## 5 Experiment Results
### Evaluation Metrics  
In this study, to comprehensively evaluate the performance of the proposed algorithm for task scheduling and resource management in STIN, we have selected the following four evaluation metrics: global objective function value, resource utilization rate, algorithm running time, and average task delay. The rationale and calculation methods for each evaluation metric are detailed below, referencing the variables defined in the Problem Definition and Formulation section.  
The global objective function value is the primary metric for assessing the overall performance of the system. It is defined in Equation (12), which integrates both task transmission delay and resource consumption, aiming to minimize the overall system delay while maximizing the effective utilization of resources. Optimizing \(f_{\text{global}}(\mathbf{X})\) ensures efficient task scheduling and optimal resource management, thereby enhancing system performance in dynamic network environments.  
Resource utilization rate \(R\) measures the efficiency of computational, storage, and bandwidth resource usage within the system. It is calculated as follows:  
\[R=\frac{\sum_{i=1}^{N}\sum_{j=1}^{M}X_{ij}(t_{j}^{s}+t_{j}^{s}+t_{j}^{b})}{ \sum_{i=1}^{N}(c_{i}+s_{i}+b_{i})} \tag{43}\]  
where \(t_{j}^{s}\), \(t_{j}^{s}\), and \(t_{j}^{b}\) represent the computational, storage, and bandwidth requirements of task \(j\), while \(c_{i}\), \(s_{i}\), and \(b_{i}\) are the respective resource capacities of node \(i\).  
The resource utilization rate quantifies the proportion of allocated resources relative to the available resources. A high resource utilization rate indicates that the system effectively leverages its existing resources, minimizing waste and enhancing overall operational efficiency. This metric is particularly crucial in the resource-constrained and dynamically changing environment of satellite networks, where optimal resource allocation is essential for maintaining system performance.  
Algorithm running time is a critical metric for assessing the efficiency of the proposed task scheduling and resource management algorithm. This metric directly reflects the computational time required by the algorithm to solve the scheduling and resource allocation problem. In the context of STIN, where the network is dynamic and potentially large-scale, the running time of the algorithm significantly impacts the responsiveness and overall performance of task scheduling. Therefore, minimizing the algorithm running time is a key objective to ensure timely task processing and maintain system efficiency.  
Average task delay \(D\) evaluates the mean time required to complete all tasks within the system. It is calculated using the following formula:  
\[D=\frac{\sum_{i=1}^{N}\sum_{j=1}^{M}d_{ij}X_{ij}}{M} \tag{44}\]  
where \(d_{ij}\) denotes the delay associated with transmitting task \(j\) from node \(i\), \(X_{ij}\) is the task assignment matrix, and \(M\) is the total number of tasks.  
The average task delay provides insight into the system's responsiveness and efficiency in handling task processing. Lower average delays indicate that tasks are being processed and completed more swiftly, which enhance user experience and ensure the reliability of the system. In STIN, timely task completion is vital for maintaining service quality and system dependability, making the optimization of average task delay a significant evaluation objective.