@article{article_1637390, title={Matrix-geometric analysis of heterogeneous server queueing systems with multiple working vacations: Comparison with ANFIS}, journal={Hacettepe Journal of Mathematics and Statistics}, volume={54}, pages={1954–1975}, year={2025}, DOI={10.15672/hujms.1637390}, author={P, Indumathi and K, Karthikeyan}, keywords={ANFIS, balking, cost analysis, feedback, heterogeneous servers, matrix geometric method, stability condition, working vacation}, abstract={This study investigates a Markovian queueing system in which server 2 operates under multiple working vacations and is subject to service-time breakdowns. Server 1 remains continuously available and provides service at a normal rate (\(\omega_1\)). Both servers adjust their service rates to manage an infinite queue of customers. The intermittent availability of server 2, which provides service at rate \(\omega_2\) during regular working periods, affects the overall performance of the system. Customers join the system with probability \(\beta\) when at least one server is available; otherwise, they leave with probability \(\overline{\beta}\). After receiving service, customers leave the system with probability \(\eta\) or return to the queue for another service attempt with probability \(1 - \eta\). The matrix-geometric method is employed to perform steady-state analysis and derive stability conditions. A cost analysis is also performed to optimize system expenditure and improve resource utilization. The computational results demonstrate the impact of various system parameters on performance metrics. Additionally, a soft computing-based Adaptive Neuro-Fuzzy Inference System is used to validate the analytical findings.}, number={5}, publisher={Hacettepe University}