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 (ω1). Both servers adjust their service rates to manage an infinite queue of customers. The intermittent availability of server 2, which provides service at rate ω2 during regular working periods, affects the overall performance of the system. Customers join the system with probability β when at least one server is available; otherwise, they leave with probability β. After receiving service, customers leave the system with probability η or return to the queue for another service attempt with probability 1 − η. 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.
Indumathi et al. (Fri,) studied this question.
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