A Multilayer Perceptron and Cost Optimization of a Single-Server Queue with Bernoulli Feedback and Customer Impatience under a Hybrid Vacation Policy

This paper deals with a single server queueing system, aiming to handle a hybrid vacation, operating within a finite space, and taking account of Bernoulli feedback and balking, alongside reneging and retention. In case of queue emptiness, coming after a normal busy period, the single server shifts to a working vacation. The server proceeds to take a vacation in case no customers are queued upon the server's return from a working vacation. For analysis purposes, we employed a recursive method to derive the system's steady-state probabilities, thereby facilitating the evaluation of key performance metrics. The numerical results are compared with analytical results and those obtained using a soft computing technique based on a Multilayer Perceptron (MLP) system. Lastly, the Grey Wolf Optimizer is applied to identify the optimal service rates that minimize costs.