# Fuzzy-Based Control System for Solar-Powered Bulk Service Queueing Model with Vacation
## 2 Literature Review  
[PERSON] and [PERSON] [1] developed a fuzzy logic controller that utilized linguistic rules, demonstrating its effectiveness in automated decision-making processes. In the healthcare domain, [PERSON] and [PERSON] [2] applied queueing models to enhance patient flow and resource allocation, highlighting the importance of service optimization. Further advancements in queueing theory were made by [PERSON] et al. [3], who analyzed a batch arrival two-phase M\({}^{\circ}\)/M\(//\)1 queueing system with impatient customers and an unreliable server, addressing key challenges in service reliability. Additionally, [PERSON] et al. [4] applied a fuzzy multi-criteria approach to evaluate green suppliers' performance, show-casing the effectiveness of fuzzy logic in complex decision-making scenarios. Collectively, these studies emphasize the integration of fuzzy logic and queueing models in enhancing service quality, reliability, and efficiency, making them particularly relevant for optimizing 4G/5G network performance. [PERSON] [5] introduced the foundational concept of fuzzy sets, providing a mathematical framework to model uncertainty and vagueness in complex systems. This pioneering work laid the groundwork for fuzzy logic applications in control systems, decision-making, and queuing models. [PERSON] and [PERSON] [6] focused on theoretical advancements by developing Fuzzy Inference Systems that preserve Moser-Navara axioms, ensuring consistency and reliability in fuzzy reasoning. [PERSON] et al. [7] extended fuzzy control applications by proposing an observer-based fuzzy adaptive predefined time control for uncertain nonlinear systems, addressing full-state error constraints and improving control accuracy under uncertainty. [PERSON] and [PERSON] [8] explored the integration of fuzzy logic with neural networks and sliding mode control, developing a hybrid neuro-fuzzy integral sliding mode control technique for optimizing Unified Power Quality Conditioners (UPQCs) in solar energy systems. Collectively, these studies demonstrate the growing sophistication of fuzzy logic applications in control systems, energy management, and nonlinear system modeling, further strengthening its relevance in optimizing complex and uncertain environments, including 4G/5G network management. Fuzzy logic has evolved significantly since its inception, with various studies contributing to its theoretical advancements and practical applications. [PERSON] [9] pioneered the application of fuzzy algorithms for controlling dynamic systems, laying the foundation for modern fuzzy control techniques. [PERSON] and [PERSON] [10] further advanced the field by introducing a fuzzy identification approach for system modeling and control, which has since become a fundamental method in fuzzy system design. Fuzzy logic has been widely explored in various applications, ranging from signal processing to renewable energy prediction and advanced control systems. [PERSON] and [PERSON] [11] introduced a fuzzy logic-based method for modulation classification in non-ideal environments, demonstrating its effectiveness in handling uncertainty in communication systems. [PERSON] and [PERSON] [12] applied fuzzy rule-based modeling for predicting daily solar radiation, highlighting the adaptability of fuzzy logic in renewable energy forecasting. Similarly, [PERSON] and [PERSON] [13] utilized high-order statistical modeling for solar data analysis, emphasizing the need for advanced mathematical techniques in energy-related predictions. [PERSON] et al. [14] provided a broad perspective on fuzzy systems and control, discussing their theoretical developments and practical implications in various fields, including automation and decision-making. [PERSON] [15] extended the concept of fuzzy sets by introducing possibility theory, further expanding the scope of fuzzy logic in uncertainty modeling and reasoning.