The paper studies the steady state behavior of a batch arrival single service channel queue in which the first service with general service time is essential and the second service with general service time is optional. We term such a two-phase service as generalized Coxian-2 service. It is further assumed that the service channel is subject to random failures occurring only while the server is proving service. As soon as there is a breakdown, the service of a customer is suspended and unlike most of other papers which assume that the server immediately undergoes a repair process we assume that the repair process does not start immediately after a breakdown occurs but there is a delay in starting the repairs. This delay time follows an exponential distribution with mean delay time 1/γ,γ>0. As soon as the repair process of the service channel is complete, the server takes up the customer at the head of the queue and resumes providing the first essential service to the customer at the head of the queue. We obtain steady state probability generating functions for the queue size at a random epoch of time. Some particular cases of interest have been discussed