An retrial queueing system with two phases of service subject to the server breakdown and repair

This paper deals with the steady state behaviour of an M / G / 1 retrial queue with an additional second phase of optional service subject to breakdowns occurring randomly at any instant while serving the customers. This model generalizes both the classical M / G / 1 retrial queue subject to random breakdown as well as M / G / 1 queue with second optional service and server breakdowns. We carry out an extensive analysis of this model.