Analytical modeling and performance optimization of an admission–retrial queue with two-mode vacation process using ANFIS–PSO

This study investigates a new approach: an admission–retrial queue that incorporates the original queue and an orbit queue with a two-mode vacation process (working vacation and complete vacation) in the M/G/1 queuing model. The mathematical framework, consisting of steady-state equations, is formulated and solved using the supplementary variable technique and the probability generating function for the proposed model. The performance metrics, including system and queue lengths and waiting time, are evaluated. The computational outcomes, including tables and graphs of the calculated results, are presented using MATLAB. The cost structure for finding the optimal cost is analyzed using the particle Swarm optimization technique. Furthermore, the adaptive neuro-fuzzy inference system is used to validate the numerical results. The way to balance the speed and stability of the system and to optimize the resource area in Stock Market Trading Servers and virtual call centers using this model is discussed briefly in the practical implications.