Asymptotic Analysis of the M/M/1/N−1 Retrial System with Priority and Feedback

Abstract

The retrial queuing system M/M/1/N−1 with instantaneous and delayed feedback is studied. The system has one server and a buffer of capacity N–1. Priority customers come with a certain probability and get into service if the server is free. If the server is busy, they get into the queue. If the buffer is full, then the customer goes into an orbit, where it waits for a random time and tries again to get into service or into the queue. Non-priority customers immediately go into the orbit. After service, the customer either leaves the system, or goes into the orbit or immediately occupies the server again. An asymptotic analysis method is used to find the stationary distribution of the customers quantity in the orbit. An asymptotic condition is a long delay between customers from the orbit. The paper shows that the asymptotic probability distribution of the customers quantity in the orbit under the condition of an increasing average waiting time in the orbit is Gaussian. Equations for the distribution parameters are obtained.