This work investigates the M/M/1/L queueing model within real-life scenarios, highlighting its substantial impact on various domains such as call centers, distributed computing systems, healthcare facilities, traffic management centers, and other service-oriented operations. It focuses on the finite capacity queueing model with general vacations and customer discouragement under the F-policy. Additionally, we consider essential queueing features that account for customers’ behaviors, such as balking and reneging. When customers encounter long queues, they may experience discouragement and consequently choose not to join the queue or leave without receiving service. Implementation of the ‘F-policy’ is an effective strategy for the admission of customers into the system to reduce congestion resulting from excessive customer arrivals. Further, the server chooses to take a vacation when no customer is present in the system. The vacation time is not exponentially distributed; instead, we consider the general case of vacation time for a more comprehensive analysis. The mathematical development of the M/M/1/L queueing model is carried out using the Chapman-Kolmogorov steady-state equations by introducing supplementary variables corresponding to remaining vacation times. Subsequently, the Laplace-Stieltjes transform and recursive method are employed to solve these equations and establish probability distributions. Further, various performance metrics, such as the number of customers in the system, throughput, customer loss, long-run probabilities, etc., are derived. These performance measures will assist system organizers in making informed decision-making strategies. A numerical example is also presented, illustrating the impact of input parameters and customers’ discouraged behavior on various performance metrics. The adaptive neuro-fuzzy inference system, which is built on an artificial neural network and a support vector regression, a machine learning technique, is employed to validate the numerical results. Moreover, the nonlinear cost function is formulated with the service and vacation rates as decision variables. The cost is minimized using quasi-Newton methods and several metaheuristics (particle swarm optimization, bat algorithm, and differential evolution variants). These algorithms are utilized to compare the optimal values of the cost function. The queueing model’s practical application is demonstrated through its implementation in fog computing systems.
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