Stochastic Modeling and Metaheuristic Optimization of Priority Retrial G-queue under Working Breakdown

The objective of this research is to investigate a novel retrial G-queue with one server. The concepts of preemptive priority, partial breakdown (working breakdown), feedback, and semi-active vacation (working vacation) are taken into consideration. There are two categories of consumers, which include priority consumers and ordinary consumers. Priority customers receive service before ordinary customers according to a non-preemptive priority discipline. Whenever the orbit becomes empty at the moment of service accomplishment for priority and ordinary consumers, the server takes several semi-active vacations. Firstly, the probability-generating functions for the framework/orbit by employing the supplementary variable approach have been deduced. Afterwards, several pertinent system performance metrics, viz., queue length and system size are addressed. Additionally, for the comparative analysis of optimal cost, we have employed the direct search method (DSM), particle swarm optimization (PSO), and teaching-learning-based optimization (TLBO). Convergence of various techniques is presented through graphs and finally various numerical instances have been given.