Computational Analysis of M/Er/1 Feedback Queue System

This paper studies a single-server queueing system with feedback and Erlang distributed service time. Customers arrive according to a Poisson process. Customers' service time distribution is an r-th order Erlang distribution. Customers who have completed the service return to the server for re-service with probability p. We deduce the steady state condition and the main queueing indexes of this queueing system. Finally, numerical examples validate the conclusions of this paper.