## 6 Experimental Study
### The Performance of Static Scheduling  
For static scheduling, the comparison is primarily made with rule-based scheduling algorithms and deep reinforcement learning-based methods. Heuristic methods were not chosen for comparison, as the deep reinforcement learning-based methods being compared have already outperformed many heuristic methods. For ease of description, the term \begin{table}
\begin{tabular}{c c c} \hline \hline \(penalty\) & \(reward_{2}\) & **Overtime Sub-Task** \\ \hline \(\frac{1}{n^{2}}t_{avg\_resp}\) & 0.285 & 5 \\ \(\frac{1}{n}t_{avg\_resp}\) & 0.290 & 3 \\ \(\frac{1}{10}t_{avg\_resp}\) & 0.314 & 2 \\ \(t_{avg\_resp}\) & Network cannot converge & - \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Influence of the Penalty. \begin{table}
\begin{tabular}{c c c} \hline \hline \(k_{1}\) & \(reward_{1}\) & \(reward_{2}\) \\ \hline
1 & 0.413 & 0.619 \\
0.7 & 0.410 & 0.482 \\
0.5 & 0.410 & 0.345 \\
0.3 & 0.404 & 0.318 \\
0.1 & 0.394 & 0.290 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Influence of the priority function coefficients. TF-WS is used to refer to the proposed method in the following figures and tables. The methods being compared are as follows:  
* First Come, First Serve (FCFS): selects the sub-tasks that arrived first to be executed first;
* Shortest Job First (SJF): prioritizes the execution of sub-tasks with the smallest execution time;
* Highest Response Ratio Next (HRRN): considers both the waiting time and execution time of sub-tasks, and selects the task with the highest response ratio (defined as \(\frac{waitingtime+executiontime}{executiontime}\)) to be executed next;
* NeuRewriter [24]: A deep reinforcement learning method that guides local search for scheduling. It uses RL techniques to improve the search process and find better solutions;
* RLPNet [41]: A scheduler based on pointer networks and trained using RL. Although some modifications have been made to the encoder part of the network to fit our specific scenario, the overall network structure remains unchanged. The optimization objectives are used as metrics for comparison. For clarity and understanding, in the following discussions, \(reward_{1}\) will be referred to as \"Resource Utilization\" and \(reward_{2}\) as \"Response Time\". Figures 7 and 8 present the experimental results. For FCFS, the algorithm schedules sub-tasks based on their weighted waiting time as long as there are sufficient resources available. However, this algorithm does not take into account how resources are utilized or make optimal decisions regarding the order of long and short sub-task. As a result, it performs poorly in terms of both resource utilization and response time. For SJF, the algorithm prioritizes the execution of short sub-tasks over  
Figure 8: Response Time in static scheduling scenario. Figure 7: Resource Utilization in static scheduling scenario. long tasks. This effectively reduces the waiting time for short sub-tasks. However, it may lead to long waiting times for multiple long sub-tasks, and it does not demonstrate a clear advantage in terms of response time compared to FCFS. For HRRN, the algorithm considers weighted waiting time, execution time, and task priorities. It avoids situations where a single task occupies resources for a long time, causing other tasks to wait for a significant duration. As a result, HRRN performs relatively well in terms of response time compared to FCFS and SJF. NeuRewriter employs a method that trains a network to continuously swap sub-task nodes in order to achieve the best possible outcome. It functions as a search algorithm that can attain optimal results in terms of response time among all methods. The original reward function of NeuRewriter primarily focuses on average job slowdown, and a priority weight was introduced to incorporate task priorities. However, resource utilization was not specifically optimized in this method.