# SLLB-DEVS: An Approach for DEVS Based Modeling of Semiconductor Lithography Load Balance
## 3 Results and Discussion  
### The Default DEVS Model Simulation  
Figure 6 is a graph illustrating how the TAT changes based on the number of cores (computation nodes) in an input interval of 3 h. This is consistent with the default (FIFO) policy, with a TAT of 3 to 4 h in a cluster of 500 cores. However, in the proposed policy, the TAT continues to increase in clusters of 500 cores. This means that the number of computation nodes is insufficient compared to the requested operation. If the same experiment is repeated by increasing the number of cores to 1000 in the proposed policy, it satisfies a TAT of 3 to 4 h with a default policy cluster of 500 cores.  
The 1.5-h graph in Figure 7 shows how the TAT changes based on the number of cores (computation nodes) in the input interval. In the default (FIFO) policy, the TAT continues to increase in cluster sizes of 1000, 1500, and 2000. This indicates that the default policy never achieves the target TAT in the 1.5-h input interval environment even if the cluster size is extended. In other words, TAT requirements that cannot be achieved with the existing FIFO policy can be achieved by expanding the cluster size. As shown in Figure 7, it was confirmed through the simulation that the policy that satisfies the TAT varies based on the cluster size and the input interval. Therefore, it is necessary to verify how the maximum input interval that satisfies the TAT changes based on the number of cores and the load balancing policies.  
Figure 5: The DEVS-based simulator for multiple inputs.  
The graph in Figure 8 illustrates the minimum input interval that the existing load balancer (default) and the newly proposed load balancer (proposed) can handle in an environment that satisfies the TAT when the number of cores increases. For the default policy, compared to the proposed policy, the input interval is relatively short, with an approximate duration of 0.5 h in a 500-core environment. This is because the E-beam cluster has 600 saturation core points. Therefore, if the number of cores is less than 600, it is optimal to use as many cores as possible as the default policy. However, when the number of cores increases, the default policy unnecessarily allocates more than 600 cores, which is the saturation core point. As a result, the input interval does not improve, and the input interval that can be processed by the cluster converges to 2.2 h. Conversely, the proposed policy allocates an appropriate core in order to consider the saturation core point and the project deadline. Therefore, as the number of cores increases, the E-beam job can be calculated much more effectively. As a result, the input interval that can be processed by the individual cluster decreases.  
Figure 6: The 3-h input interval TAT graph  
Figure 7: The 1.5-h input interval TAT graph.  
The hybrid policy is applied to both of the above characteristics. In clusters smaller than the saturation core point, the default policy is used. In clusters larger than the saturation core point, the proposed policy is modeled. The results in Figure 8 demonstrate that proposed load balancing model operates with a minimum input interval for the entire cluster size. When configuring an E-beam cluster for computation lithography, FIFO-type load balancing should be used in clusters with a size smaller than the saturation core point. When the size of the cluster is larger than the saturation core point, cost optimization can be achieved by using the proposed type of load balancing, which is modeled based on the saturation core.