# Fog Computing Architecture for Load Balancing in Parallel Production with a Distributed MES
## 4 Analysis of Results
The arrangement shown above presents an unusual feature in terms of the manufacture of Part A in MPS1, as it was intentionally designed to exceed the manufacturing process of Part A in MPS2 by 40% in terms of time and 50% in terms of energy consumption, in order to validate the implemented algorithm. On the other hand, delving deeper into the sensitivity of the algorithm reveals that its heuristic threshold is initially set at 1.3, which determines whether the cost difference between MPS1 and MPS2 is significant enough to justify reassignment. If the higher cost does not exceed the lower cost by 1.3 times, then the MPS with the lowest accumulated load is prioritized. With this background, and with the heuristic limit at 1.3, the values of \(\alpha\) and \(\beta\) impact the costs of each MPS, but there are no significant changes in order allocation, as the differences between costs remain within the threshold. This suggests that the heuristic serves as a regulator, mitigating fluctuations. In contrast, when there is no tolerance with the heuristic limit at one, the same values of \(\alpha\) and \(\beta\) do generate significant redistribution among the MPSs since minor differences in costs are sufficient to create changes. In the case where time weighting is prioritized over energy (\(\alpha=1\) and \(\beta=2\)), costs skyrocket in MPS1, but the algorithm continues to assign balanced orders when the threshold of 1.3 is maintained. Conversely, when the threshold is reduced to one, the algorithm's behavior becomes highly sensitive, with even minor differences leading to a reorientation of the assignment towards the cheapest MPS in relative terms. Table 4 summarizes the findings of the sensitivity analysis of the hybrid ILP-heuristic algorithm when assigning different configurations of \(\alpha\) and \(\beta\), and a different heuristic threshold. On the other hand, Section 3.2 discusses the processes executed by the MESs and the processing load supported by microprocessors (MPUs). However, Table 2 does not mention the time it took for the MES to execute the stock update, a process that the base study specifies caused a delay of 21 [s], indirectly indicating the possibility of reaching the thermal throttling threshold and, consequently, high %CPU consumption. Given this situation, a Coral USB TPU (edge tensor accelerator) device was integrated, designed to boost the inference speed of the YOLO V5 model, improving performance in each MES by freeing the CPU from the computational load and, consequently, significantly reducing the temperature and the time it took for the RPi 4 to update the stock to the FC node. Table 5 shows the behavior of the average performance variables of the MESs during the stock update process and other concurrent processes. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{\(\beta\)} & \multirow{2}{*}{\(\alpha\)} & **Heuristic** & **Change in** & \multirow{2}{*}{**Observations**} \\  & & **Threshold** & & **Allocation** & \\ \hline
1 & 2 & 1.3 & NO & The threshold smooths out different costs \\ \hline
1 & 2 & 1 & YES & Multiple reallocations detected \\ \hline
2 & 1 & 1.3 & NO & Costs change, but allocation remains stable \\ \hline
1 & 1 & 1 & YES & Greater sensitivity without tolerance \\ \hline \end{tabular}
\end{table} 
Table 4: Comparison of allocation under different configurations of \(\alpha\), \(\beta\), and heuristic threshold.