An M[X]/G/1 Retrial G-Queue with Server Breakdown

Abstract

Batch arrival retrial queue with positive and negative customers is considered. If the server is idle upon the arrival of a batch, one of the customers in the batch receives service immediately and others join the orbit. If the server is busy, all the customers join the orbit. The arrival of negative customer brings the server down and removes the customer in service from the system. The server is subject to random breakdown while it is working. Using supplementary variable technique, expected number of customers in the orbit and expected number of customers in the system are derived. Stochastic decomposition property is established. Some special cases are discussed and numerical results are presented.