Modeling and optimization of service systems under uncertainty: A fuzzy queueing approach with hybrid machine learning

The inherent imprecision and variability prevalent in real-world complex operational systems, such as multi-component machining, often render traditional crisp queueing models inadequate for accurate performance analysis and optimization. This paper introduces a fuzzy FM/FM/c/M queueing model to address this limitation, integrating critical features like K-variant vacations, waiting servers, catastrophic events, and customer impatience (state-dependent balking and reneging). Central to our approach is the utilization of trapezoidal fuzzy numbers to represent crucial system parameters, thereby offering a more robust and precise representation of system dynamics. We utilize parametric nonlinear programming (P-NLP) coupled with α-cut analysis to derive interval-valued fuzzy performance metrics. Efficient solutions for these P-NLP problems, particularly for cost optimization, are obtained through the application of the hybrid random forest–particle swarm optimization (RF-PSO) method, and the standard PSO algorithm. Numerical illustrations demonstrate the model’s practical utility in visualizing parameter effects on performance indices through sensitivity analysis and solving the associated cost optimization problem.