The Expected Average Queue Length of a Feedback Queue System with Four Servers Arranged Hierarchically and A Limit on the Number of Times a Customer Can Return to Any One of the Servers

Abstract

The investigation of a feedback queueing system's mean queue length is the focus of this work. Four servers are arranged hierarchically in the Queuing system to serve customers. Depending on their needs, a customer who has received service from the first server moves on to the second, third, or fourth server. She or he may return, but only a certain number of times.
It is assumed that the arrival and service patterns adhere to the Poisson process. In order to find the system's Mean Queue Length, the steady state equations were solved using the generating function technique.