# SLLB-DEVS: An Approach for DEVS Based Modeling of Semiconductor Lithography Load Balance
## 3 Results and Discussion
### Multi-Input DEVS Model Simulation  
This experiment is designed to assess whether the three load balancing algorithms, the FIFO-legacy model, the FIFO_MODEL saturation point model, and the BSF saturation point and mission time-based model, satisfy the TAT condition in a multiple input model environment according to the number of cores. First, the single input model of the existing E-beam job, which was introduced in the previous section, was used. For multiple models, three types were designed using an empirical model that requires a higher TAT for higher-density work. Table 1 contains the type setting values of the actual jobs. The colors associated with the job type in Table 1 correspond to the colors in Figure 9. The experiment was conducted by changing the core from 100 to 100 units, and measuring the queuing time, the TAT, and the processing time. The graph in Figure 9 illustrates the four points, 100, 500, 1500, and 2000, where significant inflection occurred among the changes based on the number of cores. \begin{table}
\begin{tabular}{c|c c c c} \hline
**Type** & **TAT (Hours)** & **Min Density** & **Max Density** & **Count** \\ \hline JOB\_A & 3 & 5 & 30 & 100 \\ JOB\_B & 6 & 30 & 50 & 100 \\ JOB\_C & 12 & 50 & 70 & 100 \\ \hline \end{tabular}
\end{table} 
Table 1: Multiple E-beam input data table for a multi-input DEVS-based simulation. Figure 8: The minimum input interval in which the default and proposed load balancer satisfied TAT. * Core 100  
Figure 9 shows the results of the queuing time, the TAT (in hours), and the processing time by job ID in an environment of 100 cores. The slope of the TAT for each type indicates the degree of divergence of the task. The larger the slope, the greater the number of requests compared to the throughput. The below graph shows that the FIFO, the FIFO_MODEL, and the BSF had more requests compared to throughput for all types, all of which did not satisfy the TAT. * Core 500  
Figure 10 shows the results of the queuing time, the TAT (in hours), and the processing time by job ID in an environment of 500 cores. Neither the FIFO nor the FIFO_MODEL satisfied the TAT because of the large number of requests compared to the throughput. In the case of the BSF policy, the TAT was satisfied for JOB_A. JOB_B did not emit, so in the long run the throughput versus the request was balanced. However, it did not satisfy the TAT. JOB_C of the BSF tended to diverge, and the TAT was therefore also not satisfied. * Core 1500  
Figure 11 shows the results of the queuing time, the TAT (in hours), and the processing time by job ID in an environment of 1500 cores. Neither the FIFO nor the FIFO_MODEL, satisfied the TAT because of the large amount of requests compared to the throughput. Under the BSF policy, the TAT was satisfied for JOB_A. JOB_B did not emit, so in the long run, the throughput and the request were balanced. The variance value of the TAT decreased compared to the 1000-core environment. However, it was still not satisfied with the TAT. For JOB_C under the BSF policy, the number of requests compared to the throughput began to maintain balance in the long term, but the TAT was not yet satisfied. Figure 9: The experiment results in a 100-core environment. Figure 11: Experiment results in a 1500-core environment. Figure 10: Experiment results in a 500-core environment. * Core 2000  
Figure 12 shows the result of the queuing time, the TAT (in hours), and the processing time by job ID in an environment of 2000 cores. For FIFO, none of the types satisfied the TAT because of the large number of requests compared to the throughput. On the other hand, it was confirmed that the FIFO_MODEL and the BSF satisfied the TAT for all tasks. The existing legacy load balancing method, FIFO, could not effectively handle heterogeneous tasks despite the increase in the number of cores, because all computing resources are used sequentially for incoming tasks.