An M[X]/G(a, b)/1 queueing system with server breakdown and repair, stand-by server and single vacation

In this paper, we discuss a non-Markovian batch arrival general bulk service single server queueing system with server breakdown and repair, single vacation and stand-by server. There is a stand-by server which is employed during the period for which the regular server remains under repair. Both the servers serve the customer under general bulk service rule. Suppose at the instant main servers service completion if the queue length is less than 'a' then the main server goes for a vacation. Suppose at the instant of repair completion or vacation completion if the system size is less than 'a' then the main server stays in the system and waits for the next batch of arriving customers. The probability generating function of queue size at an arbitrary time and some performance measures of the system are derived. An extensive numerical result for a particular case of the model is illustrated.