## 4 Simulation and Results
### Simulation Results
From the simulation perspective, since each target quantity configuration was independently simulated 100 times, the standard deviation of ASTR is relatively higher when the number of targets is small. In this case, the scheduling system has more flexibility, leading to greater variation in task execution order and resource allocation across different simulations. As the number of targets increases, the scheduling becomes more compact and constrained, reducing the differences between simulation results and thus lowering the standard deviation of ASTR. Figure 9 presents the time shift ratio for the execution of tasks associated with targets of different threat degrees. The blue and red \"+\" symbols in the figure represent the time-shifting ratio corresponding to tracking tasks with different threat levels, scheduled by the traditional method and the improved method, respectively. The horizontal axis represents the target threat degree, and the vertical axis represents the time shift ratio. In Figure 9b, the blue curve denotes the upper limit of time shift ratios for targets with varying threat levels, which corresponds to the time shifting threshold for targets of different threat degrees. As shown in Figure 9a, the traditional methods only consider the utilization of time resources during scheduling, without taking into account the situation of time shifting, resulting in a high time shift ratio for most of the scheduled tasks; In contrast, Figure 9b demonstrates that as the target threat degree increases, the maximum deviation between the actual and expected execution times of tasks gradually decreases. The time shift ratio of targets with different threat degrees is within the control range, making the actual execution time of high threat targets as close as possible to the expected execution time. Additionally, parameters \(\alpha\) and \(\beta\) can be adjusted according to specific work requirements or target tracking situations, thereby adjusting the upper limit of time shifting for tasks with different degrees of threat. Figure 8: Experimental results of task scheduling using the traditional time-pointer method and the proposed improved method. The orange curve represents the improved method, while the blue curve represents the traditional method. The error bars on the curves indicate the standard deviation obtained from 100 simulations for each target quantity. The figure contains the following subplots. (**a**) Average time shifting ratio. (**b–d**) Scheduling success rates for confirmation, search, and tracking tasks, respectively. (**e**) The proportion of successfully scheduled tasks among all requested tasks. (**f**) The proportion of high-priority tasks among the executed tasks. Figure 8b,d show the variation in the schedule success ratios of different task types as the number of targets increases, after being scheduled by the two methods. First, both methods consistently prioritize high-priority tasks, including confirmation and precise tracking. In addition, the improved method demonstrates higher scheduling success ratios for both search tasks and tracking tasks compared to the traditional method. This is attributed to the introduction of pulse interleaving in the improved method, thereby making more efficient use of the system's idle time resources and enhancing the overall schedule success ratio. Figure 8e,f illustrate that the total task schedule success ratio and hit value ratio for both methods decrease as the number of targets increases, with the improved method consistently outperforming the traditional method. The simulation results also reveal that, when the number of targets is large, the traditional method allocates most of the resources to higher-priority tasks such as confirmation and tracking, leaving fewer resources for search tasks. However, with the improved method, tracking tasks can be interleaved with other types of tasks.