Phase dependent breakdown in bulk arrival queueing system with vacation break-off

In this queueing model service process is split into two phases called first essential service and second essential service. Here the occurrence of breakdown during first essential service and second essential service are different. When the server got failure during first essential service, service process will be interrupted and sent to repair station immediately. On contrary during second essential service when the server got failure the service will not be interrupted, it performs continuously for current batch by doing some technical precaution arrangements. Server will be repaired after the service completion during renewal period. On service completion, if the queue length is less than 'a' then the server leaves for vacation. During vacation if the queue length reaches the value 'a' then the server breaks the vacation and performs preparatory work to start first essential service. Various performance measures and cost effective model with appropriate numerical solution of the model are presented.