Customer Returns to Any Server up to Finite Times in a Four-Server Feedback Queueing Model: An Analysis of Waiting Times in Each Queue

Abstract

This work presents a feedback queueing model that takes into account four servers, one of which is centrally connected to the other three. Customers can access the system only on the first server, after which they can proceed to the second, third, or fourth server. The customer may return to the previously visited server a limited number of times if the service does not meet their demands. It is believed that the likelihood of returning to the servers varies with each visit. Customers' waiting times in each queue have been determined using Little's law.

variations in each queue's customers waiting times have been determined using both graphical and numerical techniques.