A Geo[X]/G[X]/1 retrial queueing system with removal work and total renewal discipline

Abstract

In this paper we consider a discrete-time retrial queueing system with batch arrivals of geometric type and general batch services. The arriving group of customers can decide to go directly to the server expelling out of the system the batch of customers that is currently being served, if any, or to join the orbit. After a successful retrial all the customers in the orbit get service simultaneously. An extensive analysis of the model is carried out, and using a generating functions approach some performance measures of the model, such as the first distribution’s moments of the number of customers in the orbit and in the system, are obtained. The generating functions of the sojourn time of a customer in the orbit and in the system are also given. Finally, in the section of conclusions and research results the main contributions of the paper are commented.