Meta heuristic optimization of a batch arrival retrial queue with optional re-service and M-optional vacations

Queueing systems (QS) are essential for modelling and optimising a wide range of real-world scenarios because they effectively control the flow of entities through a system where there are queues. Addressing this, proposed QS comprises with batch arrival, retrial policy, optional re-service, and M-optional vacation alongside breakdown situations. The dynamics of the system are thoroughly investigated by utilizing the supplementary variable technique, which enables greater understanding of the system’s behaviour and performance. Furthermore, Adaptive Neuro-Fuzzy Inference System computation is used to properly validate the analytical results, improving the precision and dependability of the model’s predictions. Finally, in an effort to minimize operating efficiency, a variety of advanced cost optimization approaches have been employed to determine the system’s ideal cost structure. As a result, through this integrated approach, the proposed QS not only furnishes perceptions into operational dynamics but also furnishes practical methods to reduce costs and authenticate analytical conclusions, thereby enhancing queueing theory progressions and realistic applications across diverse fields.