# SLLB-DEVS: An Approach for DEVS Based Modeling of Semiconductor Lithography Load Balance
## 2 Methodology
### Load Balancer Policy
#### 2.2.2 The Mission Time Policy  
When allocating the computation node to the E-beam job based on the saturation core point, the operation completes as quickly as possible regardless of the characteristics of the E-beam job. However, this is an optimal model from a performance standpoint. From the standpoint of costs, there is a possibility of over-specification beyond the user's requirements. The resource costs of hardware and software should be appropriately determined, with the costs optimized to the user's actual requirements. However, there is a high possibility that the cluster has been configured with a higher performance capacity than necessary. If the actual user's requirements for the model were not applied, it can incur unnecessary license and hardware costs. Users of exposure software in the field typically have a deadline for job completion. According to related data, the industry standard deadline is known to be 3-4 h. Assigning a computation node to the job in order to match the TAT as closely as possible to the deadline allows for the allocation of the optimal number of computation nodes for the user's requirements.  
The graph in Figure 3 shows the change of TAT in relationship to the density parameter of the E-beam data in the real system. The graph illustrates that as TAT decreases, the number of cores increases. On the other hand, TAT is maintained above 600 cores, which indicates that the appropriate saturation core point of E-beam data is 600. In addition, the TAT increases proportionally to the density in a specific number of core sections. Therefore, the TAT can be modeled as a function determined by the number and density of cores. Regardless of the density, the graph shows a logarithmic trend based on the number of cores. This indicates that density and core number can be modeled as independent variables for the TAT. Core and density can be modeled mathematically as follows, using the above-described graphical characteristics.  
An empirical model of the TAT's mathematical model and real data yields a high correlation of 0.9982 on average. Therefore, in this model, the TAT formula model was used instead of the empirical model in order to improve the simulation time. The density and the TAT can be determined by the E-beam's input and the user's requirements, which  
Figure 3: The TAT based on density which represents the change of Turnaround time for the E-Beam data density parameter in the real system.  
allows for an appropriate number of computation nodes to be obtained. The obtained number of nodes can be applied to load balancing. Equations (1) and (2) below are the empirical model equations, which are based on experimental data [5].  
The core model equation.  
\[\begin{array}{l}11.1\times e^{-0.00378\times core}\quad(core\leq 400)\\ 5.45\times e^{-0.00177\times core}\quad(core\leq 600)\\ 5.45\times e^{-1.602}\quad(core>600)\\ \end{array} \tag{1}\]  
The density model equation:  
\[0.000633\times Density^{2}+0.0225\times Density+0.804 \tag{2}\]  
The TAT model equation:  
\[Core\ Model(core)\times Density\ Model(density) \tag{3}\]