Nonlinear metaheuristic cost optimization and ANFIS computing of feedback retrial queue with two dependent phases of service under Bernoulli working vacation

Today, with real-life problems, modeling is a primary step in organizing, analyzing and optimizing them. Queueing theory is a particular approach used to model this category of issues. Space constraints, feedback, service dependency, etc. are often inseparable from the issues they create. In light of this objective, this research presents a model and analysis of the steady-state behavior of an M/G/1 feedback retrial queue with two dependent phases of service under a Bernoulli vacation policy. The service times for the two stages are often independent in normal queueing frameworks. We presume that they are dependent random variables in this case. Indeed, this dependence is one-way (i.e., the service time of the second phase has no effect on the service time of the first phase). Yet, the first phase service time has an impact on the second phase service time. In order to determine the steady-state probabilities and probability-generating functions (PGF) for the different states, the supplementary variable technique (SVT) was utilized. Furthermore, a broad range of performance metrics had been established. The generated metrics are then envisioned and validated with the aid of graphs and tables. Additionally, a nonlinear cost function is constructed, which is subsequently minimized by distinct approaches like particle swarm optimization (PSO), artificial bee colony (ABC) and genetic algorithm (GA). Furthermore, we used certain figures to examine the convergence of these optimization methods. Finally, validation outcomes are compared with neuro-fuzzy results generated with the "adaptive neuro-fuzzy inference system" (ANFIS).