# Fuzzy-Based Control System for Solar-Powered Bulk Service Queueing Model with Vacation
## 4 Results and Discussion
### Comparison with Baseline Model  
To validate the effectiveness of the proposed Fuzzy-Based Control System, we conducted a comparative analysis against a traditional baseline model without fuzzy logic. In the baseline model, parameters such as service rate, vacation duration, and bulk size were fixed and not dynamically adjusted in response to system conditions. The following table summarizes the performance under identical input conditions:  
As shown, the fuzzy-based model significantly outperforms the baseline across all key performance metrics. The adaptive control enabled by fuzzy logic results in shorter waiting times, more stable queues, better energy efficiency (critical in solar-powered settings), and lower overall operational costs (Figure 10).  
\begin{table}
\begin{tabular}{p{85.4 pt} p{113.8 pt} p{113.8 pt} p{113.8 pt}} \hline \hline
**Criteria** & **Mamdani FIS** & **Sugeno FIS** & **ANFIS (Adaptive Neuro-Fuzzy Inference System)** \\ \hline \multirow{3}{*}{Output Type} & Fuzzy output (e.g., “Power Efficiency is High”), defuzzified to crisp value & Crisp numerical output (e.g., power = 0.8 \(\times\) irradiance + 0.1 \(\times\) battery level) & Learned crisp output through training (e.g., optimized energy output prediction) \\ \hline \multirow{3}{*}{Rule Interpretability} & High—easily understandable (e.g., If solar is high and battery is low, then efficiency is moderate) & Moderate—output is functional, less linguistic & Low—rules and MF relationships are hidden in trained weights \\ \hline \multirow{3}{*}{Handling Expert Knowledge} & Strong—allows direct embedding of expert-defined rules & Medium—rule structure still exists but outputs are numerical functions & Weak—relies heavily on historical data instead of expert rules \\ \hline \multirow{3}{*}{Computation Complexity} & Moderate—defuzzification adds some cost & Low—fast due to direct function-based outputs & High—training requires extensive computation, though the inference is faster \\ \hline \multirow{3}{*}{Data Requirement} & Low—can operate solely on expert knowledge & Medium—can be tuned with some data & High—requires large dataset for training \\ \hline Adaptability to Environment & Low—static rules unless manually updated & Moderate—can include adaptive output functions & High—adapts to changing solar/weather/load conditions dynamically \\ \hline \multirow{3}{*}{Use Case in Solar System} & Rule-based controller for optimizing panel angle, switching bulk service modes, and managing battery usage based on real-time irradiance & Fast-response controller for continuous power regulation and inverter control & Predictive controller for output forecasting, MPPT (maximum power point tracking), and fault detection \\ \hline \multirow{3}{*}{Defuzzification Needed} & Yes—commonly using the Centroid Method & No—output is already in crisp form & No—defuzzification is embedded in the training process \\ \hline \multirow{3}{*}{Suitability for Your Work} & Used for decision logic in queue-vacation model powered by solar & Not applied, but suitable for real-time service adjustment & Planned for the future; ideal for adaptive solar service control with historical data \\ \hline \hline \end{tabular}
\end{table}
Table 6: Comparative Evaluation of Mamdani, Sugeno, and ANFIS.  
These improvements confirm that integrating fuzzy inference allows the system to respond more effectively to dynamic conditions, validating the advantage of the proposed approach over static, rule-based control models.