Adaptive neuro-fuzzy inference system implementation in dual orbits retrial queue with Bi-level vacation policy

The study aims to analyze the performance and cost optimization of an M/G/1 retrial queueing system with dual orbits (regular and superior), focusing on scenarios where the server follows a working vacation with a complete vacation. Customers join either the regular or the superior orbit based on their purpose. Once all customers are served and the orbits are clear, the server takes a working vacation, followed by a complete vacation. The study employs the supplementary variable technique and probability generating function to derive and solve the steady-state equations. The practical utility of two different orbit types is explored in contexts such as virtual call centers and magnetic resonance imaging scan centers, aiming to improve resource allocation and reduce waiting times. Numerical results and graphs are generated using MATLAB. Cost optimization is conducted to determine the minimum cost of the model, and the Adaptive Neuro-Fuzzy Inference System verifies the numerical examples.