A non markovian retrial queueing system

Abstract

This paper studies a discrete-time queueing system in which a customer who enters in the system with a server occupied may choose to go to the retrial group or to begin its service displacing to the retrial group the customer that was in the server. If the server is idle the arriving customer begins its service immediately.

Retrial and service times are general, and the only repeated customer that can go directly to the server is the one situated at the first place of the retrial group.

A complete study of the model has been curried out noting specially the analysis of a recursive algorithm implemented by Theorems 2 and 3 and the study of the waiting time of a customer in the queue and in the system. Finally numerical examples are given.