scheduling of Newly Arrived Emergency Missions  
This section presents the dynamic scheduling algorithm which tries to insert newly arrived missions into the initial scheduling plan. The newly arrived missions are sorted by priority, from high to low, and scheduled one by one. The scheduling operations are applied to each new mission until one of the operations is successful. The operations are: insertion, reallocation, replacement, and deletion. The algorithm stops when all new missions are attempted to be scheduled, and an ideal dynamic mission scheduling plan is obtained by iteration according to the proposed method. The details of the scheduling operations are as follows:  
1. Initialize the parameters. The missions in the new mission set \(T^{\prime}\) are sorted from high to low according to mission priority, so that the mission with the highest priority in \(T^{\prime}\) is the current scheduling mission \(t^{\prime}\) with available satellite resource set \(S\). 2. Perform the insertion operation. This step involves traversing every available satellite resource of \(S\) for mission \(t^{\prime}\) to determine whether the visible time window of the current satellite resource \(S^{\prime}\) is available and whether there is a conflict between missions \(t^{\prime}\) and the scheduled mission in the current time window of satellite \(S^{\prime}\). If there is no conflict, the mission \(t^{\prime}\) is directly inserted into the current time window. If the new mission cannot be inserted, mission \(t\) which conflicts with mission t' is placed in the mission conflict set \(T^{\prime}\), and the process proceeds to step 3. 3. Perform the reallocation operation. This step traverses all missions in the conflict set \(T^{\prime}\) that conflict with the current mission \(t^{\prime}\), makes the first mission in the conflict set as the current conflict mission \(t\), and re-searches its available time window. If the current conflicting mission \(t\) can be moved to a new window, mission \(t^{\prime}\) is inserted into the current time window, and the conflicting mission \(t\) is moved to another time window for execution. If the current conflicting mission \(t\) cannot be moved to a new window, then the process proceeds to step 4. 4. Perform the replacement operation. This step assesses the priority of mission \(t^{\prime}\) and the current conflicting mission \(t\). If the priority of mission \(t^{\prime}\) is higher than that of mission \(t\), the current conflicting mission \(t\) is deleted, and then the new mission \(t^{\prime}\) is inserted into the visible time window; otherwise, the mission replacement is unsuccessful, and the process proceeds to step 5. 5. Perform the delete operation. When steps 2, 3 and 4 are not satisfied, the new mission \(t^{\prime}\) is deleted and the resource scheduling process is abandoned. 6. Determine whether the available satellite resources are traversed. If the available resources have been traversed, the solution corresponding to the maximum value in the evaluation set is selected as the final solution, and the scheduling of current mission \(t^{\prime}\) is completed.