Particle Swarm Optimization of a Single Server Retrial Queue with Delayed Repair Under Working Vacation From Optional Service to Re-Service

Queueing systems (QS) play a critical role in modeling and optimizing various real-world processes by managing the flow of entities within systems involving queues. To address this, the proposed QS integrates features such as single arrivals, a retrial mechanism, optional re-service, working vacations, and delay repair scenarios. The system's dynamics are comprehensively analyzed using the supplementary variable technique, which provides deeper insights into its behavior and performance metrics. Furthermore, to enhance operational efficiency, an advanced cost optimization technique is employed to identify the optimal cost structure for the system. This holistic approach not only sheds light on the operational intricacies of the QS but also offers practical strategies for cost reduction and validation of analytical findings, thereby advancing queueing theory and broadening its practical applications across multiple domains.